=Paper= {{Paper |id=Vol-2327/UISTDA1 |storemode=property |title=User-relative Personalized Tour Recommendation |pdfUrl=https://ceur-ws.org/Vol-2327/IUI19WS-UISTDA-1.pdf |volume=Vol-2327 |authors=Prarthana Padia,Bhavya Singhal,Kwan Hui Lim |dblpUrl=https://dblp.org/rec/conf/iui/PadiaSL19 }} ==User-relative Personalized Tour Recommendation== https://ceur-ws.org/Vol-2327/IUI19WS-UISTDA-1.pdf
     User-relative Personalized Tour Recommendation
             Prarthana Padia∗                                    Bhavya Singhal∗                          Kwan Hui Lim
    School of Computing and Information                School of Computing and Information      Information Systems Technology and
                 Systems                                             Systems                                Design Pillar
        The University of Melbourne                         The University of Melbourne          Singapore University of Technology
      ppadia@student.unimelb.edu.au                      singhalb@student.unimelb.edu.au                    and Design
                                                                                                     kwanhui_lim@sutd.edu.sg

ABSTRACT                                                                     recommended places while considering the available tour
Tour planning and recommendation is an important but te-                     budget, time and cost.
dious task for tourists visiting unfamiliar cities and places.                  There is an abundance of information available on Inter-
While there are various personalized tour recommendation                     net about travel guides and famous places, but they do not
works, they typically adopt a simple measure of user in-                     consider the user’s personal interests and preferences nor
terests based on the number of times a user has visited a                    contemplate the trip’s constraints like time and cost. Despite
place. In this paper, we propose an improved personalized                    the availability of such online information, people may end
tour recommendation system that considers a user’s interest                  up spending excessive efforts and time to plan their itinerary,
preferences in specific categories, relative to his/her overall              and yet end up with an undesired itinerary thus leaving them
interests. Using a Flickr dataset across eight cities, we com-               with an unsatisfactory and frustrating experience.
pared our proposed algorithm against various baselines and                      In recent times, personalized tour recommendation sys-
experimental results show that our algorithm obtained supe-                  tems have benefited from the advancement in web technolo-
rior performance in terms of user interest and popularity.                   gies and geo-location services. The large amount of online
                                                                             available geo-tagged photos facilitate the modelling of user
CCS CONCEPTS                                                                 interest, preferences and trip constraints while strategizing
• Information systems → Personalization; Recommender                         itinerary planning. While many works consider user interest,
systems; Location based services; Data mining; Web applica-                  they adopt a simple measure based on the number of times
tions.                                                                       a user has visited a place.

KEYWORDS
Tour Recommendations; Trip Planning; Recommendation                          Contributions
Systems; Personalization
                                                                             Unlike earlier works that adopt a simplistic definition of user
ACM Reference Format:                                                        interest based on visit counts, this paper proposes a tour
Prarthana Padia, Bhavya Singhal, and Kwan Hui Lim. 2019. User-               recommendation system that utilizes a novel user-relative
relative Personalized Tour Recommendation. In Joint Proceedings              measure of interest preferences build upon the Orienteering
of the ACM IUI 2019 Workshops, Los Angeles, USA, March 20, 2019 ,            problem.
6 pages.                                                                        We propose two variation of user-specific interest prefer-
                                                                             ences. The first approach aims to recommend an itinerary
1   INTRODUCTION                                                             with no prior knowledge about the user by taking advan-
Tour planning is an important task for ensuring satisfac-                    tage of the large collection of geo tagged photos available
tory visits to unfamiliar cities and places. However, visitors               online. Based on photo frequencies of each POI by all users,
are faced with the challenge of identifying popular places                   it determines the popularity of each POI and suggests the
aligned with their personal interests. In addition, there is an              itinerary based on most popular POIs. The second approach
added complexity due to the need to schedule visits to all                   aims to improve upon the targeted personalization level for
                                                                             each user. The benefits of this approach include having a
∗ Both authors contributed equally to this research.
                                                                             tour itinerary that is customized for each user and caters to
                                                                             the user’s categories of interest. For example, in a city full
                                                                             of many tourist attractions, this approach caters to specific
IUI Workshops’19, March 20, 2019, Los Angeles, USA
                                                                             category the user is interested in. For example, if a user has
Copyright © 2019 for the individual papers by the papers’ authors. Copying
permitted for private and academic purposes. This volume is published and
                                                                             shown to prefer outdoors and beaches more than museums
copyrighted by its editors.                                                  and multiplexes, then the recommendation system takes that
                                                                             into account while building the itinerary.
IUI Workshops’19, March 20, 2019, Los Angeles, USA                                                                              P. Padia et al.

