{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T14:10:09Z","timestamp":1773583809701,"version":"3.50.1"},"reference-count":30,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2017,11,15]],"date-time":"2017-11-15T00:00:00Z","timestamp":1510704000000},"content-version":"vor","delay-in-days":365,"URL":"http:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCF-1409130"],"award-info":[{"award-number":["CCF-1409130"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Algorithms"],"published-print":{"date-parts":[[2017,1,31]]},"abstract":"<jats:p>\n                    We study the Minimum Latency Submodular Cover (MLSC) problem, which consists of a metric (\n                    <jats:italic toggle=\"yes\">V<\/jats:italic>\n                    ,\n                    <jats:italic toggle=\"yes\">d<\/jats:italic>\n                    ) with source\n                    <jats:italic toggle=\"yes\">r<\/jats:italic>\n                    \u2208\n                    <jats:italic toggle=\"yes\">V<\/jats:italic>\n                    and\n                    <jats:italic toggle=\"yes\">m<\/jats:italic>\n                    monotone submodular functions\n                    <jats:italic toggle=\"yes\">f<\/jats:italic>\n                    <jats:sub>1<\/jats:sub>\n                    ,\n                    <jats:italic toggle=\"yes\">f<\/jats:italic>\n                    <jats:sub>2<\/jats:sub>\n                    , \u2026,\n                    <jats:italic toggle=\"yes\">\n                      f\n                      <jats:sub>m<\/jats:sub>\n                    <\/jats:italic>\n                    : 2\n                    <jats:sup>\n                      <jats:italic toggle=\"yes\">V<\/jats:italic>\n                    <\/jats:sup>\n                    \u2192 [0, 1]. The goal is to find a path originating at\n                    <jats:italic toggle=\"yes\">r<\/jats:italic>\n                    that minimizes the total \u201ccover time\u201d of all functions. This generalizes well-studied problems, such as Submodular Ranking [Azar and Gamzu 2011] and the Group Steiner Tree [Garg et al. 2000]. We give a polynomial time\n                    <jats:italic toggle=\"yes\">O<\/jats:italic>\n                    (log 1\/\u03f5 \u010b log\n                    <jats:sup>2+\u03b4<\/jats:sup>\n                    |V|)-approximation algorithm for MLSC, where \u03f5 &gt; 0 is the smallest non-zero marginal increase of any {\n                    <jats:italic toggle=\"yes\">\n                      f\n                      <jats:sub>i<\/jats:sub>\n                    <\/jats:italic>\n                    }\n                    <jats:sup>\n                      <jats:italic toggle=\"yes\">m<\/jats:italic>\n                    <\/jats:sup>\n                    <jats:sub>\n                      <jats:italic toggle=\"yes\">i<\/jats:italic>\n                      = 1\n                    <\/jats:sub>\n                    and \u03b4 &gt; 0 is any constant.\n                  <\/jats:p>\n                  <jats:p>\n                    We also consider the Latency Covering Steiner Tree (LCST) problem, which is the special case of MLSC where the\n                    <jats:italic toggle=\"yes\">\n                      f\n                      <jats:sub>i<\/jats:sub>\n                    <\/jats:italic>\n                    s are multi-coverage functions. This is a common generalization of the Latency Group Steiner Tree [Gupta et al. 2010; Chakrabarty and Swamy 2011] and Generalized Min-sum Set Cover [Azar et al. 2009; Bansal et al. 2010] problems. We obtain an\n                    <jats:italic toggle=\"yes\">O<\/jats:italic>\n                    (log\n                    <jats:sup>2<\/jats:sup>\n                    |\n                    <jats:italic toggle=\"yes\">V<\/jats:italic>\n                    |)-approximation algorithm for LCST.\n                  <\/jats:p>\n                  <jats:p>\n                    Finally, we study a natural stochastic extension of the Submodular Ranking problem and obtain an adaptive algorithm with an\n                    <jats:italic toggle=\"yes\">O<\/jats:italic>\n                    (log 1\/\u03f5)-approximation ratio, which is best possible. This result also generalizes some previously studied stochastic optimization problems, such as Stochastic Set Cover [Goemans and Vondr\u00e1k 2006] and Shared Filter Evaluation [Munagala et al. 2007; Liu et al. 2008].\n                  <\/jats:p>","DOI":"10.1145\/2987751","type":"journal-article","created":{"date-parts":[[2016,11,15]],"date-time":"2016-11-15T08:35:02Z","timestamp":1479198902000},"page":"1-28","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":7,"title":["Minimum Latency Submodular Cover"],"prefix":"10.1145","volume":"13","author":[{"given":"Sungjin","family":"Im","sequence":"first","affiliation":[{"name":"University of California, Merced, CA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Viswanath","family":"Nagarajan","sequence":"additional","affiliation":[{"name":"University of Michigan, MI, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruben Van Der","family":"Zwaan","sequence":"additional","affiliation":[{"name":"Maastricht University, MD Maastricht, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2016,11,15]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.5555\/2133036.2133117"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/1536414.1536505"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.5555\/1873601.1873726"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1006\/inco.1997.2677"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/1806689.1806719"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10878-005-1412-9"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.5555\/338219.338241"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.5555\/2018158.2018166"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/11538462_22"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.5555\/946243.946316"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2005.07.010"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.2005.9"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/1290672.1290677"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcss.2004.04.011"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-004-1110-5"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.2000.1096"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1007\/11682462_50"},{"key":"e_1_2_1_18_1","volume-title":"23rd Conference on Learning Theory (COLT). 333--345","author":"Golovin D.","unstructured":"D. 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