@inproceedings{16616462015c4337840a892b9abb74c5,

title = "Integrality gaps for sparsest cut and minimum linear arrangement problems",

abstract = "Arora, Rao and Vazirani [2] 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(√log n). They conjectured that the gap is bounded from above by a constant. In this paper, we disprove this conjecture (referred to as the ARV-Conjecture) by constructing an Ω(log log n) integrality gap instance. Khot and Vishnoi [16] had earlier disproved the non-uniform version of the ARV-Conjecture. A simple {"}stretching{"} of the integrality gap instance for the Sparsest Cut problem serves as an Ω(log log n) integrality gap instance for the SDP relaxation of the Minimum Linear Arrangement problem. This SDP relaxation was considered in [6, 11], where it was shown that its integrality gap is bounded from above by O(√log n log log n).",

keywords = "Algorithms, Theory",

author = "Devanur, {Nikhil R.} and Khot, {Subhash A.} and Rishi Saket and Vishnoi, {Nisheeth K.}",

year = "2006",

doi = "10.1145/1132516.1132594",

language = "English (US)",

isbn = "1595931341",

series = "Proceedings of the Annual ACM Symposium on Theory of Computing",

publisher = "Association for Computing Machinery",

pages = "537--546",

booktitle = "STOC'06",

note = "38th Annual ACM Symposium on Theory of Computing, STOC'06 ; Conference date: 21-05-2006 Through 23-05-2006",

}