{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/93050"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/93050","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Local computation algorithms for graphs of non-constant degrees","abstract":"In the model of local computation algorithms (LCAs), we aim to compute the queried part of the output by examining only a small (sublinear) portion of the input. Many recently developed LCAs on graph problems achieve time and space complexities with very low dependence on n, the number of vertices. Nonetheless, these complexities are generally at least exponential in d, the upper bound on the degree of the input graph. Instead, we consider the case where parameter d can be moderately dependent on n, and aim for complexities with quasi-polynomial dependence on d, while maintaining polylogarithmic dependence on n. In this thesis, we give randomized LCAs for computing maximal independent sets, maximal matchings, and approximate maximum matchings. Both time and space complexities of our LCAs on these problems are 2 0(log3 d)polylog(n), 2 0(log2 d)polylog(n) and 2 0(log3 d)polylog(n), respectively.","abstract_html":"In the model of local computation algorithms (LCAs), we aim to compute the queried part of the output by examining only a small (sublinear) portion of the input. Many recently developed LCAs on graph problems achieve time and space complexities with very low dependence on n, the number of vertices. Nonetheless, these complexities are generally at least exponential in d, the upper bound on the degree of the input graph. Instead, we consider the case where parameter d can be moderately dependent on n, and aim for complexities with quasi-polynomial dependence on d, while maintaining polylogarithmic dependence on n. In this thesis, we give randomized LCAs for computing maximal independent sets, maximal matchings, and approximate maximum matchings. Both time and space complexities of our LCAs on these problems are 2 0(log3 d)polylog(n), 2 0(log2 d)polylog(n) and 2 0(log3 d)polylog(n), respectively.","abstract_has_math":false,"creators":["Yodpinyanee, Anak"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.","school":null,"contributors":[],"advisors":["Ronitt Rubinfeld."],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014","date_published":"2014","updated_at":"2026-07-22T22:21:34Z","subjects":["Electrical Engineering and Computer Science."],"languages":["eng"],"rights":["M.I.T. theses are protected by copyright. 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Many recently developed LCAs on graph problems achieve time and space complexities with very low dependence on n, the number of vertices. Nonetheless, these complexities are generally at least exponential in d, the upper bound on the degree of the input graph. Instead, we consider the case where parameter d can be moderately dependent on n, and aim for complexities with quasi-polynomial dependence on d, while maintaining polylogarithmic dependence on n. In this thesis, we give randomized LCAs for computing maximal independent sets, maximal matchings, and approximate maximum matchings. Both time and space complexities of our LCAs on these problems are 2 0(log3 d)polylog(n), 2 0(log2 d)polylog(n) and 2 0(log3 d)polylog(n), respectively."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["S.M."]},{"key":"dc:title","label":"Title","values":["Local computation algorithms for graphs of non-constant degrees"]}]}],"canonical_facts":{"dc:contributor.advisor":["Ronitt Rubinfeld."],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science."],"dc:contributor.other":["Massachusetts Institute of Technology. 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