Cycles to the Rescue! Novel Constraints to Compute Maximum Planar Subgraphs Fast
Data Structures and Algorithms
2018-06-22 v1
Abstract
The NP-hard Maximum Planar Subgraph problem asks for a planar subgraph of a given graph such that has maximum edge cardinality. For more than two decades, the only known non-trivial exact algorithm was based on integer linear programming and Kuratowski's famous planarity criterion. We build upon this approach and present new constraint classes, together with a lifting of the polyhedron, to obtain provably stronger LP-relaxations, and in turn faster algorithms in practice. The new constraints take Euler's polyhedron formula as a starting point and combine it with considering cycles in . This paper discusses both the theoretical as well as the practical sides of this strengthening.
Keywords
Cite
@article{arxiv.1806.08283,
title = {Cycles to the Rescue! Novel Constraints to Compute Maximum Planar Subgraphs Fast},
author = {Markus Chimani and Tilo Wiedera},
journal= {arXiv preprint arXiv:1806.08283},
year = {2018}
}