Representing Pre-trip Transit Information as Graph with Constraints

Abstract— This research explores the representation of pre-trip

transit information as graph with constraints. The research is

aimed at representing pre-trip transit information for flight

travelers that is able to suggest a number of continuous travel

destinations within a route to travelers. It applies maximal join

concept to merge multiple transit information network which is

applied to centralize distributed travel destinations. Graph

similarity concept is applied to determine transit node and

alternative edges between two nodes. The research also applied

Constraint Satisfaction Problems to produce only relevant

information to travelers which suggest a destination series to

them.

Keywords-Transit Information Systems; Graph-based

Knowledge Representation; Maximal Join; Graph Similarity;

Constraints Satisfaction Problem.

I. INTRODUCTION

Everyday travelers would make fundamental travel decision about destination they want to go, time and date of travel, route they are going to traverse, mode of travel they are going to use and cost of travel they need to allocate. For air travelers, they can refer to the Internet to obtain travel information such as destination, flight schedules, price and discount, airlines bookings and other related services [1]. Usually, they would look for flight routes map or schedules while planning their itinerary.

However, people would not always know where exactly they want to go and where they can go especially when they are planning for a multi-city (multi-leg) journey. If the planning is only involving an origin and a destination; or an origin and a destination for a return trip, it would not be that bothersome. However, if they intent to go for a multi-city journey which they do not know where to go, they need to spend some time to search for suitable destinations from distributed sources of travel information.

In this case, a pre-trip transit information system is essentially needed to help the travelers in making more informed decision for their itinerary planning. Pre-trip Transit Information Systems is a significant Traveler Information Systems that provide travelers with accurate and timely information before starting their trips to allow them to make informed decision about modes as well as routes and departure times which often support itinerary planning [2].

From preliminary studies that have been done, it is discovered that existed routing applications mostly would present approach that produces a route between a given origin

and a given destinations. In contrast, this research would propose a series of travel destinations from only a given origin. The research is aimed at representing pre-trip transit information for flight travelers that is able to suggest a series of travel destinations and its routes to travelers from a given origin. The research is also aimed at completing the series by connecting the last destination to the origin through a cycle. In addition, it is aimed that the research could have produce only relevant information according to travelers’ preferences.

It is expected that this approach would support itinerary planning for flight multi-city journey by suggesting a number of destinations that travelers could go from a given origin. In addition, the suggested routes would be complimented with a cycle to the origin as in common practice, travelers would return to their origin after traveling. Another important part of this research is the outcome will be filtered relevantly based on travelers’ preferences.

Although most current traveler information systems researches focus on multimodal transportation, this research would only focus on flight mode. Compared to other transportation mode, its point-to-point destination basis makes flight routing a simpler domain to apply the suggested approach. The proposed pre-trip transit information approach would be developed using graph-based knowledge representation which best to describe a huge amount of travel information in a communicative way and to describe how cycle-to-origin concept affect the outcome. Furthermore, the outcome would be filtered using constraint satisfaction problem.

Further details will be explained throughout this paper. Related works are discussed in section II. The methodology used is discussed in section III. Explanation on the results is discussed in section IV. Lastly, the paper will be ended by a conclusion in section V.

II. RELATED WORK

Related work has been done mainly in Traveler Information Systems area which discovered current approaches used in it. From this survey, it is believed that graph-based knowledge representation has a great capability to represent transportation network. Therefore, this section is followed by surveying literatures in graph-based knowledge representation area. In order to deliver relevant result to travelers, constraints are applied in this research and related works in this area are also being discussed in this section.

978-1-4577-1884-7/11/$26.00 ©2011 IEEE

1Siti Zarinah Mohd Yusof, 2Vijanth Sagayan Asirvadam, 3Mohd Fadzil Hassan, 1,3

Computer and Information Sciences Department, 2 Electrical and Electronics Department,

Universiti Teknologi PETRONAS

A. Traveler Information Systems

Pre-trip Transit Information Systems is a significant Traveler Information Systems that provide travelers with accurate and timely information before starting their trips [2]. Several researches which discussed about traveler information systems and pre-trip transit information have been reviewed.

