Customizable Route Planning in Road Networks

We propose the first routing engine for computing driving directions in large-scale road networks that satisfies all requirements of a real-world production system. It supports arbitrary metrics (cost functions) and turn costs, enables real-time queries, and can incorporate a new metric in less than a second, which is fast enough to support real-time traffic updates and personalized cost functions. The amount of metric-specific data is a small fraction of the graph itself, which allows us to maintain several metrics in memory simultaneously. The algorithm is the core of the routing engine currently in use by Bing Maps.

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

[2]  Dorothea Wagner,et al.  Engineering Multi-Level Overlay Graphs for Shortest-Path Queries , 2006, ALENEX.

[3]  Ignaz Rutter,et al.  Search-space size in contraction hierarchies , 2016, Theor. Comput. Sci..

[4]  Daniel Delling,et al.  Faster Customization of Road Networks , 2013, SEA.

[5]  Eric V. Denardo,et al.  Flows in Networks , 2011 .

[6]  A. Goldberg,et al.  TRANSIT: Ultrafast Shortest-Path Queries with Linear-Time Preprocessing , 2006 .

[7]  Peter Sanders,et al.  Route planning with flexible edge restrictions , 2012, JEAL.

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

[9]  Andrew V. Goldberg,et al.  Customizable Route Planning , 2011, SEA.

[10]  Bastian Katz,et al.  Preprocessing Speed-Up Techniques Is Hard , 2010, CIAC.

[11]  Andrew V. Goldberg,et al.  Alternative routes in road networks , 2010, JEAL.

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

[13]  Ulrich Meyer,et al.  [Delta]-stepping: a parallelizable shortest path algorithm , 2003, J. Algorithms.

[14]  Peter Sanders,et al.  Robust, Almost Constant Time Shortest-Path Queries in Road Networks , 2006, The Shortest Path Problem.

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

[16]  Christos D. Zaroliagis,et al.  Using Multi-level Graphs for Timetable Information in Railway Systems , 2002, ALENEX.

[17]  Ben Strasser,et al.  Customizable Contraction Hierarchies , 2014, SEA.

[18]  Dennis Luxen,et al.  Candidate Sets for Alternative Routes in Road Networks , 2012, SOCS.

[19]  Dieter Pfoser,et al.  GRASP. Extending Graph Separators for the Single-Source Shortest-Path Problem , 2014, ESA.

[20]  Kurt Mehlhorn,et al.  Review of algorithms and data structures: the basic toolbox by Kurt Mehlhorn and Peter Sanders , 2011, SIGA.

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

[22]  Christos D. Zaroliagis,et al.  Engineering planar separator algorithms , 2005, JEAL.

[23]  L. Volker Route Planning in Road Networks with Turn Costs , 2008 .

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

[25]  Peter Sanders,et al.  Minimum time-dependent travel times with contraction hierarchies , 2013, JEAL.

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

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

[28]  Dorothea Wagner,et al.  High-Performance Multi-Level Routing , 2006, The Shortest Path Problem.

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

[30]  Stefan Funke,et al.  Ultrafast Shortest-Path Queries via Transit Nodes , 2006, The Shortest Path Problem.

[31]  Andrew V. Goldberg,et al.  Graph Partitioning with Natural Cuts , 2011, 2011 IEEE International Parallel & Distributed Processing Symposium.

[32]  R. Tarjan,et al.  A Separator Theorem for Planar Graphs , 1977 .

[33]  Rolf H. Möhring,et al.  Robust and Online Large-Scale Optimization: Models and Techniques for Transportation Systems , 2009, Robust and Online Large-Scale Optimization.

[34]  Andrew V. Goldberg,et al.  Hierarchical Hub Labelings for Shortest Paths , 2012, ESA.

[35]  Dorothea Wagner,et al.  Time-Dependent Route Planning , 2009, Encyclopedia of GIS.

[36]  Peter Sanders,et al.  Think Locally, Act Globally: Highly Balanced Graph Partitioning , 2013, SEA.

[37]  Hiroki Yanagisawa,et al.  A multi-source label-correcting algorithm for the all-pairs shortest paths problem , 2010, 2010 IEEE International Symposium on Parallel & Distributed Processing (IPDPS).

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

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

[40]  L FoxBennett,et al.  Shortest-Route Methods , 1979 .

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

[42]  Peter Sanders,et al.  Route Planning with Flexible Objective Functions , 2010, ALENEX.

[43]  Dorothea Wagner,et al.  Engineering multilevel overlay graphs for shortest-path queries , 2009, JEAL.

[44]  Daniel Delling,et al.  Customizable Point-of-Interest Queries in Road Networks , 2015, IEEE Trans. Knowl. Data Eng..

[45]  Andrew V. Goldberg A Practical Shortest Path Algorithm with Linear Expected Time , 2008, SIAM J. Comput..

[46]  Robert Geisberger,et al.  Efficient Routing in Road Networks with Turn Costs , 2011, SEA.

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

[48]  Jean Roman,et al.  SCOTCH: A Software Package for Static Mapping by Dual Recursive Bipartitioning of Process and Architecture Graphs , 1996, HPCN Europe.

[49]  Peter Sanders,et al.  Exact Routing in Large Road Networks Using Contraction Hierarchies , 2012, Transp. Sci..

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

[51]  Andrew V. Goldberg,et al.  Route Planning in Transportation Networks , 2015, Algorithm Engineering.

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

[53]  Daniel Delling,et al.  Customizing Driving Directions with GPUs , 2014, Euro-Par.

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

[55]  E. Denardo,et al.  Shortest-Route Methods: 1. Reaching, Pruning, and Buckets , 1979, Oper. Res..

[56]  Dorothea Wagner,et al.  Pareto Paths with SHARC , 2009, SEA.

[57]  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.

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

[59]  Sakti Pramanik,et al.  An Efficient Path Computation Model for Hierarchically Structured Topographical Road Maps , 2002, IEEE Trans. Knowl. Data Eng..

[60]  Peter Sanders,et al.  Combining hierarchical and goal-directed speed-up techniques for dijkstra's algorithm , 2008, JEAL.

[61]  Stefan Funke,et al.  Polynomial-Time Construction of Contraction Hierarchies for Multi-Criteria Objectives , 2013, SOCS.

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

[63]  D. R. Fulkerson,et al.  Flows in Networks. , 1964 .

[64]  Nikola Milosavljevic On optimal preprocessing for contraction hierarchies , 2012, IWCTS '12.

[65]  Elke A. Rundensteiner,et al.  Effective graph clustering for path queries in digital map databases , 1996, CIKM '96.

[66]  Stefan Funke,et al.  On k-Path Covers and their Applications , 2014, Proc. VLDB Endow..

[67]  Robert E. Tarjan,et al.  Fibonacci heaps and their uses in improved network optimization algorithms , 1984, JACM.

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

[69]  Lanny A. Yeske Student Research Projects , 1998 .

[70]  Andrew V. Goldberg,et al.  Hub Label Compression , 2013, SEA.

[71]  Karsten Weihe,et al.  Dijkstra's algorithm on-line: an empirical case study from public railroad transport , 1999, JEAL.

[72]  L. R. Ford,et al.  NETWORK FLOW THEORY , 1956 .

[73]  Christian Vetter,et al.  Parallel Time-Dependent Contraction Hierarchies , 2009 .

[74]  Dorothea Wagner,et al.  Combining speed-up techniques for shortest-path computations , 2004, JEAL.

[75]  Haim Kaplan,et al.  Reach for A*: Shortest Path Algorithms with Preprocessing , 2006, The Shortest Path Problem.