{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T04:27:20Z","timestamp":1788236840440,"version":"build-2803163510"},"reference-count":27,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2021,3,18]],"date-time":"2021-03-18T00:00:00Z","timestamp":1616025600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000001","name":"NSF","doi-asserted-by":"publisher","award":["DMS-1855464"],"award-info":[{"award-number":["DMS-1855464"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"name":"BSF","award":["2018267"],"award-info":[{"award-number":["2018267"]}]},{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"publisher","award":["281\/17+2304\/20+1506\/16"],"award-info":[{"award-number":["281\/17+2304\/20+1506\/16"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Parallel Comput."],"published-print":{"date-parts":[[2021,3,31]]},"abstract":"<jats:p>\n            In this article we provide a tight bound for the\n            <jats:italic>price of preemption<\/jats:italic>\n            for scheduling jobs on a single machine (or multiple machines). The input consists of a set of jobs to be scheduled and of an integer parameter\n            <jats:italic>k<\/jats:italic>\n            \u2265 1. Each job has a release time, deadline, length (also called processing time), and value associated with it. The goal is to feasibly schedule a subset of the jobs so that their total value is maximal; while preemption of a job is permitted, a job may be preempted no more than\n            <jats:italic>k<\/jats:italic>\n            times. The price of preemption is the worst possible (i.e., largest) ratio of the optimal non-bounded-preemptive scheduling to the optimal\n            <jats:italic>k<\/jats:italic>\n            -bounded-preemptive scheduling.\n          <\/jats:p>\n          <jats:p>\n            Our results show that allowing at most\n            <jats:italic>k<\/jats:italic>\n            preemptions suffices to guarantee a \u0398(min {log\n            <jats:sub>\n              <jats:italic>k<\/jats:italic>\n              +1\n            <\/jats:sub>\n            <jats:italic>n<\/jats:italic>\n            , log\n            <jats:sub>\n              <jats:italic>k<\/jats:italic>\n              +1\n            <\/jats:sub>\n            <jats:italic>P<\/jats:italic>\n            }) fraction of the total value achieved when the number of preemptions is unrestricted (where\n            <jats:italic>n<\/jats:italic>\n            is the number of the jobs and\n            <jats:italic>P<\/jats:italic>\n            the ratio of the maximal length to the minimal length), giving us an upper bound for the price; a specific scenario serves to prove the tightness of this bound. We further show that when no preemptions are permitted at all (i.e.,\n            <jats:italic>k<\/jats:italic>\n            =0), the price is \u0398 (min {\n            <jats:italic>n<\/jats:italic>\n            , log\n            <jats:italic>P<\/jats:italic>\n            }).\n          <\/jats:p>\n          <jats:p>\n            As part of the proof, we introduce the notion of the\n            <jats:italic>Bounded-Degree Ancestor-Free Sub-Forest (BAS)<\/jats:italic>\n            . We investigate the problem of computing the maximal-value BAS of a given forest and give a tight bound for the loss factor, which is \u0398(log\n            <jats:sub>\n              <jats:italic>k<\/jats:italic>\n              +1\n            <\/jats:sub>\n            <jats:italic>n<\/jats:italic>\n            ) as well, where\n            <jats:italic>n<\/jats:italic>\n            is the size of the original forest and\n            <jats:italic>k<\/jats:italic>\n            is the bound on the degree of the sub-forest.\n          <\/jats:p>","DOI":"10.1145\/3434377","type":"journal-article","created":{"date-parts":[[2021,3,18]],"date-time":"2021-03-18T10:48:30Z","timestamp":1616064510000},"page":"1-21","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["The Price of Bounded Preemption"],"prefix":"10.1145","volume":"8","author":[{"given":"Noga","family":"Alon","sequence":"first","affiliation":[{"name":"Princeton University, USA and Tel-Aviv University, Tel-Aviv, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yossi","family":"Azar","sequence":"additional","affiliation":[{"name":"Tel-Aviv University, Tel-Aviv, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mark","family":"Berlin","sequence":"additional","affiliation":[{"name":"Tel-Aviv University, Tel-Aviv, Israel"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2021,3,18]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611974317.11"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-001-0039-1"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-016-0257-1"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-005-1172-z"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-1425(199911\/12)2:6<245::AID-JOS28>3.0.CO;2-5"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.orl.2003.09.004"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/502102.502107"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539799354138"},{"key":"e_1_2_1_9_1","first-page":"27","article-title":"A local ratio theorem for approximating the weighted vertex cover problem","volume":"25","author":"Bar-Yehuda Reuven","year":"1985","unstructured":"Reuven Bar-Yehuda and Shimon Even . 1985 . 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