Route Planning in Transportation Networks

We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs.

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

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

[3]  S. Parter The Use of Linear Graphs in Gauss Elimination , 1961 .

[4]  Tom Caldwell,et al.  On finding minimum routes in a network with turn penalties , 1961, CACM.

[5]  Stephen J. Garland,et al.  Algorithm 97: Shortest path , 1962, Commun. ACM.

[6]  George B. Dantzig,et al.  Linear programming and extensions , 1965 .

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

[8]  Nils J. Nilsson,et al.  A Formal Basis for the Heuristic Determination of Minimum Cost Paths , 1968, IEEE Trans. Syst. Sci. Cybern..

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

[10]  Ira Sheldon Pohl,et al.  Bi-directional and heuristic search in path problems , 1969 .

[11]  Stuart E. Dreyfus,et al.  An Appraisal of Some Shortest-Path Algorithms , 1969, Oper. Res..

[12]  D. Rose,et al.  Generalized nested dissection , 1977 .

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

[14]  Dirck Van Vliet,et al.  IMPROVED SHORTEST PATH ALGORITHMS FOR TRANSPORT NETWORKS , 1978 .

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

[16]  Pierre Hansen,et al.  Bicriterion Path Problems , 1980 .

[17]  Nesa L'abbe Wu,et al.  Linear programming and extensions , 1981 .

[18]  Robert Schreiber,et al.  A New Implementation of Sparse Gaussian Elimination , 1982, TOMS.

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

[20]  E. Martins On a multicriteria shortest path problem , 1984 .

[21]  P. Loridan ε-solutions in vector minimization problems , 1984 .

[22]  D. J. White,et al.  Epsilon efficiency , 1986 .

[23]  Laurent Siklóssy,et al.  TRAINS, An Active Time-Table Searcher , 1988, ECAI.

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

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

[26]  Laurent Siklóssy,et al.  Searching time-table networks , 1991, Artificial Intelligence for Engineering Design, Analysis and Manufacturing.

[27]  Ariel Orda,et al.  Minimum weight paths in time-dependent networks , 1991, Networks.

[28]  Hiroshi Imai,et al.  A fast algorithm for finding better routes by AI search techniques , 1994, Proceedings of VNIS'94 - 1994 Vehicle Navigation and Information Systems Conference.

[29]  K. Nachtigall Time depending shortest-path problems with applications to railway networks , 1995 .

[30]  Dirk Theune,et al.  Robuste und effiziente Methoden zur Lösung von Wegproblemen , 1995, Teubner-Texte zur Informatik.

[31]  RadzikTomasz,et al.  Shortest paths algorithms , 1996 .

[32]  Hermann Kaindl,et al.  Bidirectional Heuristic Search Reconsidered , 1997, J. Artif. Intell. Res..

[33]  Andrew V. Goldberg,et al.  Buckets, heaps, lists, and monotone priority queues , 1997, SODA '97.

[34]  S. Pallottino,et al.  Shortest Path Algorithms in Transportation models: classical and innovative aspects , 1997 .

[35]  Roy Goldman,et al.  Proximity Search in Databases , 1998, VLDB.

[36]  Anna Sciomachen,et al.  A utility measure for finding multiobjective shortest paths in urban multimodal transportation networks , 1998, Eur. J. Oper. Res..

[37]  Elke A. Rundensteiner,et al.  Hierarchical Encoded Path Views for Path Query Processing: An Optimal Model and Its Performance Evaluation , 1998, IEEE Trans. Knowl. Data Eng..

[38]  Brian C. Dean,et al.  Continuous-time dynamics shortest path algorithms , 1999 .

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

[40]  Rolf H. Möhring,et al.  Verteilte Verbindungssuche im öffentlichen Personenverkehr Graphentheoretische Modelle und Algorithmen , 1999, Angewandte Mathematik, insbesondere Informatik.

[41]  Madhav V. Marathe,et al.  Formal-Language-Constrained Path Problems , 1997, SIAM J. Comput..

[42]  Mihalis Yannakakis,et al.  On the approximability of trade-offs and optimal access of Web sources , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[43]  David Peleg,et al.  Proximity-preserving labeling schemes , 2000, J. Graph Theory.

