Generalized planar matching

doi:10.1016/0196-6774(90)90001-U

Journal of Algorithms

Volume 11, Issue 2, June 1990, Pages 153-184

https://doi.org/10.1016/0196-6774(90)90001-U Get rights and content

Abstract

In this paper, we prove that maximum planar H-matching (the problem of determining the maximum number of node-disjoint copies of the fixed graph H contained in a variable planar graph G) is NP-complete for any connected planar graph H with three or more nodes. We also show that perfect planar H-matching is NP-complete for any connected outerplanar graph H with three or more nodes. The results generalize and unify several special-case results proved in the literature. The techniques can also be applied to determine the complexity of several problems, including the optimal tile salvage problem from wafer-scale integration and the classic dots and boxes game. Although we prove that the optimal tile salvage problem and others like it are NP-complete, we also describe provably good approximation algorithms that are suitable for practical applications.

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^☆: Fran Berman and Larry Snyder were supported by a Purdue Research Foundation Summer XL Grant, ONR Contract N00014-8-K-0360, and NSF Grant CS-80-05387. Tom Leighton and Peter Shor were supported by Air Force contract OSR-82-0326, DARPA Contract N00014-80-C-0622, and the Bantrell Foundation.

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Generalized planar matching☆

Abstract

J. Algorithms

Inform. Process. Lett.

Approximation algorithms for NP-complete problems on planar graphs

Optimal Tile Salvage

On the Complexity of Partitioning Graphs into Connected Subgraphs

Computing a perfect strategy for n × n chess requires exponential time in n

J. Combin. Theory Ser. A