SPLZ: An efficient algorithm for single source shortest path problem using compression method

Efficient solution of the single source shortest path (SSSP) problem on road networks is an important requirement for numerous real-world applications. This paper introduces an algorithm for the SSSP problem using compression method. Owning to precomputing and storing all-pairs shortest path (APSP), the process of solving SSSP problem is a simple lookup of a little data from precomputed APSP and decompression. APSP without compression needs at least 1TB memory for a road network with one million vertices. Our algorithm can compress such an APSP into several GB, and ensure a good performance of decompression. In our experiment on a dataset about Northwest USA (with 1.2 millions vertices), our method can achieve about three orders of magnitude faster than Dijkstra algorithm based on binary heap.

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

[2]  G. Gallo,et al.  SHORTEST PATH METHODS: A UNIFYING APPROACH , 1986 .

[3]  Donald E. Knuth,et al.  Fast Pattern Matching in Strings , 1977, SIAM J. Comput..

[4]  Andrew V. Goldberg,et al.  Customizable Route Planning in Road Networks , 2017, Transp. Sci..

[5]  Peter Sanders,et al.  Goal-directed shortest-path queries using precomputed cluster distances , 2010, JEAL.

[6]  Peter Sanders,et al.  Transit Node Routing Reconsidered , 2013, SEA.

[7]  Dimitri P. Bertsekas,et al.  A simple and fast label correcting algorithm for shortest paths , 1993, Networks.

[8]  Jorge A. Baier,et al.  Moving Target Search with Compressed Path Databases , 2013, ICAPS.

[9]  Hanan Samet,et al.  Efficient query processing on spatial networks , 2005, GIS '05.

[10]  Peter Sanders,et al.  [Delta]-stepping: a parallelizable shortest path algorithm , 2003, J. Algorithms.

[11]  Andrew V. Goldberg,et al.  Customizable Route Planning in Road Networks (Extended Abstract) , 2013, SOCS.

[12]  Peter Sanders,et al.  Fast Routing in Road Networks with Transit Nodes , 2007, Science.

[13]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[14]  Andrew V. Goldberg,et al.  Shortest-path feasibility algorithms: An experimental evaluation , 2008, JEAL.

[15]  Andrew V. Goldberg,et al.  Computing the shortest path: A search meets graph theory , 2005, SODA '05.

[16]  Peter Sanders,et al.  Contraction Hierarchies: Faster and Simpler Hierarchical Routing in Road Networks , 2008, WEA.

[17]  Hanan Samet,et al.  Path Oracles for Spatial Networks , 2009, Proc. VLDB Endow..

[18]  Andrew V. Goldberg,et al.  PHAST: Hardware-Accelerated Shortest Path Trees , 2011, 2011 IEEE International Parallel & Distributed Processing Symposium.

[19]  Andrew V. Goldberg,et al.  The shortest path problem : ninth DIMACS implementation challenge , 2009 .

[20]  Fred W. Glover,et al.  A New Polynomially Bounded Shortest Path Algorithm , 1985, Oper. Res..

[21]  Kurt Mehlhorn,et al.  Faster algorithms for the shortest path problem , 1990, JACM.

[22]  Amos Fiat,et al.  HLDB: location-based services in databases , 2012, SIGSPATIAL/GIS.

[23]  Timothy C. Bell,et al.  Longest‐match string searching for ziv‐lempel compression , 1993, Softw. Pract. Exp..

[24]  T. Lindvall.  ON A ROUTING PROBLEM , 2004, Probability in the Engineering and Informational Sciences.

[25]  Andrew V. Goldberg,et al.  A Hub-Based Labeling Algorithm for Shortest Paths in Road Networks , 2011, SEA.

[26]  Andrew V. Goldberg,et al.  Shortest paths algorithms: Theory and experimental evaluation , 1994, SODA '94.

[27]  Peter Sanders,et al.  Highway Hierarchies Hasten Exact Shortest Path Queries , 2005, ESA.

[28]  David A. Bader,et al.  Parallel Shortest Path Algorithms for Solving Large-Scale Instances , 2006, The Shortest Path Problem.

[29]  Abraham Lempel,et al.  A universal algorithm for sequential data compression , 1977, IEEE Trans. Inf. Theory.

[30]  Andrew V. Goldberg,et al.  The Shortest Path Problem , 2009 .

[31]  Rolf H. Möhring,et al.  Fast Point-to-Point Shortest Path Computations with Arc-Flags , 2006, The Shortest Path Problem.

[32]  Robert B. Dial,et al.  Algorithm 360: shortest-path forest with topological ordering [H] , 1969, CACM.

[33]  D. Bertsekas,et al.  Parallel asynchronous label-correcting methods for shortest paths , 1996 .

[34]  U. Pape,et al.  Implementation and efficiency of Moore-algorithms for the shortest route problem , 1974, Math. Program..

[35]  Stefano Pallottino,et al.  Shortest-path methods: Complexity, interrelations and new propositions , 1984, Networks.