In [3], the author presented a multi-objective optimum path algorithm for passenger pre-trip planning in multimodal transportation networks. A Mathematical Programming Model is used to identify the feasible paths which accounts for the delays of the different modes use and of the switching terminals. The model involves the decomposition of search space, calculation of feasible paths and identifications of optimum path through criteria selection.

In [4], Djikstra Algorithm is used to perform rational route search in Vilnius information system for drivers. It is to help Advanced Traveler Information System (ATIS) which disseminates real-time traffic information to travelers with better decision making on choosing their routes. This algorithm is believed can solve the problem of finding the quickest path between two nodes. However, one crucial challenge in the success of such an approach is the appropriate modeling of the transportation network as a graph [5]. Therefore the author presented a set of three new time-dependent models with increasing flexibility for realistic route planning specifically in flight networks.

In [6] a budget travel planning that leverages semantic web technology to provide automated travel planning service is presented. It uses ontology to aggregate related web resources and reason on them. In [7], the authors presented a development of a mutli-agent system that would allow the creation of itineraries through the given tourist’s travel preferences. A good itinerary is essential if the travelers are expected to enjoy the travel.

From this survey, there are several elements that can be considered as essential in a traveler information system. In [3] and [4], the authors focused on searching optimum and rational path. Meanwhile, the authors in [6] addressed the aggregation of distributed information resources. In [7], travelers’ preferences are taken into consideration before delivering the outcome to travelers. It is believed that these four elements would contribute to a good traveler information system. Looking from a different perspective, the authors in [5] highlight much on the route planning flexibility which the transportation network is represented using a graph model.

B. Graph and Transportation

Based on above related works, it is shown that graph plays a vital role in transportation industry. Graph had been used widely in representing transportation networks. Based on [8], the authors presented a case study to assess the survivability of a large-scale urban transportation network using graph-based analysis. It is believed that graphs are very useful to represent how things are either physically or logically linked to one another in a network structure.

In [9], the authors demonstrated the use of multilayered graph theory to identify critical components in surface transportation networks. Graph is being used to improve the reliability of the transportation system by identifying and mitigating vulnerabilities such as accidents, malicious attacks, and natural disasters. Meanwhile in [10], graph theory is being used to study the emerging, growth and evolution of new airlines in Europe and Asia.

The advantages of using graph are also being emphasized by another research work. Ryszard Raban in his work [11] stated that the graphs are not used as just another graphical representation of information system requirements, but the full power of this graphical logic system has been employed to fully and precisely capture type definitions, referential integrity constraints and global constraints.

Huge amount of travel information is distributed in the Internet or travel guide books. Flight schedules are also distributed according to its service provider’s websites. In order to aggregate and link the distributed travel destinations in guiding pre-trip decision, the information graphs need to be joined together into a single graph. Simon Polovina explained that the joining of graphs facilitates inference because more projections can be made into bigger graphs [12]. In addition, Simon Polovina mentioned in his work that maximal join, which extends the notion of join in SQL in database systems, defines the optimal method by which graphs are joined [12].

Other than that he also mentioned that maximal join occurs when graphs are joined on the most common, or maximally extended, projection [12]. Michel Chein and Marie-Laure Mugneir explained the effect of maximal join operation which is to maximally join, or merge, connected subgraphs of two graphs in [13]. Added by Dickson Lukose in his work, two graphs can be joined on maximally extended common projections. Multiple graphs could result if there is more than one maximally extended common projection [14].

It is believed that graph theory or graph representation could address the searching for optimum path and linking the distributed information together. In order to address travelers preferences, constraints need to be applied so rational and relevant outcome would be delivered to travelers.

C. Knowledge Representation Using Constraints

In order to produce related and rational outcome to the travelers, literature review on knowledge representation that applies constraints also has been done. In [15], a constraint programming model for the routing and scheduling of trains running through a junction is presented. The model which represented in mathematical formulation allows to express explicitly the influence of the signaling system on the traffic management decisions.

In [16], the authors use object-centered constraints to assist the acquisition of planning domain models. The authors established an experimental and theoretical basis for using object - centred assumptions to underlie the automated acquisition of planning domain models.

