Math @ Duke

Publications [#235617] of Pankaj K. Agarwal
Papers Published
 Agarwal, PK; Mustafa, NH, Independent set of intersection graphs of convex objects in 2D,
Lecture notes in computer science, vol. 3111
(2004),
pp. 127137, ISSN 03029743
(last updated on 2017/12/13)
Abstract: The intersection graph of a set of geometric objects is defined as a graph G = (S, E) in which there is an edge between two nodes si, sj ∈ S if si ∩ sj ≠ ∅. The problem of computing a maximum independent set in the intersection graph of a set of objects is known to be NPcomplete for most cases in two and higher dimensions. We present approximation algorithms for computing a maximum independent set of intersection graphs of convex objects in ℝ2. Specifically, given a set of n line segments in the plane with maximum independent set of size κ, we present algorithms that find an independent set of size at least (i) (κ/2 log(2n/κ))1/2 in time O(n3) and (ii) (κ/2 log(2n/κ))1/4 in time O(n4/3 logc n). For a set of n convex objects with maximum independent set of size κ, we present an algorithm that finds an independent set of size at least (κ/2 log(2n/κ))1/3 in time O(n3+τ(S)), assuming that S can be preprocessed in time τ(S) to answer certain primitive operations on these convex sets. © SpringerVerlag Berlin Heidelberg 2004.


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