[44]  A. Flatt Grasp , 2000, Proceedings.

[45]  Uri Zwick,et al.  Exact and Approximate Distances in Graphs - A Survey , 2001, ESA.

[46]  Ulrich Meyer,et al.  Single-source shortest-paths on arbitrary directed graphs in linear average-case time , 2001, SODA '01.

[47]  Ulrik Brandes,et al.  Travel Planning with Self-Made Maps , 2001, ALENEX.

[48]  Karsten Weihe,et al.  Pareto Shortest Paths is Often Feasible in Practice , 2001, WAE.

[49]  Ran Raz,et al.  Distance labeling in graphs , 2001, SODA '01.

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

[51]  Karsten Weihe,et al.  Getting Train Timetables into the Main Storage , 2002, Electron. Notes Theor. Comput. Sci..

[52]  Edith Cohen,et al.  Reachability and distance queries via 2-hop labels , 2002, SODA '02.

[53]  Stephan Winter,et al.  Modeling Costs of Turns in Route Planning , 2002, GeoInformatica.

[54]  Madhav V. Marathe,et al.  Classical and Contemporary Shortest Path Problems in Road Networks: Implementation and Experimental Analysis of the TRANSIMS Router , 2002, ESA.

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

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

[57]  Mikkel Thorup,et al.  Integer priority queues with decrease key in constant time and the single source shortest paths problem , 2003, STOC '03.

[58]  Maria Grazia Scutellà,et al.  Dynamic shortest paths minimizing travel times and costs , 2001, Networks.

[59]  David Peleg,et al.  Compact and localized distributed data structures , 2003, Distributed Computing.

[60]  Mikkel Thorup Compact oracles for reachability and approximate distances in planar digraphs , 2004, JACM.

[61]  Christos D. Zaroliagis,et al.  Timetable Information: Models and Algorithms , 2004, ATMOS.

[62]  Brian C. Dean,et al.  Algorithms for minimum‐cost paths in time‐dependent networks with waiting policies , 2004, Networks.

[63]  B. C. Dean Shortest Paths in FIFO Time-Dependent Networks : Theory and Algorithms , 2004 .

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

[65]  Thomas Willhalm,et al.  Combining Speed-Up Techniques for Shortest-Path Computations , 2004, WEA.

[66]  Gerth Stølting Brodal,et al.  Time-dependent Networks as Models to Achieve Fast Exact Time-table Queries , 2004, ATMOS.

[67]  Chak-Kuen Wong,et al.  A faster approximation algorithm for the Steiner problem in graphs , 1986, Acta Informatica.

[68]  Matthias Müller-Hannemann,et al.  Finding All Attractive Train Connections by Multi-criteria Pareto Search , 2004, ATMOS.

[69]  Jon M. Kleinberg,et al.  Triangulation and embedding using small sets of beacons , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.

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

[71]  Christos D. Zaroliagis,et al.  Experimental Comparison of Shortest Path Approaches for Timetable Information , 2004, ALENEX/ANALC.

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

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

[74]  Jeffrey Scott Vitter,et al.  Shortest paths in euclidean graphs , 2005, Algorithmica.

[75]  Dorothea Wagner,et al.  Drawing Graphs to Speed Up Shortest-Path Computations , 2005, ALENEX/ANALCO.

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

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

[78]  Ulrik Brandes,et al.  Network Analysis: Methodological Foundations (Lecture Notes in Computer Science) , 2005 .

[79]  Matthias Müller-Hannemann,et al.  Paying Less for Train Connections with MOTIS , 2005, ATMOS.

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

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

[82]  Maurizio Bielli,et al.  Object modeling and path computation for multimodal travel systems , 2006, Eur. J. Oper. Res..

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

[84]  Karsten Weihe,et al.  On the cardinality of the Pareto set in bicriteria shortest path problems , 2006, Ann. Oper. Res..

[85]  Laurence R. Rilett,et al.  Heuristic shortest path algorithms for transportation applications: State of the art , 2006, Comput. Oper. Res..

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

[87]  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.

