{"id":314,"date":"2017-07-06T11:20:12","date_gmt":"2017-07-06T02:20:12","guid":{"rendered":"http:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/?p=314"},"modified":"2017-07-06T11:20:12","modified_gmt":"2017-07-06T02:20:12","slug":"%e3%80%8c%e6%9c%80%e9%81%a9%e3%83%a2%e3%83%87%e3%83%aa%e3%83%b3%e3%82%b0%e3%80%8d%e3%82%bb%e3%83%9f%e3%83%8a%e3%83%bc%e6%a1%88%e5%86%85-711","status":"publish","type":"post","link":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/2017\/07\/06\/%e3%80%8c%e6%9c%80%e9%81%a9%e3%83%a2%e3%83%87%e3%83%aa%e3%83%b3%e3%82%b0%e3%80%8d%e3%82%bb%e3%83%9f%e3%83%8a%e3%83%bc%e6%a1%88%e5%86%85-711\/","title":{"rendered":"\u300c\u6700\u9069\u30e2\u30c7\u30ea\u30f3\u30b0\u300d\u30bb\u30df\u30ca\u30fc\u6848\u5185 (7\/11)"},"content":{"rendered":"<p>\u65e5\u6642\uff1a\u30002017\u5e747\u670811\u65e5(\u706b) 17:00\uff5e18:00<br \/>\n\u5834\u6240\uff1a\u3000\u6771\u4eac\u5927\u5b66\u5de5\u5b66\u90e8 14\u53f7\u9928 5\u968e 534\u53f7\u5ba4<br \/>\n<a href=\"http:\/\/www.u-tokyo.ac.jp\/campusmap\/cam01_04_15_j.html\" target=\"_blank\" rel=\"noopener noreferrer\">http:\/\/www.u-tokyo.ac.jp\/campusmap\/cam01_04_15_j.html<\/a><\/p>\n<p>\u8b1b\u6f14\u8005\uff1a S. Thomas McCormick<\/p>\n<p>\u8b1b\u6f14\u984c\u76ee: Computing closest vectors in zonotopal lattices<\/p>\n<p>\u8b1b\u6f14\u6982\u8981:<br \/>\nA lattice L is the set of vectors arising from integer linear<br \/>\ncombinations of given basis vectors in R^m.\u00a0 Given some vector x, the<br \/>\nClosest Vector Problem (CVP) is to find a vector v in L of minimum<br \/>\nl_2-norm distance to x.\u00a0 CVP is a fundamental problem for lattices with<br \/>\nmany applications, and it is in general NP Hard.<\/p>\n<p>A zonotopal lattice is given as the set of integer points {v | Mv = 0},<br \/>\nwhen M is an n by m totally unimodular matrix.\u00a0 We show how to adapt the<br \/>\nCancel and Tighten algorithm of Karzanov and McCormick to solve CVP for<br \/>\nzonotopal lattices in O(m^3) time via the Seymour decomposition of<br \/>\ntotally unimodular matrices.\u00a0 The algorithm uses the decomposition to<br \/>\nreduce the problem to a series of subproblems that are piecewise linear<br \/>\nconvex circulation and co-circulation network flow problems.\u00a0 The new<br \/>\nalgorithm is more general and often faster than a CVP algorithm for<br \/>\nco-circulation matrices by McKilliam, Grant, and Clarkson that runs in<br \/>\nO(n^4) time.<\/p>\n<p>S. Thomas McCormick (UBC)<br \/>\nBritta Peis, Robert Scheidweiler (RWTH Aachen)<br \/>\nFrank Vallentin (Cologne)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u65e5\u6642\uff1a\u30002017\u5e747\u670811\u65e5(\u706b) 17:00\uff5e18:00 \u5834\u6240\uff1a\u3000\u6771\u4eac\u5927\u5b66\u5de5\u5b66\u90e8 14\u53f7\u9928 5\u968e &hellip; <\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-314","post","type-post","status-publish","format-standard","hentry","category-3"],"_links":{"self":[{"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/posts\/314","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/comments?post=314"}],"version-history":[{"count":0,"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/posts\/314\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/media?parent=314"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/categories?post=314"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.opt.mist.i.u-tokyo.ac.jp\/crest-model\/wp-json\/wp\/v2\/tags?post=314"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}