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  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>Lviv, Ukraine, June</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>Methods for optimizing data fragmentation to improve the efficiency of decentralized databases in blockchain networks⋆</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Petro Petriv</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Ivan Opirskyy</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Volodymyr Khoma</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Lviv Polytechnic National University</institution>
          ,
          <addr-line>12 Stepan Bandera str., 79000 Lviv</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Opole University of Technology, Department of Control Engineering</institution>
          ,
          <addr-line>Opole, 45-758</addr-line>
          ,
          <country country="PL">Poland</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2025</year>
      </pub-date>
      <volume>30</volume>
      <issue>2024</issue>
      <fpage>09</fpage>
      <lpage>11</lpage>
      <abstract>
        <p>The article presents a comprehensive methodology for optimizing the performance of decentralized databases based on blockchain technology through the implementation of specialized data fragmentation mechanisms. The current challenges of distributed registry scalability and limitations of existing sharding approaches in high-load systems have been investigated. An innovative hierarchical data fragmentation model using dynamic shards and adaptive load redistribution based on data access pattern analysis is proposed. A mathematical model for optimizing transaction distribution between shards has been developed, taking into account the minimization of cross-shard operations and computational load balancing. An original data structure based on modified prefix trees with vector labels has been implemented for efficient query routing in a fragmented environment. Comprehensive experimental research results on a test stand with 64 nodes demonstrate an increase in overall transaction throughput by 37-42% compared to traditional sharding approaches and a reduction in query processing latency by 28% while maintaining the level of decentralization and cryptographic system resilience. Particularly significant performance improvement (up to 60%) is observed for cross-shard operations due to the implementation of an optimized two-phase protocol with batching and preliminary validation elements. The proposed methodology effectively overcomes existing limitations of the "blockchain trilemma" through intelligent optimization of data structures and consensus mechanisms, while maintaining the necessary level of system security and decentralization, which is confirmed by resistance to a wide range of attacks, even when a significant proportion of nodes in individual shards are compromised. Beyond performance improvement, the developed methodology provides several additional advantages, including: enhanced adaptability to changes in load characteristics and data access patterns; reduced resource requirements for individual network nodes through efficient computational load distribution; increased resistance to shard-specific attacks, such as "shard takeover" and attacks aimed at disrupting the atomicity of cross-shard transactions. The conducted security analysis demonstrates that the proposed model maintains a high level of protection even when up to 30% of nodes in the system are compromised, whereas traditional sharding approaches show critical reduction in resilience already at 20-25% of compromised nodes. The economic efficiency of the proposed methodology is confirmed by a 22-31% reduction in energy consumption compared to existing solutions at the same performance level, making it attractive for implementation in corporate blockchain systems. The obtained results create a foundation for further development of high-performance decentralized data storage and processing systems capable of effectively functioning under high loads while preserving the key advantages of blockchain technology in the context of transparency, integrity, and data protection.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;data fragmentation</kwd>
        <kwd>sharding</kwd>
        <kwd>scalability</kwd>
        <kwd>performance</kwd>
        <kwd>blockchain trilemma</kwd>
        <kwd>distributed registries</kwd>
        <kwd>consensus mechanisms</kwd>
        <kwd>smart contracts 1</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        Blockchain technology has had a revolutionary impact on distributed system architecture over the
past decade, opening up new possibilities for creating decentralized applications and services. Of
particular interest is the implementation of this technology in the field of distributed databases,
which allows for new levels of transparency, integrity, and data protection [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. However, the
widespread application of blockchain in industrial data processing systems faces a fundamental
scalability problem that limits the practical implementation of such solutions in high-load
environments [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ].
      </p>
      <p>
        Since the creation of the first blockchain platforms, such as Bitcoin and Ethereum, the issue of
scalability remains one of the industry's biggest challenges. The fundamental limitation of traditional
blockchain architectures lies in the need to store and verify the complete transaction history on each
network node, which creates a natural performance limit for the system. For instance, the classic
Bitcoin network has a limit of 7 transactions per second, while Ethereum has approximately 15
transactions per second, which is several orders of magnitude lower than the performance of
centralized data processing systems, such as Visa (24,000+ transactions per second) or modern
relational databases [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]. Such bandwidth limitations become a critical factor hindering the use of
blockchain technology in high-load corporate-level data storage and processing systems.
      </p>
      <p>
        The "blockchain trilemma", first formulated by Vitalik Buterin, postulates the existence of three
key blockchain system characteristics: security, decentralization, and scalability, of which only two
can be simultaneously optimized [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ]. In the context of decentralized databases, this problem
manifests particularly acutely, as requirements for data storage and processing system performance
continue to grow. Attempts to increase blockchain system scalability traditionally involve
compromises in other aspects of the trilemma:
1. Increasing block size or reducing consensus mechanism complexity increases throughput but
potentially reduces decentralization by increasing network node resource requirements
2.
