{"product_id":"the-independent-set-algorithm-ashay-dharwadker-9781466387690","title":"The Independent Set Algorithm","description":"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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Ashay Dharwadker\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 1466387696\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9781466387690\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Createspace Independent Publishing Platform\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 10\/02\/2011\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 46\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.29lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 11.00h x 8.50w x 0.12d","brand":"Ashay Dharwadker","offers":[{"title":"Paperback","offer_id":48217377669375,"sku":"9781466387690","price":15.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_809bbf1b-3c81-4f9f-b141-19abe08695ac.jpg?v=1771996839","url":"https:\/\/www.whiterainbookhouse.com\/products\/the-independent-set-algorithm-ashay-dharwadker-9781466387690","provider":"WR Book House","version":"1.0","type":"link"}