Tracking paths

Aritra Banik, Matthew J. Katz, Eli Packer, Marina Simakov

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

10 Scopus citations


We consider several problems dealing with tracking of mov-ing objects (e.g., vehicles) in networks. Given a graph G = (V, E) and two vertices (formula presented), a set of vertices T ⊆ V is a tracking set for G (w.r.t. paths from s to t), if one can distinguish between any two paths from s to t by the order in which the vertices of T appear (or do not appear) in them. We prove that the problem of finding a minimum-cardinality tracking set w.r.t. shortest paths from s to t is NP-hard and even APX-hard. On the other hand, for the common case where G is planar, we present a 2-approximation algorithm for this problem. We also consider the following related problem: Given a graph G, two vertices s and t, and a set of forbidden vertices VF⊆ V − {s, t}, find a minimum-cardinality set of trackers V⊂ V, such that a shortest path P from s to t passes through a forbidden vertex if and only if it passes through a vertex of V. We present a polynomial-time (exact) algorithm for this problem.

Original languageEnglish
Title of host publicationAlgorithms and Complexity - 10th International Conference, CIAC 2017, Proceedings
EditorsDimitris Fotakis, Aris Pagourtzis, Vangelis Th. Paschos
PublisherSpringer Verlag
Number of pages13
ISBN (Print)9783319575858
StatePublished - 1 Jan 2017
Event10th International Conference on Algorithms and Complexity, CIAC 2017 - Athens, Greece
Duration: 24 May 201726 May 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10236 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference10th International Conference on Algorithms and Complexity, CIAC 2017

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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