VC-Dimension and Shortest Path Algorithms

  • Ittai Abraham
  • Daniel Delling
  • Amos Fiat
  • Andrew V. Goldberg
  • Renato F. Werneck
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6755)

Abstract

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Ittai Abraham
    • 1
  • Daniel Delling
    • 1
  • Amos Fiat
    • 2
  • Andrew V. Goldberg
    • 1
  • Renato F. Werneck
    • 1
  1. 1.Microsoft Research Silicon ValleyUSA
  2. 2.Tel Aviv UniversityIsrael

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