      </p>
      <p>
        Using side chains and Layer 2 solutions provides increased bandwidth but introduces
additional vulnerability points and increases architectural complexity
3. Implementing private or semi-private blockchains, such as Hyperledger Fabric or R3 Corda,
ensures high throughput by limiting the number of nodes and using simplified consensus
mechanisms, but significantly reduces the system's decentralization level [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ]
      </p>
      <p>
        Data fragmentation (sharding) is one of the most promising approaches to solving blockchain
system scalability problems [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ]. This approach involves dividing a single blockchain chain into
interconnected fragments (shards) processed in parallel. The concept of sharding is not new and is
successfully applied in distributed databases (such as MongoDB, Cassandra, CockroachDB) for
horizontal scaling. However, transferring this concept to decentralized blockchain systems requires
solving unique problems associated with maintaining transaction atomicity and consensus in a
distributed environment without a central coordinator.
      </p>
      <p>
        However, existing fragmentation mechanism implementations face several technical challenges,
including data consistency issues between fragments, ensuring cross-shard transaction atomicity,
and maintaining a high security level when reducing the number of nodes confirming transactions
in individual shards [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ]. Critical issues remain:
      </p>
      <p>Optimal division of data and transactions between shards to minimize cross-shard
operations.
2. Ensuring effective inter-shard communication with minimal overhead.</p>
      <p>Maintaining data consistency between shards without a central coordinator.
4. Tensuring resilience to various attack types, including shard-specific attacks like "shard
takeover".</p>
      <p>Dynamic load balancing and data redistribution between shards in response to changing
access patterns and load.</p>
      <p>Existing projects like Ethereum 2.0, Near Protocol, Zilliqa, and Elrond implement various
sharding variations, but none offers a comprehensive solution that would ensure optimal
performance in the context of heterogeneous loads characteristic of decentralized databases.</p>
      <p>This article examines a new approach to optimizing data fragmentation mechanisms in
blockchain networks to improve decentralized database performance while preserving their
fundamental advantages in terms of security and decentralization. The proposed methodology is
based on hierarchical sharding with dynamic data distribution and adaptive inter-shard
communication mechanisms that consider the characteristics of different query and transaction
types. Unlike existing solutions, our approach involves integrating machine learning methods to
predict access patterns and optimize data placement, as well as using specialized data structures for
efficient query routing in a fragmented environment.</p>
      <sec id="sec-1-1">
        <title>1.1. Analysis of literary sources and formulation of the problem</title>
        <p>
          The issues of blockchain network scalability and improving the performance of decentralized
databases have been actively investigated by the scientific community in recent years. The
multifaceted nature of this problem leads to a variety of approaches to solving it, with most modern
research focusing on modifying blockchain system architectures to increase their throughput while
maintaining the basic characteristics of decentralization and security. A comprehensive survey
conducted by Kim et al. [
          <xref ref-type="bibr" rid="ref13">13</xref>
          ] offers a structured overview of the current scalability solutions in
blockchain systems, categorizing existing approaches and critically assessing their trade-offs with
respect to throughput, security, and decentralization — thereby providing a valuable reference
framework for the ongoing development of sharding-based architectures.
        </p>
        <p>
          Wang and colleagues [
          <xref ref-type="bibr" rid="ref6">6</xref>
          ] proposed an innovative model of parallel transaction processing in
blockchain networks based on a modified PBFT (Practical Byzantine Fault Tolerance) algorithm.
Their approach involves distributing transactions among separate node groups according to their
type and target addresses, allowing them to achieve a theoretical throughput of up to 10,000
transactions per second in a test environment. However, a detailed analysis of this approach revealed
significant limitations in processing transactions that require access to data in different groups
(analogous to cross-shard operations). In particular, the absence of an effective mechanism for
ensuring the atomicity of such operations creates risks of data integrity violation under high loads
or in network instability conditions.
        </p>
        <p>
          The research group led by Zamani [
          <xref ref-type="bibr" rid="ref7">7</xref>
          ] developed the RapidChain protocol, which represents a
comprehensive sharding solution with dynamic node redistribution. RapidChain uses an innovative
approach to shard formation based on random node sampling using a proof mechanism that ensures
resilience to Sybil and shard takeover attacks. Experimental studies showed that this protocol
provides linear growth of network throughput with the addition of new shards, reaching up to 7,300
transactions per second in a network of 4,000 nodes. However, despite solving several security
problems, RapidChain does not pay sufficient attention to optimizing data structures for efficient
information search and update. This becomes a critical factor when working with large data volumes
typical of corporate-level decentralized databases.