2   RELATED WORK                                                3   PROBLEM FORMULATION AND ALGORITHMS
Orienteering problem overview                                   Problem Formulation. Similar to many earlier works [18,
Orienteering problem is a routing problem which can be          21], we model our recommendation problem based on a vari-
viewed as a contest with multiple nodes, where each node        ant of the Orienteering problem [13, 23, 25]. In this tour
has some specific score. The goal of the contest is to maxi-    recommendation problem, our main objective is to recom-
mize the total score which is gathered by visiting different    mend a tour itinerary I = (p1, ..., p N ) that maximizes the
nodes. The contest is time constrained, which needs a strate-   total profit from visiting the list of POIs p1 to P N , while
gical plan to choose a subset of nodes visit in sequence, to    ensuring that the tour itinerary can be completed within a
maximize collected budget within given time and budget [23].    specific time budget B. Given a set of POIs P, we optimize
For a detailed review of Orienteering problem, [13, 23, 25]     for:
reviews orienteering problem and its applications, discusses
and compares published approaches and heuristics of Orien-                Õ Õ                                                     
                                                                    Max                  Pathpi ,p j ηIntu (pi ) + (1 − η)Pop(pi )          (1)
teering problem.
                                                                          pi ∈P p j ∈P

                                                                where Pathpi ,p j = 1 if a path between POI pi and p j is se-
                                                                lected as part of the itinerary, and Pathpi ,p j = 0 otherwise.
Tour recommendation variants                                    Intu (pi ) represents a user-specific interest score of how inter-
Tour recommendation is a well-studied field that typically      esting POI pi is to user u, while Pop(pi ) indicates the general
focus on maximizing user preferences within the given trip      popularity of POI pi . In addition, Equation 1 is subjected to
constraints [6, 14, 15, 17, 19]. For example, [1] proposed a    the following constraints: (i) starting and ending at specific
POI recommender system based on offline modelling (user         POIs; (ii) connectivity of POIs in the itinerary; (iii) complet-
preferences learnt from her location history) and online rec-   ing the itinerary within a specific time or distance budget
ommendation (social opinions learnt from location history       B.
of ‘local experts’). [3] modelled tour recommendation as an        In addition, Equation 1 is subjected to the following con-
instance of the Generalized Maximum coverage problem.           straints:
Building on the same, [5] suggested a solution by exploiting                     Õ                       Õ
an instance of Traveling Salesman Problem (TSP). Others                                  Pathps ,pi =             Pathp j ,pd = 1           (2)
modelled the tour recommendation problem as an instance                          pi ∈I                   p j ∈I
of the Orienteering problem [9, 10], and various variations        Constraint 2 ensures that the recommended itinerary starts
based on specific POI visit sequences [12] and POI category     at a specific POI ps , and ends at another specific POI pd . In
constraints [2]. A unique method of using POIs and route        real-life, this starting and destination POIs would correspond
information as features to a machine learning algorithm         to POIs near the hotel that a tourist is staying at.
to recommend probable tour routes was proposed by [8].
Various works also considered real life constraints like POI                   Õ                           Õ
availability and travelling time uncertainty [29, 30], queu-                             Pathpi ,pk =                 Pathpk ,p j ≤ 1       (3)
ing time awareness [16], visit duration and recency [18],                    pi ,pk ∈I                   p j ,pk ∈I

