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Algorithms"],"published-print":{"date-parts":[[2021,10,31]]},"abstract":"<jats:p>\n            This article proves strong lower bounds for distributed computing in the\n            <jats:sc>congest<\/jats:sc>\n            model, by presenting the\n            <jats:italic>bit-gadget<\/jats:italic>\n            : a new technique for constructing graphs with small cuts.\n          <\/jats:p>\n          <jats:p>The contribution of bit-gadgets is twofold. First, developing careful sparse graph constructions with small cuts extends known techniques to show a near-linear lower bound for computing the diameter, a result previously known only for dense graphs. Moreover, the sparseness of the construction plays a crucial role in applying it to approximations of various distance computation problems, drastically improving over what can be obtained when using dense graphs.<\/jats:p>\n          <jats:p>Second, small cuts are essential for proving super-linear lower bounds, none of which were known prior to this work. In fact, they allow us to show near-quadratic lower bounds for several problems, such as exact minimum vertex cover or maximum independent set, as well as for coloring a graph with its chromatic number. Such strong lower bounds are not limited to NP-hard problems, as given by two simple graph problems in P, which are shown to require a quadratic and near-quadratic number of rounds. All of the above are optimal up to logarithmic factors. In addition, in this context, the complexity of the all-pairs-shortest-paths problem is discussed.<\/jats:p>\n          <jats:p>\n            Finally, it is shown that graph constructions for\n            <jats:sc>congest<\/jats:sc>\n            lower bounds translate to lower bounds for the semi-streaming model, despite being very different in its nature.\n          <\/jats:p>","DOI":"10.1145\/3469834","type":"journal-article","created":{"date-parts":[[2021,10,5]],"date-time":"2021-10-05T01:10:42Z","timestamp":1633396242000},"page":"1-40","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Smaller Cuts, Higher Lower Bounds"],"prefix":"10.1145","volume":"17","author":[{"given":"Amir","family":"Abboud","sequence":"first","affiliation":[{"name":"Department of Computer Science and Applied Mathematics, Weizmann Instituteof Science, Rehovot, Israel"}]},{"given":"Keren","family":"Censor-Hillel","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Technion, Haifa, Israel"}]},{"given":"Seri","family":"Khoury","sequence":"additional","affiliation":[{"name":"University of California, Berkeley, USA"}]},{"given":"Ami","family":"Paz","sequence":"additional","affiliation":[{"name":"Faculty of Computer Science, University of Vienna, Wien, Austria"}]}],"member":"320","published-online":{"date-parts":[[2021,10,4]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-53426-7_3"},{"volume-title":"Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing (STOC\u201920)","author":"Abboud Amir","key":"e_1_2_1_2_1"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.5555\/2722129.2722241"},{"volume-title":"Virginia Vassilevska Williams, and Joshua R. 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