[88]  Christos D. Zaroliagis,et al.  Multiobjective Optimization: Improved FPTAS for Shortest Paths and Non-linear Objectives with Applications , 2006, ISAAC.

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

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

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

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

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

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

[95]  Madhav V. Marathe,et al.  Engineering Label-Constrained Shortest-Path Algorithms , 2008, The Shortest Path Problem.

[96]  Peter Sanders,et al.  In Transit to Constant Time Shortest-Path Queries in Road Networks , 2007, ALENEX.

[97]  Martin Zachariasen,et al.  Fast and Compact Oracles for Approximate Distances in Planar Graphs , 2007, ESA.

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

[99]  Peter Sanders,et al.  Computing Many-to-Many Shortest Paths Using Highway Hierarchies , 2007, ALENEX.

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

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

[102]  Eric Horvitz,et al.  Predestination: Where Do You Want to Go Today? , 2007, Computer.

[103]  Georgia Aifadopoulou,et al.  Multiobjective Optimum Path Algorithm for Passenger Pretrip Planning in Multimodal Transportation Networks , 2007 .

[104]  Christos D. Zaroliagis,et al.  Multiobjective Optimization: Improved FPTAS for Shortest Paths and Non-Linear Objectives with Applications , 2006, Theory of Computing Systems.

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

[106]  K. Mehlhorn,et al.  Algorithms and Data Structures: The Basic Toolbox , 2008 .

[107]  Martin Holzer Engineering planar-separator and shortest-path algorithms , 2008 .

[108]  Daniele Frigioni,et al.  Dynamic Multi-level Overlay Graphs for Shortest Paths , 2008, Math. Comput. Sci..

[109]  David Eppstein,et al.  Studying (non-planar) road networks through an algorithmic lens , 2008, GIS '08.

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

[111]  Dorothea Wagner,et al.  Engineering Time-Expanded Graphs for Faster Timetable Information , 2008, ATMOS.

[112]  Yann Disser,et al.  Multi-criteria Shortest Paths in Time-Dependent Train Networks , 2008, WEA.

[113]  Madhav V. Marathe,et al.  Engineering Label-Constrained Shortest-Path Algorithms , 2008, The Shortest Path Problem.

[114]  D. Wagner,et al.  Timetable Information Updating in Case of Delays : Modeling Issues ⋆ , 2008 .

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

[116]  Peter Sanders,et al.  Mobile Route Planning , 2008, ESA.

[117]  Dominik Schultes Route Planning in Road Networks , 2008, Ausgezeichnete Informatikdissertationen.

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

[119]  Hannah Bast,et al.  Car or Public Transport - Two Worlds , 2009, Efficient Algorithms.

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

[121]  Dorothea Wagner,et al.  Accelerating Multi-modal Route Planning by Access-Nodes , 2009, ESA.

[122]  Christos D. Zaroliagis,et al.  Efficient Route Planning in Flight Networks , 2009, ATMOS.

[123]  Matthias Müller-Hannemann,et al.  Accelerating Time-Dependent Multi-Criteria Timetable Information is Harder Than Expected , 2009, ATMOS.

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

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

[126]  Lotfi A. Zadeh,et al.  Fuzzy Logic , 2009, Encyclopedia of Complexity and Systems Science.

[127]  Matthias Müller-Hannemann,et al.  Efficient Timetable Information in the Presence of Delays , 2009, Robust and Online Large-Scale Optimization.

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

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

[130]  Matthias Müller-Hannemann,et al.  Fully Dynamic Speed-Up Techniques for Multi-criteria Shortest Path Searches in Time-Dependent Networks , 2010, SEA.

[131]  Lars Völker,et al.  Fast Detour Computation for Ride Sharing , 2010, ATMOS.

[132]  Dorothea Wagner,et al.  Space-Efficient SHARC-Routing , 2010, SEA.

[133]  Dorothea Wagner,et al.  Synthetic Road Networks , 2010, AAIM.

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

[135]  Bastian Katz,et al.  Parallel computation of best connections in public transportation networks , 2010, 2010 IEEE International Symposium on Parallel & Distributed Processing (IPDPS).

[136]  Haralampos Pozidis,et al.  Trends in Storage Technologies , 2010, IEEE Data Eng. Bull..