        </p>
        <p>
          Similar limitations have been addressed in [
          <xref ref-type="bibr" rid="ref16">16</xref>
          ], where a combination of authentication protocols
and decentralized data structures was proposed to mitigate fragmentation-related inefficiencies in
enterprise environments.
        </p>
        <p>
          Of particular interest is the Ethereum 2.0 architecture, which implements a multi-level sharding
mechanism that involves dividing the network into 64 shards with their own block chains
synchronized through the main chain (Beacon Chain) [
          <xref ref-type="bibr" rid="ref8">8</xref>
          ]. This architecture uses a Proof-of-Stake
mechanism to ensure consensus and randomly distribute validators between shards. Theoretical
performance estimates of Ethereum 2.0 indicate the possibility of achieving a throughput of up to
100,000 transactions per second with the full implementation of all development phases. However,
the practical implementation of this architecture faces several complex technical challenges,
specifically:
•
•
•
        </p>
        <p>The need to ensure effective inter-shard communication through the Beacon Chain, which
potentially becomes a system bottleneck under high load.</p>
        <p>The complexity of synchronization and coordination mechanisms between shards, leading to
increased cross-shard operation latency.</p>
        <p>The need to ensure rapid transaction finalization while maintaining a high security level.</p>
        <p>
          Dang and colleagues [
          <xref ref-type="bibr" rid="ref9">9</xref>
          ] conducted a comprehensive comparative study of the performance of
various consensus mechanisms in the context of sharding and proposed a hybrid model that
combines the advantages of different algorithms at different levels of the sharding architecture. Their
research demonstrated that optimal performance is achieved by using lightweight BFT (Byzantine
Fault Tolerance) algorithms within shards in combination with more stringent consensus
mechanisms for inter-shard communication. This approach allows achieving a balance between
speed and security, however, its effectiveness varies significantly depending on load characteristics
and network configuration. Unfortunately, the study does not offer specific mechanisms for
dynamically adapting such combinations based on load characteristics, which limits the practical
application of this approach in heterogeneous environments with changing data access patterns.
        </p>
        <p>
          In the context of blockchain-based decentralized databases, it is important to understand the
performance of various system components. Dinh and colleagues [
          <xref ref-type="bibr" rid="ref11">11</xref>
          ] developed BLOCKBENCH - a
comprehensive framework for analyzing private blockchain performance, which allows evaluating
the effectiveness of various architectural solutions, including vertical functional division.
        </p>
        <p>
          When developing a sharding architecture, it is important to consider the features of consensus
algorithms, as noted by Nguyen and Kim [
          <xref ref-type="bibr" rid="ref10">10</xref>
          ]. Different consensus mechanisms have their
advantages and disadvantages in the context of horizontal sharding, which affects the overall system
performance and security.
        </p>
        <p>A systematic analysis of existing approaches to data fragmentation in blockchain networks allows
identifying three main categories:</p>
        <p>
          Horizontal sharding, which involves dividing transactions and system state based on a specific
key (for example, address range or identifier hash value). This approach is the most common and
provides natural data divisibility, but encounters problems when processing transactions that span
multiple shards. Research by Kokoris-Kogias and colleagues [
          <xref ref-type="bibr" rid="ref12">12</xref>
          ] demonstrates that up to 30% of
transactions in typical blockchain applications are cross-shard, creating a potential bottleneck for
horizontal sharding systems.
        </p>
        <p>Vertical sharding, in which different aspects of network functionality (data storage, transaction
validation, smart contract execution) are moved to separate components operating in parallel. This
approach allows optimizing each component separately but requires complex communication and
state synchronization mechanisms between different functional shards. Particularly challenging
issues arise when ensuring atomicity and transactional integrity during interaction between
components.</p>
        <p>
          Hybrid sharding, which combines elements of horizontal and vertical approaches with dynamic
load redistribution. An example of such an approach is OmniLedger, proposed in the work of
Kokoris-Kogias and colleagues [
          <xref ref-type="bibr" rid="ref12">12</xref>
          ], which uses a two-layer architecture with horizontal data
distribution at the first level and functional distribution at the second. Experimental studies show
that this approach provides better adaptability to different load types, however, its effectiveness
strongly depends on specific resource allocation and data redistribution algorithms, which are
usually based on heuristic approaches without strict justification of optimality.
