Computational complexity of guarding connected plane graphs
نویسنده
چکیده
Computational complexity is studied for the problem of stabbing set of straight line segments with the smallest cardinality set of disks of fixed radii r > 0 where the set of segments forms a straight line drawing of some connected planar graph. We claim strong NP-hardness of the problem over the class of 4-connected (i.e. Hamiltonian) plane triangulations of bounded vertex degree for small r, although the problem is solvable in polynomial time over plane graphs for large r.
منابع مشابه
Stabbing Line Segments with Disks: Complexity and Approximation Algorithms
Computational complexity is studied for the problem of stabbing set of straight line segments with the smallest cardinality set of disks of fixed radii r > 0 where the set of segments forms straight line drawing of planar graph. This problem along with its relatives [3] arise in physical network security analysis for telecommunication, wireless and road networks represented by geometric graphs ...
متن کاملDecomposing plane cubic graphs
It was conjectured by Hoffmann-Ostenhof that the edge set of every cubic graph can be decomposed into a spanning tree, a matching and a family of cycles. We prove the conjecture for 3-connected cubic plane graphs and 3-connected cubic graphs on the projective plane. Our proof provides a polynomial time algorithm to find the decomposition for 3-connected cubic plane graphs.
متن کاملBinary labelings for bipartite graphs
Part of the authors introduced in [C. Huemer, S. Kappes, A binary labelling for plane Laman graphs and quadrangulations, in Proceedings of the 22nd European Workshop on Computational Geometry 83–86, 2006] a binary labeling for the angles of plane quadrangulations, similar to Schnyder labelings of the angles of plane triangulations since in both cases the labelings are equivalent to tree decompo...
متن کاملThe Minimum Guarding Tree Problem
Given a set L of non-parallel lines in the plane and a nonempty subset L′ ⊆ L, a guarding tree for L′ is a tree contained in the union of the lines in L such that if a mobile guard (agent) runs on the edges of the tree, all lines in L′ are visited by the guard. Similarly, given a connected arrangement S of line segments in the plane and a nonempty subset S ′ ⊆ S, we define a guarding tree for S...
متن کاملColoring intersection graphs of arc-connected sets in the plane
A family of sets in the plane is simple if the intersection of its any subfamily is arc-connected, and it is pierced by a line L if the intersection of its any member with L is a nonempty segment. It is proved that the intersection graphs of simple families of compact arc-connected sets in the plane pierced by a common line have chromatic number bounded by a function of their clique number.
متن کامل