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Approximation algorithm for maximum independent set in planar traingle-free graphs

Madhavan, CEV (1984) Approximation algorithm for maximum independent set in planar traingle-free graphs. In: Lecture Notes in Computer Science, 181 . pp. 381-392.

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The maximum independent set problem is NP-complete even when restricted to planar graphs, cubic planar graphs or triangle free graphs. The problem of finding an absolute approximation still remains NP-complete. Various polynomial time approximation algorithms, that guarantee a fixed worst case ratio between the independent set size obtained to the maximum independent set size, in planar graphs have been proposed. We present in this paper a simple and efficient, O(|V|) algorithm that guarantees a ratio 1/2, for planar triangle free graphs. The algorithm differs completely from other approaches, in that, it collects groups of independent vertices at a time. Certain bounds we obtain in this paper relate to some interesting questions in the theory of extremal graphs.

Item Type: Journal Article
Publication: Lecture Notes in Computer Science
Publisher: Springer
Additional Information: Copyright of this article belongs to Springer.
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Date Deposited: 14 Aug 2009 06:33
Last Modified: 14 Aug 2009 06:33
URI: http://eprints.iisc.ac.in/id/eprint/22325

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