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Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
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612-822-4611
The Clique Algorithm

The Clique Algorithm

Paperback

General Computers

ISBN10: 1466391219
ISBN13: 9781466391215
Publisher: Createspace
Published: Oct 2 2011
Pages: 48
Weight: 0.30
Height: 0.12 Width: 8.50 Depth: 11.00
Language: English
We present a new polynomial-time algorithm for finding maximal cliques 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 clique 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 clique. The algorithm is demonstrated by finding maximum cliques for several famous graphs, including two large benchmark graphs with hidden maximum cliques. We implement the algorithm in C++ and provide a demonstration program for Microsoft Windows.

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General Computers