In [17], the authors use hard constraint propagation to prune the search space and compactly represent the resulting

messages with Constraint Decision Diagrams (CDDs). CDDs which combine constraint reasoning and consistency techniques with a compact data structure is proved to be extremely space-efficient for highly constrained problems when compared to the extensional representation used by Distributed Constraint Optimization.

In [18], the authors used constraint satisfaction problems and logic programming techniques to reduce the collision-free and deadlock-free execution of the repetitive processes of transport operation. CSP is used to solve the decision problem and its role is widely being used to solve constraint problems.

From these literatures, it is seen that constraint problems such planning and scheduling could be represented in many form. As graph-based representation has the potential of capturing information precisely, it is believed that CSP which commonly represented as graph to solve constraint problems would lead to the desired solution of this research.

III. METHODOLOGY

In order to represent the information and produce an outcome that is useful for travelers, there are three main elements that would be covered in this research- Maximal Join, Graph Similarity and Constraint Satisfaction Problems. The methodologies used have been divided into three phase which are broadening information network using Maximal Join, finding node and edge similarity and filtering search result using constraints.

A. Finding Node and Edge Similarity

Before centralizing the distributed information, graph representation of the destinations need to be drawn first. In continuation, node and edge similarity are necessary to be figured out after that. Node similarity is essential to determine point to merge disjoint graphs and at the same time as a point of route transit which is transit from one graph to another graph. Edge similarity is needed to determine number of alternatives route.

To give a clearer view, assume that node a in graph X is similar to node b in graph Y. As the nodes are similar, these nodes could be used as the merging point of graph X and Y. In addition, the nodes could also be the transit point from graph X into graph Y. Assume that edge e in graph M and edge f in graph N are similar, these edges represent two available alternatives to go through the same route. Each nodes and edges would be labeled with some attributes and the attributes would be used to determine the similarity of the nodes and edges involved.

B. Broadening Information Network Using Maximal Join

Similar nodes from previous methodology would be used further in this part where the distributed destinations would be centralized. The distributed destinations would be represented as disjoint graphs and in order to centralize the information together, maximal join is used to merge the graph into a single graph. As stated in [9], maximal join operation would maximally join, or merge, connected subgraphs of two graphs. Michel Chein and Marie-Laure Mugnier did mentioned in their

work that the simplest way of joining two graphs is by using external join operation which consists of merging two concept nodes of two disjoint graphs [9]. The merging process would use similar nodes that have been figured out as the merging point.

C. Filtering Search Result Based on Constraints

Planning a good itinerary would involve several travelers’ preferences. These preferences would then filter the destinations so that only relevant and rational solution is delivered to travelers. Here, constraints are used in the searching process. Constraints Satisfaction Problems (CSP) provide a well-defines search space definition that enables exact formulations of all search algorithm [19]. A CSP is defined as by a set of variables and constraints. Each variable has a domain of possible values. Each constraint has some subset of the variable and specifies the allowed combinations for it to be assigned to variable. CSP would be used in this research as it could be represented using graph theory.

IV. RESULT AND DISCUSSION

After Travel destination networks provided by airlines in Malaysia such as Malaysia Airlines, Air Asia, Fire Fly and Berjaya Air are selected as the case study of this research. Before applying the concept of maximal join and graph similarity - node similarity and edge similarity; the collected data would be represented into graph first. Collected data from four airlines mentioned before is converted into four disjoint graphs. Figure 1 show four disjoint graphs that represent destinations adapted from [20], [21], [22] and [23]. Each node and edge has been labeled and could be seen in Table 1 and Table 2. Duration in Table 2 is approximately determined from departure and arrival time stated in flight schedules of each airline.

A. Node and Edges Similarity

Based on Figure 1, Table 1 and Table 2, all destinations from each airline have been represented as graph with side information assigned to each node and edge. Side information or in graph theory, it is called as labels is used to find nodes and edge similarity. In [24], the author did mention that two nodes will be similar if they have similar in/out neighbors. Referring to graphs in Fig.1 and the assigned labels for each node and edge, it is seen that many similar nodes are available. Similar node is determined by looking at the airport codes and city name assigned to each node.

