<\/p>\n
Arora, Rao and Vazirani showed that the standard semi-definite programming (SDP) relaxation of the sparsest cut problem with the triangle inequality constraints has an integrality gap of $O(\\sqrt{\\log n})$. They conjectured that the gap is bounded from above by a constant. In this paper, we disprove this conjecture by constructing an $\\Omega(\\log \\log n)$ integrality gap instance. Khot and Vishnoi had earlier disproved the non-uniform version of this Conjecture. A simple “stretching” of the integrality gap instance for the sparsest cut problem serves as an $\\Omega(\\log \\log n)$ integrality gap instance for the SDP relaxation of the Minimum Linear Arrangement problem. This SDP relaxation was considered in Charikar et. al. and Feige and Lee, where it was shown that its integrality gap is bounded from above by $O(\\sqrt{\\log n} \\log \\log n).$<\/span><\/p>\n<\/div>\n<\/li>\n<\/ul>\n <\/p>\n <\/p>\n","protected":false},"excerpt":{"rendered":" Arora, Rao and Vazirani showed that the standard semi-definite programming (SDP) relaxation of the sparsest cut problem with the triangle inequality constraints has an integrality gap of $O(\\sqrt{\\log n})$. They conjectured that the gap is bounded from above by a constant. In this paper, we disprove this conjecture by constructing an $\\Omega(\\log \\log n)$ […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"Association for Computing Machinery, Inc.","msr_publisher_other":"","msr_booktitle":"STOC","msr_chapter":"","msr_edition":"STOC","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"537-546","msr_page_range_start":"537","msr_page_range_end":"546","msr_series":"","msr_volume":"","msr_copyright":"Copyright \u00a9 2007 by the Association for Computing Machinery, Inc. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and\/or a fee. Request permissions from Publications Dept, ACM Inc., fax +1 (212) 869-0481, or permissions@acm.org. The definitive version of this paper can be found at ACM's Digital Library --http:\/\/www.acm.org\/dl\/.","msr_conference_name":"STOC","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"Nikhil R. 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