{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T05:40:23Z","timestamp":1792129223766,"version":"4.4.0"},"reference-count":40,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Comput."],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats:p>We consider the \\sf Unconstrained Submodular Maximization problem in which we are given a nonnegative submodular function $f:2^{\\mathcal{N}}\\rightarrow \\mathbb{R}^+$, and the objective is to find a subset $S\\subseteq \\mathcal{N}$ maximizing $f(S)$. This is one of the most basic submodular optimization problems, having a wide range of applications. Some well-known problems captured by \\sf Unconstrained Submodular Maximization include \\sf Max-Cut, \\sf Max-DiCut, and variants of \\sf Max-SAT and maximum facility location. We present a simple randomized linear time algorithm achieving a tight approximation guarantee of 1\/2, thus matching the known hardness result of Feige, Mirrokni, and Vondr\u00e1k [SIAM J. Comput., 40 (2011), pp. 1133--1153]. Our algorithm is based on an adaptation of the greedy approach which exploits certain symmetry properties of the problem.<\/jats:p>","DOI":"10.1137\/130929205","type":"journal-article","created":{"date-parts":[[2015,10,28]],"date-time":"2015-10-28T00:12:15Z","timestamp":1445991135000},"page":"1384-1402","source":"Crossref","is-referenced-by-count":158,"title":["A Tight Linear Time (1\/2)-Approximation for Unconstrained Submodular Maximization"],"prefix":"10.1137","volume":"44","author":[{"given":"Niv","family":"Buchbinder","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Moran","family":"Feldman","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joseph","family":"Seffi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Roy","family":"Schwartz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,10,27]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"A. 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Cherenin,\n                      Solving some combinatoiral problems of optimal planning by the method of successive calculations (in Russian)\n                      , in Proceedings of the Conference on Experiences and Perspectives on the Applications of Mathematical Methods and Electronic Computers in Planning, Novosibirsk, 1962."},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.23.8.789"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-5060(08)70732-5"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1145\/2213977.2214076"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.4086\/toc.2012.v008a005"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/090779346"},{"key":"atypb13","first-page":"342","author":"Feldman M.","year":"2011","journal-title":"Proceedings of ICALP"},{"key":"atypb14","first-page":"570","author":"Feldman M.","year":"2011","journal-title":"Proceedings of FOCS"},{"key":"atypb15","first-page":"1098","author":"Gharan S. O.","year":"2011","journal-title":"Proceedings of SODA"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1145\/227683.227684"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-004-5909-z"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.45.11.1539"},{"key":"atypb19","unstructured":"B. Goldengorin, G. A. Tijssen, and M. Tso,\n                      The Maximization of Submodular Functions: Old and New Proofs for the Correctness of the Dichotomy Algorithm\n                      , Research report 99A17, Research Institute SOM (Systems, Organisations and Management), University of Groningen, 1999."},{"key":"atypb20","first-page":"246","author":"Gupta A.","year":"2010","journal-title":"New York"},{"key":"atypb21","first-page":"1","author":"Halperin E.","year":"2001","journal-title":"Proceedings of SODA"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1145\/1367497.1367524"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1145\/502090.502098"},{"key":"atypb24","unstructured":"N. Huang and A. Borodin,\n                      Bounds on Double-Sided Myopic Algorithms for Unconstrained Non-Monotone Submodular Maximization\n                      , CoRR abs\/1312.2173, 2013."},{"key":"atypb25","first-page":"671","author":"Iwata S.","year":"2009","journal-title":"Proceedings of FOCS"},{"key":"atypb26","unstructured":"S. Jegelka and J. Bilmes,\n                      Cooperative Cuts: Graph Cuts with Submodular Edge Weights\n                      , \\newblock Technical report 189-03-2010, Max Planck Institute for Biological Cybernetics, Tuebingen, 2010."},{"key":"atypb27","first-page":"85","author":"Karp R. M.","year":"1972","journal-title":"New York"},{"key":"atypb28","unstructured":"V. R. 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