[137]  Hanan Samet,et al.  Roads Belong in Databases , 2010, IEEE Data Eng. Bull..

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

[139]  Erik Carlsson,et al.  Fast Routing in Very Large Public Transportation Networks Using Transfer Patterns , 2010, ESA.

[140]  Robert Geisberger,et al.  Heuristic Contraction Hierarchies with Approximation Guarantee , 2010, SOCS.

[141]  Hanan Samet,et al.  Query Processing Using Distance Oracles for Spatial Networks , 2010, IEEE Transactions on Knowledge and Data Engineering.

[142]  Peter Sanders,et al.  Distributed Time-Dependent Contraction Hierarchies , 2010, SEA.

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

[144]  Farnoush Banaei Kashani,et al.  A case for time-dependent shortest path computation in spatial networks , 2010, GIS '10.

[145]  Thomas Erlebach,et al.  Length-bounded cuts and flows , 2006, TALG.

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

[147]  Amos Fiat,et al.  Highway dimension, shortest paths, and provably efficient algorithms , 2010, SODA '10.

[148]  Jörg-Rüdiger Sack,et al.  Shortest Paths in Time-Dependent FIFO Networks , 2010, Algorithmica.

[149]  Peter Sanders,et al.  Engineering Time-Dependent Many-to-Many Shortest Paths Computation , 2010, ATMOS.

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

[151]  Robert Geisberger Contraction of Timetable Networks with Realistic Transfers , 2010, SEA.

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

[153]  Dennis Luxen,et al.  Real-time routing with OpenStreetMap data , 2011, GIS.

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

[155]  Matthias Müller-Hannemann,et al.  Stochastic Delay Prediction in Large Train Networks , 2011, ATMOS.

[156]  David Eisenstat,et al.  Random Road Networks: The Quadtree Model , 2010, ANALCO.

[157]  Stefan Funke,et al.  Optimal Route Planning for Electric Vehicles in Large Networks , 2011, AAAI.

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

[159]  Subhash Suri,et al.  On the Complexity of Time-Dependent Shortest Paths , 2011, Algorithmica.

[160]  Stefan Funke,et al.  Algorithms for Matching and Predicting Trajectories , 2011, ALENEX.

[161]  Peter Sanders,et al.  Hierarchy Decomposition for Faster User Equilibria on Road Networks , 2011, SEA.

[162]  Amos Fiat,et al.  VC-Dimension and Shortest Path Algorithms , 2011, ICALP.

[163]  Leo Liberti,et al.  UniALT for regular language contrained shortest paths on a multi-modal transportation network , 2011, ATMOS.

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

[165]  Dieter Pfoser,et al.  Efficient data management in support of shortest-path computation , 2011, CTS '11.

[166]  Petr Hlinený,et al.  Scope-Based Route Planning , 2011, ESA.

[167]  Matthias Müller-Hannemann,et al.  How to find good night train connections , 2011, Networks.

[168]  Andrew V. Goldberg,et al.  Faster Batched Shortest Paths in Road Networks , 2011, ATMOS.

[169]  Adi Botea Ultra-Fast Optimal Pathfinding without Runtime Search , 2011, AIIDE.

[170]  Roland Bader,et al.  Alternative Route Graphs in Road Networks , 2011, TAPAS.

[171]  Peter Sanders,et al.  Time-Dependent Route Planning with Generalized Objective Functions , 2012, ESA.

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

[173]  Dorothea Wagner,et al.  User-Constrained Multi-Modal Route Planning , 2012, ALENEX.

[174]  Mattia D'Emidio,et al.  Fully Dynamic Maintenance of Arc-Flags in Road Networks , 2012, SEA.

[175]  Feng Lu,et al.  Advanced multi-modal routing approach for pedestrians , 2012, 2012 2nd International Conference on Consumer Electronics, Communications and Networks (CECNet).

[176]  Stefan Funke,et al.  Cruising with a Battery-Powered Vehicle and Not Getting Stranded , 2012, AAAI.

[177]  Yuan Tian,et al.  ROAD: A New Spatial Object Search Framework for Road Networks , 2012, IEEE Transactions on Knowledge and Data Engineering.