        </p>
        <p>Based on the analysis of literature sources, the following key unresolved problems can be
identified in the field of optimizing data fragmentation mechanisms in blockchain networks:</p>
        <p>Firstly, there is a lack of effective load balancing mechanisms between shards, taking into account
the heterogeneity of data and transactions. Existing approaches are mostly based on static resource
distribution or use simple heuristics for dynamic balancing that do not consider complex
interconnections between data objects and their access patterns. This leads to uneven load
distribution, where some shards become overloaded ("hot spots"), while others remain underutilized.</p>
        <p>Secondly, there is limited scalability of cross-shard operations, which potentially creates
bottlenecks under high load. Most existing solutions for ensuring cross-shard transaction atomicity
and consistency are based on blocking protocols like two-phase commit, which significantly limit
parallelism and introduce additional delays. Moreover, such protocols often require coordinator
participation, creating a potential single point of failure and reducing system decentralization.</p>
        <p>
          The integration of blockchain with SSO-based access control models has been explored in [
          <xref ref-type="bibr" rid="ref17">17</xref>
          ],
demonstrating how identity federation mechanisms can be adapted to fragmented architectures with
strong decentralization guarantees.
        </p>
        <p>Thirdly, there is insufficient optimization of data structures for quick access and updates in
sharding conditions. Traditional blockchain systems use data structures optimized for a single chain
(for example, modified Merkle trees), which are ineffective in the context of a fragmented
architecture. Specialized data structures are needed that provide efficient query routing between
shards, quick information search and update, and support for cryptographic verification of data
integrity.</p>
        <p>Fourthly, there is a noted absence of adaptive algorithms for redistributing nodes between shards
depending on current load and network characteristics. Static node distribution, even if based on
random selection to ensure security, cannot adapt to changes in network topology, node
computational power, and load characteristics. This leads to suboptimal resource utilization and
potential performance degradation of the system as a whole.</p>
        <p>These problems clearly demonstrate the complexity of achieving an optimal balance between
performance, security, and decentralization in the context of fragmented blockchain systems. Figure
1 presents a visualization of the relationship between key sharding aspects and their impact on the
overall performance of decentralized databases.</p>
        <p>Thus, the need for developing a comprehensive methodology for optimizing data fragmentation
mechanisms becomes evident. Such a methodology should take into account the specifics of
decentralized databases based on blockchain technology and ensure increased performance while
maintaining a high level of security and decentralization. This methodology should include:
•
•
•
•</p>
        <p>Mathematically substantiated models for distributing data and transactions between shards
to minimize cross-shard operations.</p>
        <p>Adaptive load balancing mechanisms using machine learning methods to predict access
patterns.</p>
        <p>Optimized data structures for efficient query routing and maintaining data integrity in a
fragmented environment.</p>
        <p>Non-blocking protocols to ensure atomicity and consistency of cross-shard transactions.</p>
        <sec id="sec-1-1-1">
          <title>Latency of cross- Level of Resistance to</title>
          <p>sharding decentralization attacks
operations</p>
          <p>The data presented in Table 1 are based on published experimental research results and
theoretical assessments and demonstrate that none of the existing approaches provides an optimal
combination of all key characteristics. This confirms the relevance of developing new methodologies
for optimizing data fragmentation mechanisms in blockchain networks.</p>
          <p>Additionally, [20] examined the use of blockchain technologies for GDPR-compliant data
protection, identifying architectural modifications necessary for securing personal data across
dynamically restructured shard environments.</p>
        </sec>
      </sec>
      <sec id="sec-1-2">
        <title>1.2. Purpose and objectives of the research</title>
        <p>The aim of this work is to develop and experimentally verify a comprehensive methodology for
improving the performance of decentralized databases by optimizing data fragmentation
mechanisms in blockchain networks. The research is aimed at overcoming the fundamental
scalability limitations of blockchain systems while preserving their key properties of decentralization
and security. To implement the set goal, the creation of a mathematical apparatus for hierarchical
data fragmentation is anticipated, taking into account the specifics of distributed blockchain systems,
development of algorithms for dynamic data redistribution based on access pattern analysis,
implementation of optimized data structures for efficient search and information update in a
fragmented environment, as well as creating effective mechanisms for synchronization and
validation of cross-shard transactions with minimizing overhead costs. A comprehensive
experimental study of the proposed solutions aims to quantitatively assess their effectiveness
compared to existing approaches and confirm the possibility of practical application of the developed
methodology in industrial-level decentralized databases.</p>
      </sec>
      <sec id="sec-1-3">
        <title>1.3. Research Objectives</title>
        <p>To achieve the research goal, the following specific objectives have been formulated:
•
•
•
•
•
•
•
•</p>
        <p>Conduct a systematic analysis of existing approaches to data fragmentation in blockchain
networks, identify their limitations and potential optimization directions.</p>
        <p>Develop a mathematical model of hierarchical data fragmentation that takes into account the
characteristics of distributed blockchain systems and provides a formal framework for
optimizing data distribution.</p>
        <p>Create algorithms for dynamic load balancing and data redistribution between shards based
on access pattern analysis and transaction execution frequency.</p>
        <p>Propose optimized data structures to accelerate search and update operations in a fragmented
architecture.</p>
        <p>Develop mechanisms for synchronization and validation of cross-shard transactions that
ensure atomicity and consistency of operations while minimizing overhead costs.
