Algorithms for Polytope Covering and Approximation
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Reachability and Distance Queries via 2-Hop Labels
SIAM Journal on Computing
Journal of Algorithms
Journal of the ACM (JACM)
A Las Vegas algorithm for linear programming when the dimension is small
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Engineering Route Planning Algorithms
Algorithmics of Large and Complex Networks
Hitting sets when the VC-dimension is small
Information Processing Letters
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
Contraction hierarchies: faster and simpler hierarchical routing in road networks
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
Highway dimension, shortest paths, and provably efficient algorithms
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A hub-based labeling algorithm for shortest paths in road networks
SEA'11 Proceedings of the 10th international conference on Experimental algorithms
PHAST: Hardware-Accelerated Shortest Path Trees
IPDPS '11 Proceedings of the 2011 IEEE International Parallel & Distributed Processing Symposium
Highway hierarchies hasten exact shortest path queries
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Exact distance oracles for planar graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Algorithm engineering for route planning: an update
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Candidate sets for alternative routes in road networks
SEA'12 Proceedings of the 11th international conference on Experimental Algorithms
Hierarchical hub labelings for shortest paths
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
On optimal preprocessing for contraction hierarchies
Proceedings of the 5th ACM SIGSPATIAL International Workshop on Computational Transportation Science
Search-Space size in contraction hierarchies
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Shortest-path queries in static networks
ACM Computing Surveys (CSUR)
IS-Label: an independent-set based labeling scheme for point-to-point distance querying
Proceedings of the VLDB Endowment
Fast approximation of betweenness centrality through sampling
Proceedings of the 7th ACM international conference on Web search and data mining
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We explore the relationship between VC-dimension and graph algorithm design. In particular, we show that set systems induced by sets of vertices on shortest paths have VC-dimension at most two. This allows us to use a result from learning theory to improve time bounds on query algorithms for the point-to-point shortest path problem in networks of low highway dimension, such as road networks. We also refine the definitions of highway dimension and related concepts, making them more general and potentially more relevant to practice. In particular, we define highway dimension in terms of set systems induced by shortest paths, and give cardinality-based and average case definitions.