Bound for the 2-Page Fixed Linear Crossing Number of Hypercube Graph via SDP Relaxation
© 2017 A. Suebsriwichai and T. Mouktonglang. The crossing number of graph G is the minimum number of edges crossing in any drawing of G in a plane. In this paper we describe a method of finding the bound of 2-page fixed linear crossing number of G. We consider a conflict graph G′ of G. Then, instead...
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th-cmuir.6653943832-575242018-09-05T03:45:07Z Bound for the 2-Page Fixed Linear Crossing Number of Hypercube Graph via SDP Relaxation A. Suebsriwichai T. Mouktonglang Mathematics © 2017 A. Suebsriwichai and T. Mouktonglang. The crossing number of graph G is the minimum number of edges crossing in any drawing of G in a plane. In this paper we describe a method of finding the bound of 2-page fixed linear crossing number of G. We consider a conflict graph G′ of G. Then, instead of minimizing the crossing number of G, we show that it is equivalent to maximize the weight of a cut of G′. We formulate the original problem into the MAXCUT problem. We consider a semidefinite relaxation of the MAXCUT problem. An example of a case where G is hypercube is explicitly shown to obtain an upper bound. The numerical results confirm the effectiveness of the approximation. 2018-09-05T03:45:07Z 2018-09-05T03:45:07Z 2017-01-01 Journal 16870042 1110757X 2-s2.0-85019549547 10.1155/2017/7640347 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85019549547&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/57524 |
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Mathematics A. Suebsriwichai T. Mouktonglang Bound for the 2-Page Fixed Linear Crossing Number of Hypercube Graph via SDP Relaxation |
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© 2017 A. Suebsriwichai and T. Mouktonglang. The crossing number of graph G is the minimum number of edges crossing in any drawing of G in a plane. In this paper we describe a method of finding the bound of 2-page fixed linear crossing number of G. We consider a conflict graph G′ of G. Then, instead of minimizing the crossing number of G, we show that it is equivalent to maximize the weight of a cut of G′. We formulate the original problem into the MAXCUT problem. We consider a semidefinite relaxation of the MAXCUT problem. An example of a case where G is hypercube is explicitly shown to obtain an upper bound. The numerical results confirm the effectiveness of the approximation. |
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Journal |
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A. Suebsriwichai T. Mouktonglang |
| author_facet |
A. Suebsriwichai T. Mouktonglang |
| author_sort |
A. Suebsriwichai |
| title |
Bound for the 2-Page Fixed Linear Crossing Number of Hypercube Graph via SDP Relaxation |
| title_short |
Bound for the 2-Page Fixed Linear Crossing Number of Hypercube Graph via SDP Relaxation |
| title_full |
Bound for the 2-Page Fixed Linear Crossing Number of Hypercube Graph via SDP Relaxation |
| title_fullStr |
Bound for the 2-Page Fixed Linear Crossing Number of Hypercube Graph via SDP Relaxation |
| title_full_unstemmed |
Bound for the 2-Page Fixed Linear Crossing Number of Hypercube Graph via SDP Relaxation |
| title_sort |
bound for the 2-page fixed linear crossing number of hypercube graph via sdp relaxation |
| publishDate |
2018 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85019549547&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/57524 |
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