[178]  Leo Liberti,et al.  Bidirectional A* search on time‐dependent road networks , 2012, Networks.

[179]  Sabine Storandt,et al.  Route Planning for Bicycles - Exact Constrained Shortest Paths Made Practical via Contraction Hierarchy , 2012, ICAPS.

[180]  Ignaz Rutter,et al.  On the Complexity of Partitioning Graphs for Arc-Flags , 2012, ATMOS.

[181]  Leo Liberti,et al.  A Label Correcting Algorithm for the Shortest Path Problem on a Multi-modal Route Network , 2012, SEA.

[182]  Vassilis J. Tsotras,et al.  Exact Graph Search Algorithms for Generalized Traveling Salesman Path Problems , 2012, SEA.

[183]  Dieter Pfoser,et al.  Crowdsourcing computing resources for shortest-path computation , 2012, SIGSPATIAL/GIS.

[184]  T. Walsh,et al.  Finding Multi-criteria Optimal Paths in Multi-modal Public Transportation Networks using the Transit Algorithm , 2012 .

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

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

[187]  Peter Sanders,et al.  Efficient Route Compression for Hybrid Route Planning , 2012, MedAlg.

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

[189]  Stefan Funke,et al.  Transit Nodes - Lower Bounds and Refined Construction , 2012, ALENEX.

[190]  Vassilis J. Tsotras,et al.  Bidirectional A* Search with Additive Approximation Bounds , 2021, SOCS.

[191]  Eric Horvitz,et al.  Some help on the way: opportunistic routing under uncertainty , 2012, UbiComp.

[192]  Peter Sanders,et al.  Distributed Evolutionary Graph Partitioning , 2011, ALENEX.

[193]  Dorothea Wagner,et al.  The Shortcut Problem - Complexity and Algorithms , 2012, J. Graph Algorithms Appl..

[194]  Chris Arney Network Analysis: Methodological Foundations , 2012 .

[195]  Daniel Delling,et al.  Robust Mobile Route Planning with Limited Connectivity , 2012, ALENEX.

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

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

[198]  Giacomo Nannicini,et al.  Core Routing on Dynamic Time-Dependent Road Networks , 2012, INFORMS J. Comput..

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

[200]  Stefan Funke,et al.  Sequenced route queries: getting things done on the way back home , 2012, SIGSPATIAL/GIS.

[201]  Matthias Müller-Hannemann,et al.  Recoverable Robust Timetable Information , 2013, ATMOS.

[202]  Adi Botea,et al.  Path Planning with Compressed All-Pairs Shortest Paths Data , 2013, ICAPS.

[203]  Marcel Radermacher,et al.  Evolution and Evaluation of the Penalty Method for Alternative Graphs , 2013, ATMOS.

[204]  Dennis Luxen,et al.  Multi-Hop Ride Sharing , 2013, SOCS.

[205]  Andrew V. Goldberg,et al.  PHAST: Hardware-accelerated shortest path trees , 2013, J. Parallel Distributed Comput..

[206]  Dorothea Wagner,et al.  Computing Multimodal Journeys in Practice , 2013, SEA.

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

[208]  Xavier Gandibleux,et al.  Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys , 2013 .

[209]  Dorothea Wagner,et al.  Energy-optimal routes for electric vehicles , 2013, SIGSPATIAL/GIS.

[210]  Moritz Kobitzsch An Alternative Approach to Alternative Routes: HiDAR , 2013, ESA.

[211]  Sabine Storandt,et al.  Result Diversity for Multi-Modal Route Planning , 2013, ATMOS.

[212]  Matús Mihalák,et al.  Robust Routing in Urban Public Transportation: How to Find Reliable Journeys Based on Past Observations , 2013, ATMOS.

[213]  John Krumm,et al.  From destination prediction to route prediction , 2013, J. Locat. Based Serv..

[214]  Mirko Brodesser Multi-Modal Route Planning , 2013 .

[215]  Giuseppe F. Italiano,et al.  Is Timetabling Routing Always Reliable for Public Transport? , 2013, ATMOS.

