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Parallel Comput."],"published-print":{"date-parts":[[2015,11,2]]},"abstract":"<jats:p>Greedy algorithms are practitioners\u2019 best friends\u2014they are intuitive, are simple to implement, and often lead to very good solutions. However, implementing greedy algorithms in a distributed setting is challenging since the greedy choice is inherently sequential, and it is not clear how to take advantage of the extra processing power.<\/jats:p>\n          <jats:p>\n            Our main result is a powerful sampling technique that aids in parallelization of sequential algorithms. Armed with this primitive, we then adapt a broad class of greedy algorithms to the MapReduce paradigm; this class includes maximum cover and submodular maximization subject to\n            <jats:italic>p<\/jats:italic>\n            -system constraint problems. Our method yields efficient algorithms that run in a logarithmic number of rounds while obtaining solutions that are arbitrarily close to those produced by the standard sequential greedy algorithm. We begin with algorithms for modular maximization subject to a matroid constraint and then extend this approach to obtain approximation algorithms for submodular maximization subject to knapsack or\n            <jats:italic>p<\/jats:italic>\n            -system constraints.\n          <\/jats:p>","DOI":"10.1145\/2809814","type":"journal-article","created":{"date-parts":[[2015,9,15]],"date-time":"2015-09-15T12:09:15Z","timestamp":1442318955000},"page":"1-22","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":62,"title":["Fast Greedy Algorithms in MapReduce and Streaming"],"prefix":"10.1145","volume":"2","author":[{"given":"Ravi","family":"Kumar","sequence":"first","affiliation":[{"name":"Google, CA"}]},{"given":"Benjamin","family":"Moseley","sequence":"additional","affiliation":[{"name":"Washington University in St. Louis, MO"}]},{"given":"Sergei","family":"Vassilvitskii","sequence":"additional","affiliation":[{"name":"Google, CA"}]},{"given":"Andrea","family":"Vattani","sequence":"additional","affiliation":[{"name":"University of California at San Diego"}]}],"member":"320","published-online":{"date-parts":[[2015,9,8]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1498759.1498766"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.14778\/1687627.1687686"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.5555\/1283383.1283429"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.14778\/2140436.2140442"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.14778\/2180912.2180915"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcss.2003.11.006"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/2500121"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-0000(05)80068-6"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/1989493.1989497"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1137\/080733991"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.14778\/1988776.1988781"},{"key":"e_1_2_1_12_1","volume-title":"18th Annual IEEE Conference on Computational Complexity (Complexity 2003","author":"Chakrabarti A.","year":"2003","unstructured":"A. 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