Create a software implementation of the proposed methodology for experimental research.
Design and implement a test environment for objective evaluation of the effectiveness of the
proposed solutions.</p>
        <p>Conduct a comprehensive experimental study of the performance, scalability, and security of
the proposed methodology in comparison with existing approaches.
•</p>
        <p>Analyze the obtained results and formulate recommendations for the practical application of
the developed methodology.</p>
      </sec>
      <sec id="sec-1-4">
        <title>1.4. Research Methodology</title>
        <p>The research was conducted according to a developed comprehensive methodology that combined
theoretical and experimental methods.</p>
        <p>At the preparatory stage, a systematic analysis of scientific publications, technical specifications,
and documentation of existing blockchain platforms was carried out. Special attention was paid to
works devoted to sharding mechanisms and data fragmentation in distributed systems. The analysis
results revealed key limitations of existing approaches and helped formulate requirements for a new
optimization methodology.</p>
        <p>During the theoretical modeling stage, a mathematical model of hierarchical data fragmentation
was developed, describing the relationships between system components and allowing formalization
of the optimization process. The model includes defining performance and efficiency metrics,
formalizing the optimization objective function, and mathematical description of load balancing and
data redistribution algorithms.</p>
        <p>For practical verification of theoretical concepts, a software implementation of the proposed
methodology was created with components including: a blockchain network emulator supporting
various sharding configurations, implementation of the hierarchical data fragmentation model,
implementation of dynamic data redistribution algorithms, implementation of optimized data
structures, and cross-shard transaction synchronization mechanisms.</p>
        <p>For conducting experiments, a test environment was designed that provides network emulation
with 64 nodes distributed among 8 shards, generation of realistic transaction sets with different data
access patterns, the ability to change system configuration, and collection and analysis of
performance metrics.</p>
        <p>The experimental methodology involved determining key efficiency metrics: throughput, query
processing latency, computational resource utilization, percentage of successfully executed
transactions, data search time, and resistance to various types of attacks. For objective comparison,
the proposed methodology was tested alongside existing approaches: traditional blockchain without
sharding, static horizontal sharding, static vertical sharding, and traditional hybrid sharding.</p>
        <p>The developed testing scenarios included: performance evaluation at fixed load (10,000
transactions/s), scalability research with increasing load (from 5,000 to 30,000 transactions/s),
analysis of cross-sharding operations efficiency, evaluation of search speed for different data
volumes, and simulation of various attack types for security assessment.</p>
        <p>Each experiment was conducted following a uniform sequence of actions: setting up the test
environment, launching the blockchain network emulator and waiting for system stabilization,
generating and submitting the test load, collecting metrics in real-time, and processing and analyzing
the obtained results. To increase the accuracy of results, each experiment was repeated 10 times with
calculation of average metric values and standard deviation.</p>
      </sec>
      <sec id="sec-1-5">
        <title>1.5. Test Environment Characteristics</title>
      </sec>
      <sec id="sec-1-6">
        <title>1.5.1. Hardware Configuration</title>
        <p>The experimental research was conducted on a cluster of 8 physical servers with the following
characteristics:
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
RAM: 128 GB DDR4 ECC.</p>
        <p>Storage: NVMe SSD 2 TB.</p>
        <p>Network: 10 Gbps Ethernet with full duplex</p>
      </sec>
      <sec id="sec-1-7">
        <title>1.5.3. Blockchain Network Configuration</title>
        <p>The basic network configuration included:
Total number of nodes: 64
Number of shards: 8 (8 nodes in each shard)</p>
        <sec id="sec-1-7-1">
          <title>Intensity: from 5,000 to 30,000 transactions per second</title>
          <p>Read/write operations ratio: 70%/30%
Transaction size: from 0.5 KB to 5 KB
Access patterns:</p>
          <p>Uniform random access</p>
          <p>Virtual machines were deployed on each physical server to emulate blockchain network nodes (8
nodes per server, 64 nodes in total).</p>
        </sec>
      </sec>
      <sec id="sec-1-8">
        <title>1.5.2. Software</title>
        <p>Operating System: Ubuntu Server 20.04 LTS
Virtualization: Docker 20.10 with Kubernetes 1.21.</p>
        <p>Programming Language: Golang 1.17 for implementing the core components.
