SHARC: Fast and robust unidirectional routing

During recent years, impressive speed-up techniques for Dijkstra's have been developed. Unfortunately, the most advanced techniques use bidirectional search, which makes it hard to use them in scenarios where a backward search is prohibited. Even worse, such scenarios are widely spread (e.g., timetable-information systems or time-dependent networks). In this work, we present a unidirectional speed-up technique, which competes with bidirectional approaches. Moreover, we show how to exploit the advantage of unidirectional routing for fast exact queries in timetable information systems and for fast approximative queries in time-dependent scenarios. By running experiments on several inputs other than road networks, we show that our approach is very robust to the input.

[1]  Haim Kaplan,et al.  Better Landmarks Within Reach , 2007, WEA.

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

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

[4]  Dorothea Wagner,et al.  Speed-Up Techniques for Shortest-Path Computations , 2007, STACS.

[5]  I C M Ingrid Flinsenberg,et al.  Route Planning Algorithms for Car Navigation , 2009 .

[6]  Peter Sanders,et al.  Dynamic Highway-Node Routing , 2007, WEA.

[7]  Burkhard Monien,et al.  Graph partitioning with the Party library: helpful-sets in practice , 2004, 16th Symposium on Computer Architecture and High Performance Computing.

[8]  Daniel Delling,et al.  SHARC: Fast and robust unidirectional routing , 2008, JEAL.

[9]  E. Carpenter.  Language and Environment. , 1968 .

[10]  Rolf H. Möhring,et al.  Partitioning Graphs to Speed Up Dijkstra's Algorithm , 2005, WEA.

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

[12]  Ulrich Lauther,et al.  An Experimental Evaluation of Point-To-Point Shortest Path Calculation on Road Networks with Precalculated Edge-Flags , 2006, The Shortest Path Problem.

[13]  Frank Schulz,et al.  High-Performance Multi-Level Graphs ∗ , 2006 .

[14]  Dorothea Wagner,et al.  14. Experimental Study on Speed-Up Techniques for Timetable Information Systems , 2007 .

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

[16]  Christos D. Zaroliagis,et al.  Efficient models for timetable information in public transportation systems , 2008, JEAL.

[17]  Dorothea Wagner,et al.  Landmark-Based Routing in Dynamic Graphs , 2007, WEA.

[18]  U. Brandes.  A faster algorithm for betweenness centrality , 2001 .

[19]  Daniel Delling.  Time-Dependent SHARC-Routing , 2008, ESA.

[20]  Peter Sanders,et al.  Highway Hierarchies Star , 2006, The Shortest Path Problem.

[21]  Dorothea Wagner,et al.  Partitioning graphs to speedup Dijkstra's algorithm , 2007, ACM J. Exp. Algorithmics.

[22]  Haim Kaplan,et al.  Reach for A*: Efficient Point-to-Point Shortest Path Algorithms , 2006, ALENEX.

[23]  Peter Sanders,et al.  Combining Hierarchical and Goal-Directed Speed-Up Techniques for Dijkstra's Algorithm , 2008, WEA.

[24]  Christos D. Zaroliagis,et al.  Geometric containers for efficient shortest-path computation , 2005, JEAL.

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

[26]  Rolf H. Möhring,et al.  Acceleration of Shortest Path and Constrained Shortest Path Computation , 2005, WEA.

[27]  Peter Sanders,et al.  Engineering Fast Route Planning Algorithms , 2007, WEA.

[28]  Dorothea Wagner,et al.  Shortest-Path Indices: Establishing a Methodology for Shortest-Path Problems , 2007 .

[29]  Andrew V. Goldberg,et al.  Computing Point-to-Point Shortest Paths from External Memory , 2005, ALENEX/ANALCO.

[30]  Vipin Kumar,et al.  A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs , 1998, SIAM J. Sci. Comput..

[31]  Ronald J. Gutman,et al.  Reach-Based Routing: A New Approach to Shortest Path Algorithms Optimized for Road Networks , 2004, ALENEX/ANALC.

[32]  Peter Sanders,et al.  Better Approximation of Betweenness Centrality , 2008, ALENEX.

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

[34]  K. Cooke,et al.  The shortest route through a network with time-dependent internodal transit times , 1966 .

[35]  Peter Sanders,et al.  Engineering Route Planning Algorithms , 2009, Algorithmics of Large and Complex Networks.

[36]  Roger Wattenhofer,et al.  Worst-Case optimal and average-case efficient geometric ad-hoc routing , 2003, MobiHoc '03.

[37]  Daniel Delling,et al.  Time-Dependent SHARC-Routing , 2008, Algorithmica.

[38]  Dominik Schultes,et al.  Route Planning in Road Networks , 2008 .

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

[40]  Dorothea Wagner,et al.  Experimental study of speed up techniques for timetable information systems , 2011, Networks.

[41]  Peter Sanders,et al.  Time-Dependent Contraction Hierarchies , 2009, ALENEX.

[42]  Peter Sanders,et al.  Engineering highway hierarchies , 2012, JEAL.