TY - GEN

T1 - Tracking paths

AU - Banik, Aritra

AU - Katz, Matthew J.

AU - Packer, Eli

AU - Simakov, Marina

N1 - Publisher Copyright:
© Springer International Publishing AG 2017.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85018380579&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-57586-5_7

DO - 10.1007/978-3-319-57586-5_7

M3 - Conference contribution

AN - SCOPUS:85018380579

SN - 9783319575858

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 67

EP - 79

BT - Algorithms and Complexity - 10th International Conference, CIAC 2017, Proceedings

A2 - Fotakis, Dimitris

A2 - Pagourtzis, Aris

A2 - Paschos, Vangelis Th.

PB - Springer Verlag

T2 - 10th International Conference on Algorithms and Complexity, CIAC 2017

Y2 - 24 May 2017 through 26 May 2017

ER -