Solving the Maximum Weight Planar Subgraph Problem by Branch and Cut (1993)
| Venue: | PROCEEDINGS OF THE THIRD CONFERENCE ON INTEGER PROGRAMMING AND COMBINATORIAL OPTIMIZATION |
| Citations: | 8 - 1 self |
BibTeX
@INPROCEEDINGS{Jünger93solvingthe,
author = {Michael Jünger and Petra Mutzel},
title = {Solving the Maximum Weight Planar Subgraph Problem by Branch and Cut},
booktitle = {PROCEEDINGS OF THE THIRD CONFERENCE ON INTEGER PROGRAMMING AND COMBINATORIAL OPTIMIZATION},
year = {1993},
pages = {479--492},
publisher = {}
}
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Abstract
In this paper we investigate the problem of identifying a planar subgraph of maximum weight of a given edge weighted graph. In the theoretical part of the paper, the polytope of all planar subgraphs of a graph G is defined and studied. All subgraphs of a graph G, which are subdivisions of K 5 or K 3;3 , turn out to define facets of this polytope. We also present computational experience with a branch and cut algorithm for the above problem. Our approach is based on an algorithm which searches for forbidden substructures in a graph that contains a subdivision of K 5 or K 3;3 . These structures give us inequalities which are used as cutting planes.