DBMS: LevelDB for storing blockchain state
Monitoring: Prometheus and Grafana for metric collection and visualization
Load Generator: Customized Hyperledger Caliper
Consensus mechanism: Modified PBFT within shards, Tendermint for inter-shard
communication.</p>
        <p>Block time: 5 seconds</p>
        <p>Block size: Dynamic, up to 5 MB</p>
      </sec>
      <sec id="sec-1-9">
        <title>1.5.4. Test Load Generation Methodology</title>
        <p>To ensure test realism, a transaction generator with the following configuration options was used:</p>
        <p>Zipf distribution (skewed)</p>
        <p>Clustered access
•</p>
        <p>Proportion of cross-shard transactions: from 10% to 50%</p>
      </sec>
      <sec id="sec-1-10">
        <title>1.5.5. Attack Simulation Methodology</title>
        <p>To evaluate the security of the proposed methodology, a method for simulating various types of
attacks was developed:</p>
        <p>Double-spending: Emulation of attempts to use the same resources for different transactions
Shard takeover: Compromising nodes (from 10% to 45% of the total number)
Message delay: Artificial introduction of delays in message delivery between shards
Network partition: Simulation of network connection failure between groups of shards
•
•
•
•
•
•
•
•
•
•
•</p>
      </sec>
      <sec id="sec-1-11">
        <title>1.5.6. Data Collection and Analysis</title>
        <p>A distributed monitoring system was used for data collection:</p>
        <p>Monitoring agents on each node for collecting low-level metrics
Prometheus for aggregation and storage of time series
Grafana for visualization and primary analysis
Data export to CSV for further processing</p>
        <p>Statistical analysis using R and Python (pandas, numpy, matplotlib)</p>
        <p>This comprehensive approach to designing and conducting experimental research provided an
objective assessment of the effectiveness of the proposed methodology and its comparison with
existing approaches to data fragmentation in blockchain networks.</p>
      </sec>
    </sec>
    <sec id="sec-2">
      <title>2. Proposed Optimization Model</title>
      <sec id="sec-2-1">
        <title>2.1. Hierarchical Data Fragmentation Model</title>
        <p>The proposed methodology is based on a hierarchical model of data fragmentation, which involves
organizing shards into a tree-like structure with dynamic load redistribution. The model is formally
described as follows.</p>
        <p>Let  =  1,  2, … ,   be a set of shards in the system, where each shard   contains a subset of
data and transactions. The hierarchical structure is defined as a tree  = ( ,  ), where E is the set of
connections between shards.</p>
        <p>For each shard   , the following characteristics are defined:
  - computational power of the shard;
  - volume of data in the shard;
where:
(1)
(2)</p>
      </sec>
      <sec id="sec-2-2">
        <title>2.2. Dynamic Data Redistribution Algorithm</title>
        <p>For efficient load balancing between shards, an algorithm for dynamic data redistribution has been
developed, which is based on the analysis of access patterns and transaction execution frequency.
The algorithm consists of the following stages:</p>
        <p>Monitoring shard performance and identifying "hot spots" - shards with excessive load or
low query processing efficiency;
Data clustering based on analysis of the connection graph between data objects and the
frequency of their joint use in transactions;
Making decisions about data redistribution based on a predictive load model using machine
learning methods;
4. Performing atomic data redistribution with minimal impact on system availability.</p>
      </sec>
      <sec id="sec-2-3">
        <title>2.3. Optimized Data Structure for Efficient Search</title>
        <p>To accelerate search and update operations in a fragmented architecture, the use of a modified data
structure based on prefix trees with additional metadata for optimizing cross-shard queries is
proposed. The key feature is the use of vector labels for efficient query routing between shards:
  - throughput of the shard (number of transactions per unit time);
  - average latency of query processing.</p>
        <p>Optimal distribution of data between shards is achieved by minimizing the objective function:</p>
        <p>= (ℎ1, ℎ2, . . . , ℎ )
where ℎ is a hash value that determines the data object's membership to the corresponding shard
at level j of the hierarchy.</p>
      </sec>
      <sec id="sec-2-4">
        <title>2.4. Cross-Shard Transaction Synchronization Mechanism</title>
        <p>To ensure atomicity and consistency of cross-shard transactions, a two-phase confirmation protocol
using a quorum approach has been developed:
1. Preparation phase: the transaction is validated in all involved shards without committing
changes;
shards.</p>
        <p>Confirmation phase: after receiving positive responses from a quorum of nodes in each
involved shard, atomic fixation of changes is performed;
3. In case of failure of any shard at the preparation stage, the transaction is rolled back in all</p>
        <p>To optimize protocol performance, a mechanism for batching cross-shard transactions is
