Finding the Cost-Optimal Path with Time Constraint over Time-Dependent Graphs

Shortest path query is an important problem and has been well studied in static graphs. However, in practice, the costs of edges in graphs always change over time. We call such graphs as time-dependent graphs. In this paper, we study how to find a cost-optimal path with time constraint in time-dependent graphs. Most existing works regarding the Time-Dependent Shortest Path (TDSP) problem focus on finding a shortest path with the minimum travel time. All these works are based on the following fact: the earliest arrival time at a vertex v can be derived from the earliest arrival time at v's neighbors. Unfortunately, this fact does not hold for our problem. In this paper, we propose a novel algorithm to compute a cost-optimal path with time constraint in time-dependent graphs. We show that the time and space complexities of our algorithm are O(kn log n + mk) and O((n + m)k) respectively. We confirm the effectiveness and efficiency of our algorithm through conducting experiments on real datasets with synthetic cost.

[1]  Ariel Orda,et al.  Shortest-path and minimum-delay algorithms in networks with time-dependent edge-length , 1990, JACM.

[2]  Jeffrey Xu Yu,et al.  Relational Approach for Shortest Path Discovery over Large Graphs , 2011, Proc. VLDB Endow..

[3]  Shashi Shekhar,et al.  Spatio-temporal Network Databases and Routing Algorithms: A Summary of Results , 2007, SSTD.

[4]  Ismail Chabini,et al.  Discrete Dynamic Shortest Path Problems in Transportation Applications: Complexity and Algorithms with Optimal Run Time , 1998 .

[5]  Jiawei Han,et al.  Adaptive Fastest Path Computation on a Road Network: A Traffic Mining Approach , 2007, VLDB.

[6]  Chak-Kuen Wong,et al.  Time-varying shortest path problems with constraints , 1997, Networks.

[7]  Christian Sommer,et al.  Shortest-path queries in static networks , 2014, ACM Comput. Surv..

[8]  Takuya Akiba,et al.  Fast exact shortest-path distance queries on large networks by pruned landmark labeling , 2013, SIGMOD '13.

[9]  Shuigeng Zhou,et al.  Shortest Path and Distance Queries on Road Networks: An Experimental Evaluation , 2012, Proc. VLDB Endow..

[10]  Libin Jiang,et al.  Time-Dependent Network Pricing and Bandwidth Trading , 2008, NOMS Workshops 2008 - IEEE Network Operations and Management Symposium Workshops.

[11]  Ronald L. Rivest,et al.  Introduction to Algorithms, Second Edition , 2001 .

[12]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[13]  Shashi Shekhar,et al.  Time-Aggregated Graphs for Modeling Spatio-temporal Networks , 2006, J. Data Semant..

[14]  Jonathan Leape.  The London Congestion Charge , 2006 .

[15]  Chak-Kuen Wong,et al.  Shortest Path Problems with Time Constraints , 1996, MFCS.

[16]  James Cheng,et al.  Efficient processing of distance queries in large graphs: a vertex cover approach , 2012, SIGMOD Conference.

[17]  Soondal Park,et al.  Shortest paths in a network with time-dependent flow speeds , 1998, Eur. J. Oper. Res..

[18]  Jeffrey Xu Yu,et al.  Finding time-dependent shortest paths over large graphs , 2008, EDBT '08.

[19]  Shuigeng Zhou,et al.  Shortest path and distance queries on road networks: towards bridging theory and practice , 2013, SIGMOD '13.

[20]  Nectaria Tryfona,et al.  Dynamic travel time provision for road networks , 2008, GIS '08.

[21]  Yang Du,et al.  Finding Fastest Paths on A Road Network with Speed Patterns , 2006, 22nd International Conference on Data Engineering (ICDE'06).

[22]  Nectaria Tryfona,et al.  Dynamic Travel Time Maps - Enabling Efficient Navigation , 2006, 18th International Conference on Scientific and Statistical Database Management (SSDBM'06).

[24]  Hong Cheng,et al.  Approximate Shortest Distance Computing: A Query-Dependent Local Landmark Scheme , 2012, 2012 IEEE 28th International Conference on Data Engineering.