pedestrian crowdedness [26], transport costs [11]. Similarly,       Constraint 3 ensures that the recommended itinerary ful-
various web and mobile applications have been developed         fills two conditions, namely: (i) all selected paths are con-
for tour recommendation purposes [4, 7, 20, 24, 27].            nected as a full itinerary; and (ii) no POIs are visited more
   Differences with earlier work. Our proposed work dif-        than once.
fers from these earlier works in several aspects. We auto-
matically derive a measure of user-based interest from the                        ÕÕ
                                                                                                Cost(pi , p j )Pathpi ,p j ≤ B              (4)
user’s photo frequency at POIs of a specific category, rel-
                                                                                 pi ∈I p j ∈I
ative to: (i) The average photo frequencies of other users
at that POI; and (ii) The average photo frequency of that          Constraint 4 ensures that the recommended itinerary can
user at all POIs. In contrast, these earlier works either use   be completed within a specific time or distance budget B.
time-based user interest, frequency-based user interest or         Algorithms and Baselines. We developed an Integer
explicitly mentioned user interest preferences. In addition,    program to solve the problem defined in Section 3, along
we improve upon the targeted personalization level for each     with novel approaches to defining user interest preferences.
user by recommending customized itineraries that cater to       The two proposed approaches based on photo frequency are
the user interest categories.                                   as follows:
User-relative Personalized Tour Recommendation                                       IUI Workshops’19, March 20, 2019, Los Angeles, USA

    (i) POI based Photo frequency (PF P ): Given a set of travel              relative to the average visit frequency for a better personal-
        history of all users U , the system determines the pop-               ization.
        ularity of the POI using average photo frequency at
        each POI.                                                             Definition 3: Photo Frequency based User Interest.
   (ii) User based photo frequency (PFU ): Given a set of travel                 As described earlier, the category of a POI p is denoted as
        history of a user u, the system determines the popular-               Catp . Given that C represents the set of all POI categories,
        ity of that category of POI for the user using average                the interest of a user u in POI category c is determined as
        photos taken by that user at that category of the POI.                follows:
   In a city, there can be multiple categories of places com-                    (1) PF P :        Õ (f phpx )
prising of multiple POIS. Consider m POIs for a particular                              f ph
                                                                                     Intu (c) =                  δ (Catpx = C) ∀c ∈ C (7)
city. Let P = {p1, .., pm } be the set of POIs in that city. Each                                px ∈Sph ph(px )
POI p has a category Catp (e.g., church, park, beach) and                            where δ (Catpx = C) = 1, if Catpx = C and 0, otherwise.
latitude/longitude coordinates associated with it. The popu-
larity function Pop(p) that indicates the popularity of a POI
p, based on the average frequency of photos clicked at that                       (2) PFU :
                                                                                      f ph
                                                                                                    Õ            (f phux )
POI. We now introduce the key notations and definitions                            Intu (c) =                                δ (Catp = C) ∀c ∈ C   (8)
used in this work.                                                                              u x ∈Sph ,p ∈P   ph(u x )
                                                                                     where δ (Catp = C) = 1, if Catp = C and 0, otherwise.
Definition 1: Travel History.
                                                                                 Briefly, the above equations model the interest of a user in
  (1) PF P : Given a user u who has visited n POIs, the travel                a particular POI category c based on photo frequency at each
      history is modelled as an ordered sequence, Sph =                       POI of category c, relative to the average photo frequency
      ((p1, f php1 ), (p2, f php2 )...), with each duplet (px , f phpx )      (of all users and a single user) at the same POI. The reason
      comprising the visited POI px , and number of photos                    is that a user is likely to click more photos of the POI that
      at POI px .                                                             he/she is interested in.
  (2) PFU : Given a POI p visited by n users, the travel record                  Hence, firstly by calculating how many more (or less)
      of POI p is modelled as an ordered sequence, Sph =                      photos a user has taken, the interest level of this user in POIs
      ((u 1, f phu1 ), (u 2, f phu2 )...), with each duplet (u x , f phux )   of this category can be determined. Secondly, by calculating
      comprising the user u x , and number of photos taken                    how many more (or less) photos have been taken by all users,
      by u x .                                                                the overall interest level of all users in POIs of this category
Definition 2: Average POI Photo Frequency.                                    can be determined.
  (1) PF P : Given a set of travel history of all users U , the
      system determines the popularity of the POI using
      average photo frequency at each POI.                                    4    EXPERIMENT METHODOLOGY
                  1 Õ Õ                                                       Dataset. For our experiments, we utilized the Yahoo! Flickr
       ph(p) =                     (f phpx )δ (Px = P)∀p ∈ P          (5)     Creative Commons 100M dataset [22, 28], focusing on a
                  n u ∈U p ∈S
                              x   ph                                          dataset of 814k geo-tagged photos across eight cities in-
       where n is the number of photos at POI p by all users                  cluding Toronto, Osaka, Glasglow, Budapest, Perth, Vienna,
       U and δ (px = p) = 1, if px = p and 0, otherwise.                      Delhi and Edinburgh. As provided in [18], these geotagged
                                                                              photos were mapped to a list of POIs based on their re-
  (2) PFU : Given a set of travel record for all POIs P, we                   spective Wikipedia entries, i.e., proximity of geo-tagged
      determine the preference of user u using average photo                  photos to Wikipedia entries of POIs based on their lati-
      frequency of user u at all POIs P.                                      tude/longitude coordinates. Similarly, the categories of POIs
                                                                              are based on their respective Wikipedia entries. The dataset
                  1Õ Õ                                                        also comprises information like the geo-location coordinates,
       ph(u) =                (f phux )δ (Ux = U ) ∀u ∈ U            (6)
                  n p ∈P u ∈S                                                 date/timestamp of the photos taken. To ensure accuracy and
                          x       ph
                                                                              generalizability of results, only photos with the highest geo-
       where n is the number of photos taken by user u at all                 location accuracy have been chosen.
       POIs P and δ (u x = u) = 1, if u x = u and 0, otherwise.                  Evaluation and Metrics. We evaluated our algorithm
   In tour recommendation problems, the user interest pref-                   and the baselines using leave-one-out cross-validation, which
erences are typically derived from POI visit frequency [3, 5,                 involves evaluating a specific travel sequence of a user while
8, 16]. In contrast, we consider a user’s POI visit frequency                 using his/her other travel sequences as training data. The
IUI Workshops’19, March 20, 2019, Los Angeles, USA                                                                                                              P. Padia et al.