proposed, which reduces the communication overhead between shards.</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>3. Research Results</title>
      <p>To evaluate the effectiveness of the proposed methodology, a series of experimental studies was
conducted on a test stand that simulates the operation of a decentralized database based on
blockchain technology with various sharding configurations. The test environment consisted of 64
nodes distributed among 8 shards with different computational power.</p>
      <sec id="sec-3-1">
        <title>3.1. Performance Evaluation Across Different Sharding Configurations</title>
        <p>The results demonstrate that the proposed model provides a 40% increase in throughput
compared to traditional hybrid sharding and a 28.7% reduction in latency.</p>
      </sec>
      <sec id="sec-3-2">
        <title>3.2. System Scalability with Increasing Load</title>
        <p>4560
5400
3125</p>
        <p>Proposed model
Traditional hybrid
Static vertical
Static horizontal
No sharding
10970
6145
4700
5550
3150
15000 20000
Load (transactions/s)
25000
30000</p>
        <p>Experimental data show that the proposed model demonstrates better scalability compared to
other approaches, maintaining stable performance even with a significant increase in load. When
the load increases from 5,000 to 25,000 transactions per second, throughput decreases by only 12%,
while for traditional hybrid sharding this decrease is 31%.</p>
      </sec>
      <sec id="sec-3-3">
        <title>3.3. Efficiency of Cross-Shard Operations</title>
        <p>Special attention was paid to evaluating the efficiency of cross-shard operations, which is a critical
factor for the performance of distributed databases. Table 3 provides a comparison of latency and
success rate of cross-shard transactions for different approaches.</p>
        <sec id="sec-3-3-1">
          <title>Latency (ms) Success Rate (%)</title>
        </sec>
        <sec id="sec-3-3-2">
          <title>Overhead (%)</title>
          <p>The proposed method provides a 40% reduction in latency of cross-shard operations compared to
the traditional approach based on two-phase commit and increases transaction success rate to 98.2%.</p>
          <p>
            Prior research in [
            <xref ref-type="bibr" rid="ref18">18</xref>
            ] proposed an early version of such synchronization techniques tailored for
messaging-based blockchain systems, laying foundational principles for low-latency confirmation
protocols in multi-shard environments.
          </p>
          <p>Approach</p>
          <p>Two-phase commit</p>
          <p>Asynchronous replication
Traditional sharding with quorum</p>
          <p>Proposed method
943
486
628
376
91.4
87.2
94.6
98.2
38.5
23.1
29.8
17.3</p>
        </sec>
      </sec>
      <sec id="sec-3-4">
        <title>3.4. Influence of Data Structure on Search Efficiency</title>
        <p>To evaluate the effectiveness of the proposed data structure, a comparison of information search
speed in a fragmented architecture was conducted. The experimental results are presented in Table
4.</p>
        <p>
          For effective analysis and interpretation of results, modern blockchain data visualization methods
described in paper [
          <xref ref-type="bibr" rid="ref14">14</xref>
          ] were used.
        </p>
        <p>The proposed data structure demonstrates a 30-40% increase in search speed compared to
traditional approaches, especially with increasing data volume. An earlier concept for applying
blockchain-structured indexing in educational platforms was proposed in [19], emphasizing efficient
routing in use-case-specific decentralized learning systems.</p>
      </sec>
      <sec id="sec-3-5">
        <title>3.5. Evaluation of Security and Attack Resistance</title>
        <p>
          When designing secure sharding blockchain systems, special attention should be paid to the selection
and configuration of distributed consensus protocols. A comprehensive analysis of such protocols,
presented in paper [
          <xref ref-type="bibr" rid="ref15">15</xref>
          ], demonstrates that different consensus mechanisms have varying resistance
to attacks in the context of sharding architecture.
        </p>
        <p>An important aspect of evaluating the proposed methodology is a comprehensive analysis of its
security and resistance to various types of attacks characteristic of distributed blockchain systems
with data fragmentation. The security of decentralized databases directly depends on the reliability
of consensus mechanisms and the system's ability to resist malicious actions from both external and
internal network participants.</p>
        <p>As part of the research, a series of experiments was conducted simulating various types of attacks
aimed at compromising the integrity and availability of the system. In particular, the following attack
scenarios were modeled:</p>
        <p>Double-spending attack - an attempt to use the same resources for different transactions by
manipulating the distributed state of the system. In the context of sharding, such an attack
can potentially be facilitated due to the reduced number of nodes participating in transaction
confirmation in a particular shard.
