A new semidefinite programming hierarchy for cycles in binary matroids and cuts in graphs

João Gouveia, Monique Laurent, Pablo A. Parrilo, Rekha Thomas
<span title="2010-10-28">2010</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/o653fqsowvcyrhw6p4gdmpdkwm" style="color: black;">Mathematical programming</a> </i> &nbsp;
The theta bodies of a polynomial ideal are a series of semidefinite programming relaxations of the convex hull of the real variety of the ideal. In this paper we construct the theta bodies of the vanishing ideal of cycles in a binary matroid. Applied to cuts in graphs, this yields a new hierarchy of semidefinite programming relaxations of the cut polytope of the graph. If the binary matroid avoids certain minors we can characterize when the first theta body in the hierarchy equals the cycle
more &raquo; ... tope of the matroid. Specialized to cuts in graphs, this result solves a problem posed by Lov\'asz.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10107-010-0425-z">doi:10.1007/s10107-010-0425-z</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xpm65vet5zfl7g4dffhd3tt7qm">fatcat:xpm65vet5zfl7g4dffhd3tt7qm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171009015432/http://publisher-connector.core.ac.uk/resourcesync/data/Springer-OA/pdf/114/aHR0cDovL2xpbmsuc3ByaW5nZXIuY29tLzEwLjEwMDcvczEwMTA3LTAxMC0wNDI1LXoucGRm.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/4e/ee/4eee1c2dc7ab483aea172698aca90e5834b55f0a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10107-010-0425-z"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>