Table 1: Comparison between Time-based User Interest (PT − .5T and PT − 1T ), Photo Frequency-based User Interest with
respect to all users (PT − .5PA and PT − 1PA ) and Photo Frequency-based User Interest with respect to a single user (PT − .5PU
and PT − 1PU ).

                                       Osaka                                                                                   Toronto
  Algorithm   Popularity        Interest      Precision        Recall        F1 Score      Algorithm   Popularity       Interest       Precision       Recall        F1 Score
  PT − .5PU   1.107 ± .939    1.551 ± .228    0.652 ± .037   0.739 ± .027   0.685 ± .033   PT − .5PU   2.015 ± .062   1.803 ± .084    0.680 ± .013   0.761 ± .009   0.709 ± .011
  PT − 1PU    0.772 ± 0.068   1.576 ± .228    0.581 ± .032   0.661 ± .024   0.608 ± .028   PT − 1PU    1.574 ± .047   1.898 ± .088    0.675 ± .013   0.730 ± .010   0.691 ± .011
  PT − .5PA   1.118 ± .093    1.652 ± .235    0.650 ± .037   0.752 ± .025   0.689 ± .032   PT − .5PA   2.022 ± .064   1.863 ± .086    0.679 ± .013   0.763 ± .009   0.710 ± .011
  PT − 1PA    0.772 ± .067    1.683 ± .237    0.585 ± .032   0.676 ± .023   0.618 ± .027   PT − 1PA    1.517 ± .047   2.012 ± .089    0.672 ± .013   0.730 ± .010   0.689 ± .011
  PT − .5T    1.144 ± .092    1.171 ± .205    0.662 ± .037   0.759 ± .026   0.699 ± .033   PT − .5T    1.960 ± .064   1.223 ± .061    0.706 ± .013   0.779 ± .010   0.732 ± .012
  PT − 1T     0.737 ± .067    1.205 ± .211    0.622 ± .032   0.682 ± .025   0.641 ± .029   PT − 1T     1.420 ± .043   1.350 ± .069    0.710 ± .013   0.744 ± .011   0.718 ± .012



