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2010

NP-completeness and FPT Results for Rectilinear Covering Problems

8 years 10 months ago
NP-completeness and FPT Results for Rectilinear Covering Problems
Abstract: This paper discusses three rectilinear (that is, axis-parallel) covering problems in d dimensions and their variants. The first problem is the Rectilinear Line Cover where the inputs are n points in Rd and a positive integer k, and we are asked to answer if we can cover these n points with at most k lines where these lines are restricted to be axis parallel. We show that this problem has efficient fixed-parameter tractable (FPT) algorithms. The second problem is the Rectilinear k-Links Spanning Path Problem where the inputs are also n points in Rd and a positive integer k but here we are asked to answer if there is a piecewise linear path through these n points having at most k line-segments (links) where these line-segments are axisparallel. We prove that this second problem is FPT under the assumption that no two line-segments share the same line. The third problem is the Rectilinear Hyperplane Cover problem and we are asked to cover a set of n points in d dimensions with...
Vladimir Estivill-Castro, Apichat Heednacram, Fran
Added 29 Jan 2011
Updated 29 Jan 2011
Type Journal
Year 2010
Where JUCS
Authors Vladimir Estivill-Castro, Apichat Heednacram, Francis Suraweera
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