The Vertex Cover Algorithm

ยท Institute of Mathematics
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1 แƒ›แƒ˜แƒ›แƒแƒฎแƒ˜แƒšแƒ•แƒ
แƒ”แƒšแƒฌแƒ˜แƒ’แƒœแƒ˜
48
แƒ’แƒ•แƒ”แƒ แƒ“แƒ˜
แƒ แƒ”แƒ˜แƒขแƒ˜แƒœแƒ’แƒ”แƒ‘แƒ˜ แƒ“แƒ แƒ›แƒ˜แƒ›แƒแƒฎแƒ˜แƒšแƒ•แƒ”แƒ‘แƒ˜ แƒ“แƒแƒฃแƒ“แƒแƒกแƒขแƒฃแƒ แƒ”แƒ‘แƒ”แƒšแƒ˜แƒ ย แƒจแƒ”แƒ˜แƒขแƒงแƒ•แƒ”แƒ— แƒ›แƒ”แƒขแƒ˜

แƒแƒ› แƒ”แƒšแƒฌแƒ˜แƒ’แƒœแƒ˜แƒก แƒจแƒ”แƒกแƒแƒฎแƒ”แƒ‘

We present a new polynomial-time algorithm for finding minimal vertex covers in graphs. The algorithm finds a minimum vertex cover 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 minimum vertex cover. The algorithm is demonstrated by finding minimum vertex covers for several famous graphs, including two large benchmark graphs with hidden minimum vertex covers. We implement the algorithm in C++ and provide a demonstration program for Microsoft Windows.

แƒจแƒ”แƒคแƒแƒกแƒ”แƒ‘แƒ”แƒ‘แƒ˜ แƒ“แƒ แƒ›แƒ˜แƒ›แƒแƒฎแƒ˜แƒšแƒ•แƒ”แƒ‘แƒ˜

5,0
1 แƒ›แƒ˜แƒ›แƒแƒฎแƒ˜แƒšแƒ•แƒ

แƒแƒ•แƒขแƒแƒ แƒ˜แƒก แƒจแƒ”แƒกแƒแƒฎแƒ”แƒ‘

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.

แƒจแƒ”แƒแƒคแƒแƒกแƒ”แƒ— แƒ”แƒก แƒ”แƒšแƒฌแƒ˜แƒ’แƒœแƒ˜

แƒ’แƒ•แƒ˜แƒ—แƒฎแƒแƒ แƒ˜แƒ— แƒ—แƒฅแƒ•แƒ”แƒœแƒ˜ แƒแƒ–แƒ แƒ˜.

แƒ˜แƒœแƒคแƒแƒ แƒ›แƒแƒชแƒ˜แƒ แƒฌแƒแƒ™แƒ˜แƒ—แƒฎแƒ•แƒแƒกแƒ—แƒแƒœ แƒ“แƒแƒ™แƒแƒ•แƒจแƒ˜แƒ แƒ”แƒ‘แƒ˜แƒ—

แƒกแƒ›แƒแƒ แƒขแƒคแƒแƒœแƒ”แƒ‘แƒ˜ แƒ“แƒ แƒขแƒแƒ‘แƒšแƒ”แƒขแƒ”แƒ‘แƒ˜
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แƒšแƒ”แƒžแƒขแƒแƒžแƒ”แƒ‘แƒ˜ แƒ“แƒ แƒ™แƒแƒ›แƒžแƒ˜แƒฃแƒขแƒ”แƒ แƒ”แƒ‘แƒ˜
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แƒ”แƒšแƒฌแƒแƒ›แƒ™แƒ˜แƒ—แƒฎแƒ•แƒ”แƒšแƒ”แƒ‘แƒ˜ แƒ“แƒ แƒกแƒฎแƒ•แƒ แƒ›แƒแƒฌแƒงแƒแƒ‘แƒ˜แƒšแƒแƒ‘แƒ”แƒ‘แƒ˜
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