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What and Who
Title:A Structural Lemma in 2-Dimensional Packing, and its Implications on Approximability
Speaker:Lars Prädel
coming from:University of Kiel
Speakers Bio:
Event Type:AG1 Mittagsseminar (own work)
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Level:AG Audience
Date, Time and Location
Date:Friday, 27 November 2009
Duration:30 Minutes
Building:E1 4
We study an interesting geometric optimization problem called Rectangle Packing with Area Maximization (RPA). We are given a set of rectangles and a rectangular target area called bin. The goal is to find a feasible packing of a subset of the given rectangles into the bin, i.e. an orthogonal packing without rotation and overlap. The objective is to maximize the total area of rectangles packed. This problem is a generalization of the Subset Sum problem, which is one of the most fundamental and well-known problems in combinatorial optimization and has many practical applications, such as VLSI layout and the cutting problem.

RPA is strongly NP-hard even for squares, therefore there is no fully polynomial time approximation scheme (FPTAS) for this problem, unless P=NP. The previously best result is a (1/2-epsilon)-approximation by Jansen & Zhang for our problem. We present a polynomial time approximation scheme (PTAS) for this problem, i.e. a family of algorithms which compute for any accuracy epsilon>0 in polynomial time a solution with ratio (1-epsilon).

Name(s):Rolf Harren
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  • Rolf Harren, 11/12/2009 03:23 PM
  • Rolf Harren, 11/12/2009 03:22 PM -- Created document.