Patrolling a Street Network is Strongly NP-Complete but in P for Tree Structures
Computational Geometry
2015-03-14 v1 Computational Complexity
Discrete Mathematics
Data Structures and Algorithms
Combinatorics
Abstract
We consider the following problem: Given a finite set of straight line segments in the plane, determine the positions of a minimal number of points on the segments, from which guards can see all segments. This problem can be interpreted as looking for a minimal number of locations of policemen, guards, cameras or other sensors, that can observe a network of streets, corridors, tunnels, tubes, etc. We show that the problem is strongly NP-complete even for a set of segments with a cubic graph structure, but in P for tree structures.
Keywords
Cite
@article{arxiv.1004.0744,
title = {Patrolling a Street Network is Strongly NP-Complete but in P for Tree Structures},
author = {Valentin E. Brimkov},
journal= {arXiv preprint arXiv:1004.0744},
year = {2015}
}