2. Shard takeover attack - compromising a sufficient number of nodes in a specific shard to gain
control over the transaction validation process. This is a specific type of attack characteristic
of sharding blockchain architectures.</p>
        <p>Message delay attack - manipulating the delivery time of messages between shards in order
to violate the atomicity of cross-shard transactions or create inconsistencies in the system
state.</p>
        <p>Network partition attack - artificially creating conditions under which communication
between shards becomes impossible, leading to the division of a single network into isolated
segments.</p>
        <p>The experimental study was conducted in a controlled environment using a network of 64 nodes
distributed among 8 shards. For each type of attack, the proportion of compromised nodes (from 10%
to 45%) and the level of their distribution among shards (uniform or concentrated in specific shards)
were varied.</p>
        <p>The experimental results are presented in Figure 3, which shows the relationship between attack
success rate and the proportion of compromised nodes for different sharding approaches.</p>
        <p>100%
90%
80%
n% 70%
i
ity 60%
l
iab 50%
t
sm40%
e
tsy 30%
S 20%
10%
0%
10%
15%
20% 25% 30% 35% 40%
Share of compromised nodes in %
45%
50%</p>
        <p>Proposed model
Traditional hybryd
Static vertical
Static horizontal
Without sharding</p>
        <p>Analysis of the obtained results demonstrates that the proposed model maintains a high level of
security even when up to 30% of nodes in individual shards are compromised, which corresponds to
the theoretical guarantees of blockchain systems' resilience based on BFT consensus. Meanwhile,
traditional sharding approaches show a significant decrease in resistance already at 20-25% of
compromised nodes.</p>
        <p>The key factors ensuring enhanced security of the proposed model are:</p>
        <p>Dynamic distribution of validators between shards - unlike static assignment of nodes to
specific shards, the proposed model provides for regular rotation of validators between
shards based on a deterministic but unpredictable function for the attacker. This significantly
complicates the coordination of malicious actions and increases the cost of attack.
Multi-level consensus - the proposed architecture uses different consensus mechanisms at
different levels of the shard hierarchy. In particular, an optimized version of PBFT (Practical
Byzantine Fault Tolerance) is used within shards, while a modified Tendermint algorithm is
used for coordination between shards. This combination provides an optimal balance
between performance and security.
3. Proactive verification of cross-shard transactions - to prevent "double-spending" attacks in
the context of cross-shard operations, a proactive verification mechanism using inclusion
proofs (Merkle proofs) is proposed. This allows effective detection of attempts to manipulate
the system state without the need to verify the entire blockchain.
4. Secure inter-shard communication mechanism - to protect against "message delay" and
"network partition" attacks, a reliable inter-shard communication protocol has been
developed using cryptographic proofs of message delivery and timeout mechanisms with
automatic transaction rollback.</p>
        <p>Additionally, an analysis of the system's resistance to failures and malfunctions of individual
components was conducted. The results showed that the proposed model is able to maintain
operability even with the failure of up to 40% of nodes in the system, which significantly exceeds the
indicators of traditional sharding architectures (20-30%).</p>
        <p>It should be noted that system resistance to "shard takeover" attacks is a particularly important
characteristic for sharding blockchain architectures. Table 5 presents a comparison of the minimum
proportion of nodes required for successful implementation of such an attack for different sharding
approaches.</p>
        <p>As can be seen from the table, the proposed model demonstrates significantly higher resistance
to "shard takeover" attacks compared to other approaches. This is achieved through a combination
of dynamic validator distribution, hierarchical shard structure, and specialized cross-shard
verification mechanisms.</p>
        <p>Thus, the conducted experiments confirm that the proposed methodology not only improves the
performance of decentralized databases but also maintains, and in some aspects even enhances, the
security and resilience of the system against various types of attacks characteristic of blockchain
networks with data fragmentation.</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>Conclusions</title>
      <p>This paper presents a methodology for improving the performance of decentralized databases
through optimization of data fragmentation mechanisms in blockchain networks. The main research
results are:</p>
      <p>A hierarchical model of data fragmentation has been developed, providing efficient load
distribution taking into account the characteristics of data and transactions;</p>
      <p>An algorithm for dynamic data redistribution based on access pattern analysis has been
proposed, allowing adaptation of the sharding configuration to changes in the nature of the
workload;
An optimized data structure for efficient search and information updates in a fragmented
architecture has been developed;
A synchronization mechanism for cross-shard transactions has been presented, ensuring
atomicity and consistency while minimizing overhead costs.</p>
      <p>Experimental studies have confirmed the effectiveness of the proposed methodology,
demonstrating an increase in system throughput by 37-42% and a reduction in operation latency by
28% compared to traditional sharding approaches. A particularly significant performance
improvement is observed for cross-shard operations, which is a critical factor for the practical
application of decentralized databases in high-load environments.</p>
      <p>The proposed methodology partially overcomes the limitations of the "blockchain trilemma,"
providing simultaneous improvement in system scalability while maintaining a high level of security
and decentralization. This opens new opportunities for the practical implementation of blockchain
technology in enterprise-level data processing systems.</p>
      <p>Future research will focus on improving mechanisms for adaptive data redistribution using
machine learning methods and developing specialized consensus algorithms for optimizing
crossshard operations.</p>
      <sec id="sec-4-1">
        <title>Declaration on Generative AI</title>
        <p>The authors have not employed any Generative AI tools.</p>
      </sec>
    </sec>
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