Linear-time computation of optimal subgraphs of decomposable graphs

doi:10.1016/0196-6774(87)90039-3

Journal of Algorithms

Volume 8, Issue 2, June 1987, Pages 216-235

https://doi.org/10.1016/0196-6774(87)90039-3 Get rights and content

Abstract

A general problem in computational graph theory is that of finding an optimal subgraph H of a given weighted graph G. The matching problem (which is easy) and the traveling salesman problem (which is not) are well-known examples of this general problem. In the literature one can also find a variety of ad hoc algorithms for solving certain special cases in linear time. We suggest a general approach for constructing linear-time algorithms in the case where the graph G is defined by certain rules of composition (as are trees, series-parallel graphs, and outerplanar graphs) and the desired subgraph H satisfies a property that is “regular” with respect to these rules of composition (as do matchings, dominating sets, and independent sets for all the classes just mentioned). This approach is applied to obtain a linear-time algorithm for computing the irredundance number of a tree, a problem for which no polynomial-time algorithm was previously known.

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^☆: A preliminary version of this paper appeared under the title “Why Certain Subgraph Computations Require Only Linear Time” in the proceedings of the 26th Annual IEEE Symposium on the Foundations of Computer Science, 1985.

^†: Research supported in part by the NSF under Grant MCS-8311422.

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Linear-time computation of optimal subgraphs of decomposable graphs☆

Abstract

Discrete Math.

Discrete Math.

Inform. Process. Lett.

Discrete Appl. Math.

Inform. Process. Lett.

Independent domination in trees

Graph theoretic parameters concerning domination, independence, and irredundance

J. Graph Theory

Halin graphs and the Traveling Salesman Problem

Math. Programming

Algorithms for generalized stability numbers of tree graphs

J. Austral. Math. Soc.

Computers and Intractability: A Guide to the Theory of NP-Completeness

B-matchings in trees

SIAM J. Comput.