The Independent Set Algorithm
aug 2006 · Institute of Mathematics
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We present a new polynomial-time algorithm for finding maximal independent sets in graphs. As a corollary, we obtain new bounds on the famous Ramsey numbers in terms of the maximum and minimum vertex degrees of the corresponding Ramsey graphs. The algorithm finds a maximum independent set in all known examples of graphs. In view of the importance of the P versus NP question, we ask if there exists a graph for which the algorithm cannot find a maximum independent set. The algorithm is demonstrated by finding maximum independent sets for several famous graphs, including two large benchmark graphs with hidden maximum independent sets. We implement the algorithm in C++ and provide a demonstration program for Microsoft Windows.
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Ashay Dharwadker is the Distinguished Professor of Mathematics & Natural Sciences at the Institute of Mathematics, Gurgaon, India. He is the author of a dozen exquisitely illustrated books describing his fundamental contributions to combinatorics, graph theory, computer science and the foundations of physics.
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