[216]  Stefan Funke,et al.  Enabling E-Mobility: Facility Location for Battery Loading Stations , 2013, AAAI.

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

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

[219]  Sabine Storandt,et al.  Delay-Robustness of Transfer Patterns in Public Transportation Route Planning , 2013, ATMOS.

[220]  Peter Sanders,et al.  Parallel Label-Setting Multi-objective Shortest Path Search , 2013, 2013 IEEE 27th International Symposium on Parallel and Distributed Processing.

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

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

[223]  Dieter Pfoser,et al.  Optimizing Landmark-Based Routing and Preprocessing , 2013, IWCTS '13.

[224]  Ben Strasser,et al.  Intriguingly Simple and Fast Transit Routing , 2013, SEA.

[225]  Kian-Lee Tan,et al.  G-tree: an efficient index for KNN search on road networks , 2013, CIKM.

[226]  Christos D. Zaroliagis,et al.  Improved Alternative Route Planning , 2013, ATMOS.

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

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

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

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

[231]  Salima Benbernou,et al.  A survey on service quality description , 2013, CSUR.

[232]  Harris Kaufmann Towards Mobile Time-Dependent Route Planning , 2013 .

[233]  Takuya Akiba,et al.  Fast Shortest-path Distance Queries on Road Networks by Pruned Highway Labeling , 2014, ALENEX.

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

[235]  Mattia D'Emidio,et al.  Engineering graph-based models for dynamic timetable information systems , 2017, J. Discrete Algorithms.

[236]  Mathias Weller Optimal Hub Labeling is NP-complete , 2014, ArXiv.

[237]  Matthias Müller-Hannemann,et al.  The Price of Strict and Light Robustness in Timetable Information , 2014, Transp. Sci..

[238]  Peter Sanders,et al.  Parallel Bi-objective Shortest Paths Using Weight-Balanced B-trees with Bulk Updates , 2014, SEA.

[239]  Andrew V. Goldberg,et al.  Robust Distance Queries on Massive Networks , 2014, ESA.

[240]  Giuseppe F. Italiano,et al.  Better transit routing by exploiting vehicle GPS data , 2014, IWCTS '14.

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

[242]  Sabine Storandt,et al.  Frequency-based search for public transit , 2014, SIGSPATIAL/GIS.

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

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

[245]  Andrew V. Goldberg,et al.  Hub Labels: Theory and Practice , 2014, SEA.

[246]  Ben Strasser,et al.  Connection Scan Accelerated , 2014, ALENEX.

[247]  Giuseppe F. Italiano,et al.  Exploiting GPS Data in Public Transport Journey Planners , 2014, SEA.

[248]  Michael T. Goodrich,et al.  Two-phase bicriterion search for finding fast and efficient electric vehicle routes , 2014, SIGSPATIAL/GIS.

[249]  Sabine Storandt,et al.  Flow-Based Guidebook Routing , 2014, ALENEX.

[250]  Julian Dibbelt,et al.  Speed-Consumption Tradeoff for Electric Vehicle Route Planning , 2014, ATMOS.

[251]  Stefan Funke,et al.  Placement of Loading Stations for Electric Vehicles: No Detours Necessary! , 2014, AAAI.

[252]  Daniel Delling,et al.  Round-Based Public Transit Routing , 2012, Transp. Sci..

[253]  Christos D. Zaroliagis,et al.  Distance Oracles for Time-Dependent Networks , 2015, Algorithmica.

[254]  Dieter Pfoser,et al.  SALT. A Unified Framework for All Shortest-Path Query Variants on Road Networks , 2015, SEA.

[255]  Daniel Delling,et al.  Customizable Point-of-Interest Queries in Road Networks , 2013, IEEE Transactions on Knowledge and Data Engineering.

[256]  S. Funke,et al.  On k-Path Covers and their applications , 2014, The VLDB Journal.

[257]  Sascha Witt Trip-Based Public Transit Routing , 2015, ESA.

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

[259]  Amos Fiat,et al.  Highway Dimension and Provably Efficient Shortest Path Algorithms , 2016, J. ACM.

[260]  Andrew V. Goldberg,et al.  Algorithms for Hub Label Optimization , 2013, ICALP.

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

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