Playing Unique Games on Certified Small-Set Expanders

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Abstract:

We give an algorithm for solving unique games (UG) instances whose constraints correspond to edges of graphs with a sum-of-squares (SoS) small-set-expansion certificate. As corollaries, we obtain the first polynomial-time algorithms for solving UG on the noisy hypercube and the short code graphs. The prior best algorithm for such instan...More

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s constraints. As a corollary, we get a polynomial-time algorithm $A$ such that if $I$ is a $1-\\epsilon$ satisfiable instance over the $\\alpha$-noisy hypercube or short code graph, then $A(I)$ outputs an assignment satisfying an $\\exp(-O(\\sqrt{\\epsilon}\u002F\\alpha))$ fraction of the constraints. Our techniques can be extended even to graphs that are not SSE, and in particular we obtain a new efficient algorithm for solving UG instances over the Johnson graph. ","authors":[{"name":"Mitali Bafna"},{"id":"543348c4dabfaeb4c6ab4c32","name":"Boaz Barak"},{"id":"53f4ceb9dabfaeed1af820af","name":"Pravesh Kothari"},{"id":"53f434bedabfaec09f16e053","name":"Tselil Schramm"},{"id":"53f433fadabfaeb1a7bdca27","name":"David Steurer"}],"id":"5eede0b091e0116a23aafbd9","is_downvoted":false,"is_starring":false,"is_upvoted":false,"num_citation":0,"num_starred":0,"num_upvoted":0,"num_viewed":41,"title":"Playing Unique Games on Certified Small-Set Expanders","urls":["https:\u002F\u002Farxiv.org\u002Fabs\u002F2006.09969"],"versions":[{"id":"5eede0b091e0116a23aafbd9","sid":"2006.09969","src":"arxiv","year":2020}],"year":2020,"cited_pubs":0,"total_ref":0,"total_sim":0},"bestpaper":undefined,"simpapers":undefined,"authorsData":[{"name":"Mitali Bafna"},{"avatar":"https:\u002F\u002Fstatic.aminer.cn\u002Fupload\u002Favatar\u002F1504\u002F1317\u002F1506\u002F543348c4dabfaeb4c6ab4c32_2.png","id":"543348c4dabfaeb4c6ab4c32","name":"Boaz Barak","name_zh":""},{"id":"53f4ceb9dabfaeed1af820af","name":"Pravesh Kothari"},{"id":"53f434bedabfaec09f16e053","name":"Tselil Schramm","name_zh":""},{"avatar":"https:\u002F\u002Fstatic.aminer.org\u002Fupload\u002Favatar\u002F1660\u002F1403\u002F512\u002F53f433fadabfaeb1a7bdca27.jpeg","id":"53f433fadabfaeb1a7bdca27","name":"David Steurer","name_zh":""}],"redirect_id":undefined,"notfound":undefined,"pdfInfo":{}};