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 - https://doi.org/10.1007/978-3-319-57586-5_7
DO - https://doi.org/10.1007/978-3-319-57586-5_7
M3 - Conference contribution
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 -