                                       Glasgow                                                                                Edinburgh
  Algorithm   Popularity        Interest       Precision        Recall        F1 Score     Algorithm   Popularity       Interest       Precision       Recall        F1 Score
  PT − .5PU   1.552 ± .126    1.181 ± .216    0.744 ± .030   0.806 ± .021   0.766 ± .026   PT − .5PU   1.961 ± .052   2.499 ± .115    0.599 ± .012   0.729 ± .008   0.645 ± .010
  PT − 1PU    1.113 ± .093    1.199 ± .205    0.708 ± .030   0.730 ± .024   0.707 ± .027   PT − 1PU    1.482 ± .050   2.543 ± .123    0.558 ± .012   0.664 ± .009   0.590 ± .010
  PT − .5PA   1.591 ± .947    1.077 ± 1.511   0.764 ± .225   0.802 ± .185   0.764 ± .225   PT − .5PA   1.975 ± .042   2.525 ± .092    0.594 ± .010   0.726 ± .007   0.641 ± .009
  PT − 1PA    1.075 ± .087    1.151 ± .192    0.708 ± .029   0.728 ± .024   0.708 ± .026   PT − 1PA    1.461 ± .049   2.582 ± .125    0.554 ± .012   0.662 ± .009   0.587 ± .010
  PT − .5T    1.578 ± .125    0.614 ± .106    0.778 ± .028   0.821 ± .020   0.794 ± .025   PT − .5T    2.007 ± .054   1.568 ± .089    0.652 ± .012   0.739 ± .008   0.670 ± .010
  PT − 1T     1.001 ± .066    0.676 ± .135    0.736 ± .030   0.739 ± .026   0.727 ± .027   PT − 1T     1.297 ± .049   1.660 ± .103    0.594 ± .011   0.660 ± .010   0.611 ± .010


                                           Perth                                                                                   Delhi
  Algorithm    Popularity       Interest       Precision        Recall        F1 Score     Algorithm   Popularity       Interest       Precision       Recall        F1 Score
  PT − .5PU    1.847 ± .190   1.680 ± .263    0.693 ± .047   0.772 ± .037   0.722 ± .042   PT − .5PU   1.647 ± .166   1.294 ± .316    0.731 ± .047   0.804 ± .034   0.757 ± .041
  PT − 1PU     1.289 ± .166   1.765 ± .332    0.626 ± .040   0.694 ± .036   0.650 ± .037   PT − 1PU    1.139 ± .145   1.422 ± .352    0.610 ± .042   0.671 ± .036   0.630 ± .038
  PT − .5PA    1.786 ± .195   2.025 ± .302    0.680 ± .051   0.780 ± .037   0.718 ± .045   PT − .5PA   1.559 ± .134   1.275 ± .334    0.727 ± .047   0.793 ± .036   0.750 ± .042
  PT − 1PA     1.283 ± .196   1.988 ± .271    0.610 ± .049   0.697 ± .038   0.641 ± .043   PT − 1PA    1.130 ± .109   1.332 ± .346    0.614 ± .038   0.676 ± .030   0.636 ± .034
  PT − .5T     1.828 ± .168   1.595 ± .206    0.759 ± .041   0.827 ± .029   0.784 ± .036   PT − .5T    1.610 ± .133   0.954 ± .252    0.746 ± .045   0.807 ± .036   0.769 ± .041
  PT − 1T      1.274 ± .170   1.710 ± .272    0.677 ± .047   0.740 ± .038   0.699 ± .042   PT − 1T     1.128 ± .100   1.000 ± .256    0.632 ± .042   0.674 ± .036   0.648 ± .039


                                      Budapest                                                                                 Vienna
  Algorithm   Popularity       Interest       Precision        Recall        F1 Score      Algorithm   Popularity      Interest       Precision        Recall        F1 Score
  PT − .5PU   2.871 ± .297    3.254 ± .454    0.520 ± .038   0.662 ± .024   0.568 ± .033   PT − .5PU   1.513 ± .052   2.470 ± .122    0.604 ± .013   0.707 ± .010   0.637 ± .012
  PT − 1PU    2.106 ± .293    3.216 ± .486    0.503 ± .042   0.616 ± .031   0.530 ± .037   PT − 1PU    1.175 ± .049   2.561 ± .134    0.562 ± .012   0.652 ± .010   0.588 ± .011
  PT − .5PA   2.697 ± .308    3.357 ± .484    0.524 ± .037   0.653 ± .025   0.568 ± .032   PT − .5PA   1.573 ± .052   2.460 ± .126    0.614 ± .013   0.710 ± .010   0.644 ± .012
  PT − 1PA    2.082 ± .286    3.402 ± .490    0.499 ± .043   0.614 ± .031   0.536 ± .037   PT − 1PA    1.168 ± .049   2.608 ± .134    0.562 ± .012   0.652 ± .009   0.587 ± .011
  PT − .5T    2.791 ± .293    1.850 ± .309    0.551 ± .042   0.663 ± .028   0.589 ± .036   PT − .5T    1.577 ± .054   1.576 ± .103    0.629 ± .013   0.713 ± .010   0.656 ± .011
  PT − 1T     1.806 ± .226    2.019 ± .334    0.558 ± .037   0.624 ± .029   0.580 ± .032   PT − 1T     1.022 ± .042   1.690 ± .111    0.596 ± .012   0.651 ± .010   0.609 ± .011



