{"604927":{"#nid":"604927","#data":{"type":"event","title":"ARC Colloquium:  Nima Anari (Stanford)","body":[{"value":"\u003Cp align=\u0022center\u0022\u003E\u003Cstrong\u003EAlgorithms \u0026amp; Randomness Center (ARC)\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp align=\u0022center\u0022\u003E\u003Cstrong\u003ENima Anari\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp align=\u0022center\u0022\u003E\u003Cstrong\u003EMonday, April 30, 2018\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp align=\u0022center\u0022\u003E\u003Cstrong\u003EKlaus 1116 East \u0026ndash; Noon\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cbr \/\u003E\r\n\u003Cstrong\u003ETitle:\u0026nbsp; \u003C\/strong\u003EEntropy, Log-Concavity, and a Deterministic Approximation Algorithm for Counting Bases of Matroids\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003EAbstract:\u003C\/strong\u003E\u0026nbsp; We give a deterministic 2^O(rank) approximation algorithm to count the number of bases of a given matroid and the number of common bases of any two matroids. Based on a lower bound of Azar et al., this is almost the best possible result assuming oracle access to independent sets of matroids.\u003C\/p\u003E\r\n\r\n\u003Cp\u003EThere are two main ingredients in our result: For the first ingredient, we build upon recent results of Huh et al. and Adiprasito et al. on combinatorial hodge theory to derive a connection between matroids and log-concave polynomials. We expect that several new applications in approximation algorithms will be derived from this connection in future. Formally, we prove that the multivariate generating polynomial of the bases of any matroid is log-concave as a function over the positive orthant. For the second ingredient, we use a general framework for approximate counting in discrete problems, based on convex optimization and sub-additivity of the entropy. For matroids, we prove that an approximate super-additivity of the entropy holds, yielding an approximation algorithm, by relying on log-concavity of the corresponding polynomials.\u003C\/p\u003E\r\n\r\n\u003Cp\u003EJoint work with Shayan Oveis Gharan and Cynthia Vinzant.\u003C\/p\u003E\r\n\r\n\u003Cp\u003E----------------------------------\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Ca href=\u0022https:\/\/nimaanari.com\/\u0022\u003ESpeaker\u0026#39;s Webpage\u003C\/a\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cem\u003EVideos of recent talks are available at \u003C\/em\u003E\u003Ca href=\u0022https:\/\/smartech.gatech.edu\/handle\/1853\/46836\u0022\u003E\u003Cem\u003Ehttps:\/\/smartech.gatech.edu\/handle\/1853\/46836\u003C\/em\u003E\u003C\/a\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Ca href=\u0022https:\/\/mailman.cc.gatech.edu\/mailman\/listinfo\/arc-colloq\u0022\u003E\u003Cem\u003EClick here to subscribe to the seminar email list: arc-colloq@cc.gatech.edu \u003C\/em\u003E\u003C\/a\u003E\u003C\/p\u003E","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":"","field_summary_sentence":[{"value":"Entropy, Log-Concavity, and a Deterministic Approximation Algorithm for Counting Bases of Matroids - Klaus 1116E at 11 am"}],"uid":"27544","created_gmt":"2018-04-10 19:32:13","changed_gmt":"2018-04-24 18:15:29","author":"Francella Tonge","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2018-04-30T13:00:00-04:00","event_time_end":"2018-04-30T14:00:00-04:00","event_time_end_last":"2018-04-30T14:00:00-04:00","gmt_time_start":"2018-04-30 17:00:00","gmt_time_end":"2018-04-30 18:00:00","gmt_time_end_last":"2018-04-30 18:00:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"70263","name":"ARC"}],"categories":[],"keywords":[],"core_research_areas":[],"news_room_topics":[],"event_categories":[],"invited_audience":[{"id":"78761","name":"Faculty\/Staff"},{"id":"78771","name":"Public"},{"id":"78751","name":"Undergraduate students"}],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[],"email":[],"slides":[],"orientation":[],"userdata":""}}}