Based on the analysis, Kuala Lumpur with two airport code, KUL and SZB have many neighbours within the four disjoint graphs. Node m8 has the same city name, airport code and neighbours as node n6 meanwhile node m10 has the same labels as node 09 and p2. These nodes are considered as similar to each other. Therefore these nodes would also be considered as the transit point to move from one graph to another graph. For instance, it is possible to move from m9 which is Kuantan (KUA) using Malaysia Airlines to n2 which is Alor Setar (AOR) using Air Asia with Kuala Lumpur, KUL as transit point between these two nodes.

Edge similarity could be determined through labels assigned to each edge and nodes it is connected to. Based on Table 2, time in minutes and routes is labeled to each edge. From these labels, it is possible to determine edge similarity. For instance, a15, b8 and c5 have the same routes which are LGK-PEN and PEN-LGK and duration of 35 minutes. As these

nodes connecting similar nodes between Langkawi and Penang; and have the same duration, we could consider these edges as similar. Similar edges show alternative of the same path which routes from LGK to PEN or LGK-PEN is provided by three airlines.

Figure 1. Airlines destinations represented as graph. (a) Malaysia Airlines. (b) Air Asia. (c) Fire Fly. (d) Berjaya Air.

TABLE I. LABELS OF NODES

TABLE II. LABELS OF EDGES

There are many other similar nodes and edges existed in these four disjoint graph. The mentioned nodes and edges above is the best example from all to describe the concept of node similarity and edge similarity. However, going from one graph to another graph to check for transit point and alternative of same path would be quite hassle and in reality, this information would be very distributed. Here, centralizing the information is needed to ease itinerary planning.

B. Maximal Join

In order to centralize the distributed information or more specific to centralize the disjoint graphs, unification between those graphs is needed. The disjoint graph need to be merged into a single graph and the merging point need to be figured out. Maximal join occurs when graphs are joined on the most common, or maximally extended, projection. In Figure 1, node m8 and node n6 are similar and could lead to maximally extended projection. This makes it possible to merge graph a with graph b meanwhile the same criteria shown in node m10, node 09 and p2 which these nodes are similar to each other. It would be the point for graph a, c and d.

Figure 2. Merged Graphs

Figure 2 shows the merged graphs. Table 3 lists the labels of nodes after four disjoint graphs are merged into a single graph. Table 4 lists the labels of edges after the merging process. It is quite challenging to merge graphs that have multi-label in its nodes and edges. The nodes are represented with variable X1, X2, X3, …, X13 and the edges are represented with variable Y1, Y2, Y3, …, Y20. Different line styles are used in Figure 2 to shows edges similarity between four graphs. Merging disjoint graphs into a single graph could centralize the distributed information which a step to support multi-city itinerary planning. However, it would be a complicated graph when it involves more nodes and edges. Therefore, a search technique is required to help in figuring out the most relevant itinerary.

TABLE III. LABEL OF NODES AFTER FOUR DISJOINT GRAPH ARE

MERGED

TABLE IV. LABEL OF EDGES AFTER FOUR DISJOINT GRAPH ARE

MERGED

C. Analysing Result Using Constraint Satisfaction Problems

(CSP)

Producing relevant solution based on preferences could be grouped as a constraint problem. CSP is seen as a potential approach in searching for data-driven solution. From the merged graphs produced in previous discussion, the same graph is represented using CSP. Goal, variable, domain and constraints of the problem is constructed before with the representation. The goal of the problem is selecting N number of destinations within T accumulated itinerary duration which every suggested itinerary must have a cycle to the origin. In this problem, a variable with route, duration, service provider as the domain. Constraints that need to be followed are to search a series of nodes, given the number of expected node; total duration of the itinerary is less or equal to given accumulated duration; final node of the itinerary could make a cycle to the root; and in every node searching, returning back to previous node is not allowed.

Figure 3 shows a tree search that has been constructed using backtracking algorithm to perform the searching process. It is assumed that number of expected nodes is 2, accumulated duration is 100 minutes, JHB is the origin and AOR is the first state of the tree search. The itinerary solution gained from this searching is JHB � KUL � PEN � JHB. Note that although KUA, TGG and KBR have accumulated duration less than 100, these nodes do not have a cycle to the root/origin which is JHB. Therefore, PEN is chosen as the second node.

