Secure Sets and Defensive Alliances in Graphs: A Faster Algorithm and Improved Bounds

Kazuyuki AMANO; Kyaw May OO; Yota OTACHI; Ryuhei UEHARA

doi:10.1587/transinf.2014FCP0007

Special Section on Foundations of Computer Science - New Spirits in Theory of Computation and Algorithm -

Secure Sets and Defensive Alliances in Graphs: A Faster Algorithm and Improved Bounds

Kazuyuki AMANO, Kyaw May OO, Yota OTACHI, Ryuhei UEHARA

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Keywords: secure set, defensive alliance, fixed-parameter tractability, hypercube

JOURNAL FREE ACCESS

2015 Volume E98.D Issue 3 Pages 486-489

DOI https://doi.org/10.1587/transinf.2014FCP0007

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Abstract

Secure sets and defensive alliances in graphs are studied. They are sets of vertices that are safe in some senses. In this paper, we first present a fixed-parameter algorithm for finding a small secure set, whose running time is much faster than the previously known one. We then present improved bound on the smallest sizes of defensive alliances and secure sets for hypercubes. These results settle some open problems paused recently.

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