Allocating data fragments in distributed database systems is an important issue in distributed database (DDB) systems. In this research work, we will show how rule based policy languages can be used to represent di erent data fragment allocation techniques. Results indicate that, using rule based languages like prolog can signi cantly simplify the representation of such algorithms for any further developments and optimizations. Our examples show that our approach can be extended to be used in di erent areas of distributed systems.
Developments in distributed algorithms, network technologies, and database theory in the past few decades led to advances in distributed database systems (DDS). A DDS is a collection of database nodes connected by a communication network, in which each node is a database system in its own right, but the nodes have agreed to work together, so that a user at any node can access data anywhere in the network exactly as if the data were all stored at the users own node.
The primary concern of fragmentation in a DDS is to show how data should be divided and distributed among nodes in the underlying database. Fragmentation problem in a DDS is how to divide the data while allocation issue means how those fragments should be distributed over di erent DDS nodes. The data allocation problem, is NP-complete, and thus requires fast heuristics to generate e cient solutions [1]. Furthermore, the optimal allocation of database objects highly depends on the query execution strategy employed by a distributed database system, and the given query execution strategy usually assumes an allocation of the fragments.
A major cost in executing queries in a distributed database system is the data transfer cost incurred in transferring relations (fragments) accessed by a query from di erent nodes to the node where the query is initiated. The objective of a data allocation algorithm is to determine an assignment of fragments at di erent nodes so as to minimize the total data transfer cost incurred in executing a set of queries. This is equivalent to minimizing the average query execution time, which is of primary importance in a wide class of distributed conventional as well as multimedia database systems.
An optimal, but not practical, solution for fragment allocation in DDS has been appeared in [2]. There are also a few fragment allocation algorithms [3{ 8] that are proven to be practical and show a reasonable performance. Several surveys of those algorithms are provided by [9{12]. Since all of these fragment allocation algorithms are expressed and implemented by imperative programming languages, they are usually di cult to understand and con gured.
In this paper, using declarative rule based languages, we propose a novel
technique that can be used to represent fragment allocation algorithms. In our
technique, we consider fragment allocation strategy as a rule-based policy,
implemented in a logic programming framework. The declarative representation of
fragment allocation algorithms results in two major bene ts: (
The rest of this paper is structured as follows: in section 2 we will brie y review some of major parameters of fragment allocation problem, section 3 is about our representation technique and section 4 brie y explains the implementation of our prototype model. Finally section 6 is our conclusion. 2
Fragment and data allocation algorithms are categorized into two major groups: static and dynamic. In static fragment allocation algorithms, data allocation has been completed prior to the design of a database depending on some static data access patterns and/or static query patterns. However, dynamic fragment allocation algorithms can change the data fragment allocation automatically during the deployment of the database. In a dynamic environment where these probabilities change over time, the static allocation solution would degrade the database performance.
Depending on the complexity of a data allocation algorithm, it may take the following parameters as inputs: 1. The fragment dependency graphs. 2. Unit data transfer costs between nodes. 3. The allocation limit on the number of fragments that can be allocated at a node. 4. The query execution frequencies from the nodes.
The fragment dependency graph models the dependencies between the fragments and the amount of data transfer incurred to execute a query. A fragment dependency graph (as shown in gure 1) is a rooted directed acyclic graph with the root as the query execution site (Node Q in Figure 1) and all other nodes as fragment nodes (Node G, etc., in Figure 1) at potential nodes accessed by a query.
Q
J G
E
Assume that rij indicates the frequency of requirements by node i for fragment j, each fragment i is characterized by its size, ni and tij indicates the cost for node i to access a fragment located on node j. Clearly, tij is a function of the following parameters: { The average size of data fragments: sj . { The bandwidth of network link between i and j: wij . { The delay of network link between i and j: dij . { Other types of costs on network link between i and j, e.g. communication expenses: oij .
Therefore, users of the distributed database systems must be able to de ne
tij for a fragment allocation algorithm based on the above mention parameters.