Figure 3. Using tree search as a technique to solve Constraint Satisfaction Problems

V. CONCLUSION

Representing pre-trip transit information using graph have been discussed throughout the paper. Utilizing graph to represent information would produce an outcome that is very useful especially when the information involved multiple connections. Node and edge similarity is applied in order to find few other important information such as merging point, point of transit and also alternative of the same path. The uses of maximal join helps in merging several disjoint graphs into a single as a mean of linking or centralizing the distributed

information. Although all information has been centralized, only relevant and rational final result that ought to be delivered at the end of the process. Therefore, concept of constraint satisfaction problems is applied within the representation.

REFERENCES

[1] E. Stephen “Explaining International IT Application Leadership: Intelligent Transportation Systems,” The Information Technology and Innovation Foundation, 2010

[2] A.H. Lester, J. G. Nicholas, W. S. Adel, “Transportaion Infrastructure Engineering: A Multimodal Integration,” Nelson, 2008.

[3] Z. Athanasios, A. Georgia, C. Evangelia, “A Multi-objective Optimum Path Algorithm for Passenger Pre-trip Planning in Multimodal Transportation Networks,” 2006.

[4] J. Marius, B. Marija “Route Planning Methodology of An Advanced Traveler Information System in Vilnius City,” 2010.

[5] D. Daniel, P. Thomas, W. Dorothea, Z. Christos “Effcient Route Planning in Flight Networks,” 2009.

[6] Y. Yan, T. Shengqun, X. Youwei, X. Yang, “A Budget Travel Planning System Using Ontologies for Web Information Aggregation,” 2006.

[7] V. Miguel, C. Claudio, “A Multiagent System for Touristic Travel Planning,” 2009.

[8] D. Easley, J. Kleinberg, “Networks, Crowds, and Markets: Reasoning About a Highly Connected World,” To be published by Cambridge University Press, 2010.

[9] A. Abdel-Rahim, P. Oman, B. K. Johnson, R. A. Sadiq, “Assessing Surface Transportation Network Component Criticality: A Multi-Layer Graph-Based Approach,” IEEE, 2010.

[10] “Air Transportation Systems. Department of Aeronautics and Astronautics,” School of Engineering, Massachusetts Institute of Technology, 2007.

[11] R. Ryszard, “Information Systems Modeling with CGs Logic,” unpublished.

[12] P. Simon, “Combining Graph: An Introduction to Conceptual Graphs,” Berlin Heidelberg: Springer-Verlag, 2007.

[13] C. Michael, M. Marie-Laurie, “Graph-based Knowledge Representation: Computational Foundations of Conceptual Graphs,” London: Springer-Verlag, ch. 8, 2009.

[14] Lukose, “CGKEE: Conceptual Graph Knowledge Engineering Environment,” unpublished.

[15] R. A. Joaquı´n, “ A Constraint Programming Model for Real-time Train Scheduling at Junctions,” Elsevier Ltd., 2006.

[16] M. M. S. Shah, T. L. McCluskey, West, M. Margaret “A Study of Synthesizing Artificial Intelligence (AI) Planning Domain Models by Using Object Constraints,” Proceedings of Computing and Engineering Annual Researchers' Conference 2009: CEARC’09. University of Huddersfield, Huddersfield, pp. 64-69, 2009.

[17] K. Akshat, P. Adrian, F. Boi, “H-DPOP: Using Hard Constraints to Prune the Search Space,” Distributed Constraints Reasoning, 2007.

[18] B. Grzegorz, W. Robert, B. Zbigniew, “Design of Admissible Schedules for AGV Systems with Constraints: A Logic-Algebraic Approach,” Berlin Heidelberg: Springer-Verlag, 2007.

[19] M. Ammon, “Distributed Search by Constrained Agents: Algorithm, Performance and Communication,” Springer-Verlang, London, 2008.

[20] Malaysia Airlines Timetable. Available: www.malaysiaairlines.com.

[21] Air Asia Flight Schedule. Available: www.airasia.com.

[22] FireFly Schedule. Available: www.fireflyz.com.my.

[23] Berjaya Air Destinations Route Map. Available: www.berjaya-air.com.

[24] L. Ninove, “Graph Similarity Algorithms,” Mathematical Engineering Department, Universit ´e Catholique de Louvain, unpublished, 2005.