Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, September 03, 2015, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Helmut Alt (FU Berlin)

An Approximation Algorithm for Packing Planar Convex Objects

Efficiently packing geometric objects is a natural question with many applications, e.g., in transportation, apparel, or steel industries. Packing of regular objects, like disks , higher dimensional spheres or axis-parallel rectangles has been considered intensely in pure mathematics as well as in operations research. Since even the most simple variants of the problem are NP-hard, efficient constant factor approximations are interesting.

In the lecture, we will consider more irregular objects, namely, convex polygons in the plane. We investigate the problem of finding a minimum-area container for packing a set of convex polygons by translations. In particular, we consider axis-parallel rectangles or arbitrary convex sets as containers. For both optimization problems we develop efficient constant factor approximation algorithms.

Joint work with Mark de Berg and Christian Knauer.

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