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Independent set of intersection graphs of convex objects in 2D
 in 2D. Comput. Geometry: Theory & Appls
, 2004
"... Abstract. The intersection graph of a set of geometric objects is defined as agraph G = (S; E) in which there is an edge between two nodes si; sj 2 S if si " sj 6 =;. The problem of computing a maximum independent set in the intersection graph of a set of objects is known to be NPcomplete ..."
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Abstract. The intersection graph of a set of geometric objects is defined as agraph G = (S; E) in which there is an edge between two nodes si; sj 2 S if si &quot; sj 6 =;. The problem of computing a maximum independent set in the intersection graph of a set of objects is known to be NPcomplete for most casesin two and higher dimensions. We present approximation algorithms for computing a maximum independent set of intersection graphs of convex objects in R 2. Specifically, given a set of n line segments in the plane with maximum independent set of size ^, we present algorithms that find an independent set of size atleast ( i) (^=2 log(2n=^)) 1=2 in time O(n
An Approximation Algorithm for Cutting Out Convex Polygons
 PROCEEDINGS OF THE FOURTEENTH ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS, (SODA '03
, 2004
"... We provide an O(log n)approximation algorithm for the following problem. Given a convex ngon P, drawn on a convex piece of paper, cut P out of the piece of paper in the cheapest possible way. No polynomialtime approximation algorithm was known for this problem posed in 1985. ..."
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Cited by 6 (1 self)
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We provide an O(log n)approximation algorithm for the following problem. Given a convex ngon P, drawn on a convex piece of paper, cut P out of the piece of paper in the cheapest possible way. No polynomialtime approximation algorithm was known for this problem posed in 1985.
The Cost of Cutting Out Convex nGons
, 2003
"... Given a convex ngon P drawn on a piece of paper Q of unit diameter we prove that it can be cut with a total cost of O(log n). This bound is shown to be asymptotically tight: a regular ngon (whose circumscribed circle has radius, say, 1/3) drawn on a square piece of paper of unit diameter requires ..."
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Cited by 1 (0 self)
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Given a convex ngon P drawn on a piece of paper Q of unit diameter we prove that it can be cut with a total cost of O(log n). This bound is shown to be asymptotically tight: a regular ngon (whose circumscribed circle has radius, say, 1/3) drawn on a square piece of paper of unit diameter requires a cut cost of 37 n).