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What and Who

Independent set of convex polygons: from n^eps to 1+eps via shrinking

Andreas Wiese
Max-Planck-Institut für Informatik - D1
AG1 Mittagsseminar (own work)
AG 1, MMCI  
AG Audience

Date, Time and Location

Thursday, 28 April 2016
20 Minutes
E1 4


In the Independent Set of Convex Polygons problem we are given a set of weighted convex polygons in the plane and we want to compute a maximum weight subset of non-overlapping polygons. This is a very natural and well-studied problem with applications in many different areas. Unfortunately, there is a very large gap between the known upper and lower bounds for this problem. The best polynomial time algorithm we know has an approximation ratio of n^epsilon and the best known lower bound shows only strong NP-hardness.

In this paper we close this gap completely, assuming that we are allowed to shrink the polygons a little bit, by a factor 1-delta for an arbitrarily small constant delta>0, while the compared optimal solution cannot do this (resource augmentation). In this setting, we improve the approximation ratio from n^epsilon to 1+epsilon which matches the above lower bound that still holds if we can shrink the polygons.


Andreas Wiese
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Andreas Wiese, 04/21/2016 15:58 -- Created document.