Moreover, the frequency of the execution of each type k of the queries executed
by node i on data item j, fijk, is another important factor for the fragment
allocation algorithm. Note that, di erent types of database queries have
different transfer costs. For instance, select (se) queries (specially those require
joins on tables) may require large data transfers while update (up) and delete
(de) queries do not require large data transfers. In fact, an e cient fragment
allocation algorithm results in minimization of execution cost, which is shown
in (
X m n
X X fijk k2fse;up;deg i=1 j=1
The distributed database allocation problem is to nd the optimal placement
of the fragments at the nodes. That is, we wish to nd the placement, P =
fp1; p2; p3; : : : ; pj ; : : : ; png (where pj = i indicates fragment j is located at node
i) for the n fragments so that the capacity of any node is not exceeded, that is
shown in (
m
X rij nj cij (
By restricting the use of the requirements matrix and having zero transmission cost, the distributed database allocation problem can be transformed to the bin packing problem, which is known to be NP-complete. 3
In this paper, our goal is to develop a exible and dynamic fragment allocation
algorithm. Clearly, such algorithm must be considered as a distributed algorithms.
Otherwise, adding a coordinator node can drastically decrease the exibility of
such algorithm. At the rst glance, developing such distributed algorithm may
look di cult as distributed logic programming and rule based frameworks are
required for such algorithm. But, fortunately, this problem is not as di cult as
what it looks. Because synchronizing the fragment allocation and its parameters,
each node can act independently while we make sure the result of our executions
for di erent nodes are same. Then, we just need to represent our fragment
allocation algorithm using a rule based language and make sure the rules of each
node and facts are properly synchronized.
delay(
In order to develop a fragment allocation algorithm in a rule-based language, rst we need to represent above mentioned parameters as sets of facts. Then, we need to develop our algorithm in terms of rules|similar to representation of policies using rule based languages. Obviously, the set of rules de ning the fragmentation algorithm should be synchronized in each node as well.
The over all representation of network parameters in a rule based language
is simple and natural. We can use simple sets of facts to represent sj, wij, dij,
and oij. For instance, Figure 3 shows that the delay between node 1 and 3 is 5
milliseconds, the reverse of the bandwidth is 05 1=mega-bytes, and the cost of
communication for each mega-byte is 5 dollars. Then, tij can be computed as
shown by (
tij = ij
sj
wij
dij
oij
(
T is U*S*W*D*O.
Similarly, the execution statistics, fijk can also be generated as a set of fact by the execution engine of DDS. The pre-de ned parameter to show the execution cost of query type k on node i for the fragment j, eijk, is also de ned as a fact by users. Therefore, for the simplest fragment allocation policy, where fragments are moved if the execution cost is larger than fragment relocation cost. In such algorithm, the trigger for moving the data item j from i1 to i2, movei1i2j, can be computed through the following rule:
Accordingly, this trigger runs two major events: physically moving the data
item j from i1 to i2 and updating fragment allocation information in all of the
nodes. Using rules of type (
?
moveX;Y;Z :
(
Simply, one can use prolog assert and retract instructions in synchronization unit to update fragment allocation information. Based on this executions, the main procedure of fragment allocation component can be developed as shown in Figure 5.
As mentioned before, rule based representation of fragment allocation algorithm makes those algorithms simple and easy to understand. For instance, let ai1i2 be a fact representing that there is a direct link between i1 and i2. Therefore, NNA [4] fragment allocation algorithm can be simply represented as
Similarly, FNA [5][3] and BGBR [6] parameters can be imported to our algorithms. Complicated reasoning for FNA also needs supporting Fuzzy logic resolutions and libraries by resolution frameworks. 4
As mentioned in the previous section, in our approach, each node is considered as an independent system, synchronized with other nodes on fragment allocation mechanisms. Figure 6 shows the design of a node in our DDS. We are still working on the implementation of this project. The inference engine in our system will be XSB Prolog [14]. The implementation will be evaluated using the parameters introduced in [3, 4].
Synchronization is one of the most important components of our system. Synchronization is repeated in a period of time. The frequency of synchronization also depends on the speed of the execution of fragment allocation algorithm by inference engine. Apparently, each node must wait until receive the synchronization information from the rest of the nodes before each execution of the fragment allocation algorithm. 5
In this paper, we discussed a novel method for representing fragment allocation algorithms in a rule based system. Our results show that such representation makes a fragment allocation algorithm. The simplicity of the resulted algorithm can help one to extend existing algorithms and improve their performances. Moreover, the simplicity of the resulted algorithms eases con guring fragment allocation component in DDS.
We are planning to investigate using defeasible reasoning and argumentation theory [15][16] to extend our developments. Another promising direction for this research is to investigate other rule based system, e.g. Answer Set Programming [17][18] , and possibly get more speedups.