VC-dimension and shortest path algorithms

Ittai Abraham; Daniel Delling; Amos Fiat; Andrew V. Goldberg; Renato F. Werneck

doi:10.1007/978-3-642-22006-7_58

VC-dimension and shortest path algorithms

Ittai Abraham^*
, Daniel Delling
, Amos Fiat
, Andrew V. Goldberg
, Renato F. Werneck

^*Corresponding author for this work

School of Computer Science and AI

Microsoft USA

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

63 Scopus citations

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.

Original language	English
Title of host publication	Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings
Pages	690-699
Number of pages	10
Edition	PART 1
DOIs	https://doi.org/10.1007/978-3-642-22006-7_58
State	Published - 2011
Event	38th International Colloquium on Automata, Languages and Programming, ICALP 2011 - Zurich, Switzerland Duration: 4 Jul 2011 → 8 Jul 2011

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Number	PART 1
Volume	6755 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	38th International Colloquium on Automata, Languages and Programming, ICALP 2011
Country/Territory	Switzerland
City	Zurich
Period	4/07/11 → 8/07/11

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 11 Sustainable Cities and Communities

Access to Document

10.1007/978-3-642-22006-7_58

Cite this

Abraham, I., Delling, D., Fiat, A., Goldberg, A. V., & Werneck, R. F. (2011). VC-dimension and shortest path algorithms. In Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings (PART 1 ed., pp. 690-699). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6755 LNCS, No. PART 1). https://doi.org/10.1007/978-3-642-22006-7_58

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author = "Ittai Abraham and Daniel Delling and Amos Fiat and Goldberg, \{Andrew V.\} and Werneck, \{Renato F.\}",

year = "2011",

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Abraham, I, Delling, D, Fiat, A, Goldberg, AV & Werneck, RF 2011, VC-dimension and shortest path algorithms. in Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings. PART 1 edn, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), no. PART 1, vol. 6755 LNCS, pp. 690-699, 38th International Colloquium on Automata, Languages and Programming, ICALP 2011, Zurich, Switzerland, 4/07/11. https://doi.org/10.1007/978-3-642-22006-7_58

VC-dimension and shortest path algorithms. / Abraham, Ittai; Delling, Daniel; Fiat, Amos et al.
Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings. PART 1. ed. 2011. p. 690-699 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6755 LNCS, No. PART 1).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Abraham I, Delling D, Fiat A, Goldberg AV, Werneck RF. VC-dimension and shortest path algorithms. In Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings. PART 1 ed. 2011. p. 690-699. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); PART 1). doi: 10.1007/978-3-642-22006-7_58

VC-dimension and shortest path algorithms

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