starting/ending POI and travel duration are set to that of the                                  (5) Tour F 1 −score: TF1 (I ). The harmonic mean of both
specific travel sequence being evaluated, which is used as                                          the recall and precision of a recommended tour itinerary
a representation of a person’s real-life visit. The following                                       I.
evaluation metrics were used:

  (1) Tour Popularity: Tpop (I ). The total popularity of all
      POIs in itinerary I.                                                                  5    RESULTS AND DISCUSSION
  (2) Tour Interest: TIunt (I ). The total interest of all POIs                             Table 1 show the comparison between Time-based User In-
      in itinerary I to user u.                                                             terest (PT − .5T and PT − 1T ), Photo Frequency-based User
  (3) Tour Precision: Tp (I ). The proportion of POIs recom-                                Interest with respect to all users (PT − .5PA and PT − 1PA )
      mended in itinerary I, which matched user’s real-life                                 and Photo Frequency-based User Interest with respect to
      travel sequence.                                                                      single user (PT − .5PU and PT − 1PU ). Overall results show
  (4) Tour Recall: Tr (I ). The proportion of POIs in a user’s                              that our Photo Frequency-based algorithms outperform the
      actual travel sequence that were also recommended in                                  baselines in terms of popularity and interest, while offering
      itinerary I.                                                                          comparable performance in terms of other metrics.
User-relative Personalized Tour Recommendation                           IUI Workshops’19, March 20, 2019, Los Angeles, USA

   Comparison of Popularity and Interest. In terms of             equal stand; and (ii) The proposed algorithms outperform
Interest (Tint ) metric, the proposed algortihms outperform       one of the baseline algorithms of time-based user interest in
the baselines in all the cities, with PT − 1PA being the best     terms of overall precision, recall and F1-score.
performing algorithm, followed by PT − 1PU . In terms of             In this work, our focus was to recommend user-relative
Popularity (Tpop ) metric, PT − .5PU performs equally good        personalized tour itineraries. Some possible future work
as the baseline PT − .5T . In four cities PT − .5PU performs      directions are: (i) Using sentiment awareness on content
the best and in other four PT − .5T . The results show that       obtained from location based social network tags to com-
the Photo Frequency-based algorithms reflects on the overall      bine sentiment analysis techniques with personalization ap-
popularity and overall interests of the POIs better than the      proaches and path planning algorithms for recommending
baselines, for recommending itineraries.                          itineraries that consider user interest preferences and senti-
   Comparison between Time based and Photo-Frequency              ments; and (ii) Recommending tour itineraries by considering
based User Interest. With regards to precision (Tp ), recall      the public transport arrival and departure time to facilitate
(Tr ) and f1-score (TF1 ) the proposed algorithms outperform      realistic tour planning and minimize public transport wait-
one of the baselines (PT − 1T ) in all the cities, standing the   ing time. Moreover, real time uncertainty of public transport
second best. In terms of Tp , PT − .5PU performs the second       could be modelled to improve the suitability.
best in five cities, followed by PT − .5PA performing the sec-
ond best in one city. In terms of Tr , PT − .5PU performs the     ACKNOWLEDGMENTS
second best in four cities and PT − .5PA performs the second      This research is partly supported by the Singapore University
best in rest four. Here, PT − .5PU and PT − .5PA perform          of Technology and Design under grant SRG-ISTD-2018-140,
equally good. These two proposed algorithms outperform            and Defence Science and Technology, Australia. The authors
the baseline (PT − 1T ) with regards to recall. In concern to     thank Jeffrey Chan, Aaron Harwood and the anonymous
the F1-score TF1 metric, the proposed algorithm PT − 1PA          reviewers for their useful comments on this work.
performs the best on one city, PT − .5PU performs the sec-
ond best in five cities, followed by PT − .5PA performing the     REFERENCES
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