{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T18:59:55Z","timestamp":1767034795123,"version":"3.41.0"},"reference-count":41,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2008,5,1]],"date-time":"2008-05-01T00:00:00Z","timestamp":1209600000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100004965","name":"Sixth Framework Programme","doi-asserted-by":"publisher","award":["IST-1999-14084"],"award-info":[{"award-number":["IST-1999-14084"]}],"id":[{"id":"10.13039\/501100004965","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCR-0105548","CCR-0122581"],"award-info":[{"award-number":["CCR-0105548","CCR-0122581"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000143","name":"Division of Computing and Communication Foundations","doi-asserted-by":"publisher","award":["CCF-448095"],"award-info":[{"award-number":["CCF-448095"]}],"id":[{"id":"10.13039\/100000143","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001742","name":"United States-Israel Binational Science Foundation","doi-asserted-by":"publisher","award":["2002-276"],"award-info":[{"award-number":["2002-276"]}],"id":[{"id":"10.13039\/501100001742","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":[[2008,5]]},"abstract":"<jats:p>\n            Consider the following classical network design problem: a set of terminals\n            <jats:italic>T<\/jats:italic>\n            = {\n            <jats:italic>\n              t\n              <jats:sub>i<\/jats:sub>\n            <\/jats:italic>\n            } wishes to send traffic to a root\n            <jats:italic>r<\/jats:italic>\n            in an\n            <jats:italic>n<\/jats:italic>\n            -node graph\n            <jats:italic>G<\/jats:italic>\n            = (\n            <jats:italic>V<\/jats:italic>\n            ,\n            <jats:italic>E<\/jats:italic>\n            ). Each terminal\n            <jats:italic>\n              t\n              <jats:sub>i<\/jats:sub>\n            <\/jats:italic>\n            sends\n            <jats:italic>\n              d\n              <jats:sub>i<\/jats:sub>\n            <\/jats:italic>\n            units of traffic and enough bandwidth has to be allocated on the edges to permit this. However, bandwidth on an edge\n            <jats:italic>e<\/jats:italic>\n            can only be allocated in\n            <jats:italic>integral<\/jats:italic>\n            multiples of some base capacity\n            <jats:italic>\n              u\n              <jats:sub>e<\/jats:sub>\n            <\/jats:italic>\n            and hence provisioning\n            <jats:italic>k<\/jats:italic>\n            \u00d7\n            <jats:italic>\n              u\n              <jats:sub>e<\/jats:sub>\n            <\/jats:italic>\n            bandwidth on edge\n            <jats:italic>e<\/jats:italic>\n            incurs a cost of \u2308k\u2309 times the cost of that edge. The objective is a minimum-cost feasible solution.\n          <\/jats:p>\n          <jats:p>This is one of many network design problems widely studied where the bandwidth allocation is governed by side constraints: edges can only allow a subset of cables to be purchased on them or certain quality-of-service requirements may have to be met.<\/jats:p>\n          <jats:p>\n            In this work, we show that this problem and, in fact, several basic problems in this general network design framework cannot be approximated better than \u03a9(log log\n            <jats:italic>n<\/jats:italic>\n            ) unless NP \u2286 DTIME (\n            <jats:italic>n<\/jats:italic>\n            <jats:sup>\n              <jats:italic>O<\/jats:italic>\n              (log log log\n              <jats:italic>n<\/jats:italic>\n              )\n            <\/jats:sup>\n            ), where |\n            <jats:italic>V<\/jats:italic>\n            | =\n            <jats:italic>n<\/jats:italic>\n            . In particular, we show that this inapproximability threshold holds for (i) the Priority-Steiner Tree problem, (ii) the (single-sink) Cost-Distance problem, and (iii) the single-sink version of an even more fundamental problem, Fixed Charge Network Flow. Our results provide a further breakthrough in the understanding of the level of complexity of network design problems. These are the first nonconstant hardness results known for all these problems.\n          <\/jats:p>","DOI":"10.1145\/1361192.1361200","type":"journal-article","created":{"date-parts":[[2008,6,3]],"date-time":"2008-06-03T15:11:43Z","timestamp":1212505903000},"page":"1-17","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":23,"title":["On the approximability of some network design problems"],"prefix":"10.1145","volume":"4","author":[{"given":"Julia","family":"Chuzhoy","sequence":"first","affiliation":[{"name":"Computer Science and Artificial Intelligence Laboratory, MIT and, University of Pennsylvania"}]},{"given":"Anupam","family":"Gupta","sequence":"additional","affiliation":[{"name":"Carnegie Mellon University, Pittsburgh, PA"}]},{"given":"Joseph (Seffi)","family":"Naor","sequence":"additional","affiliation":[{"name":"Technion, Israel, Haifa, Israel"}]},{"given":"Amitabh","family":"Sinha","sequence":"additional","affiliation":[{"name":"University of Michigan, Ann Arbor, MI"}]}],"member":"320","published-online":{"date-parts":[[2008,5,29]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2004.32"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-002-0968-3"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/278298.278306"},{"volume-title":"Proceedings of the 38th Annual IEEE Symposium on Foundations of Computer Science. 542--547","author":"Awerbuch B.","key":"e_1_2_1_4_1"},{"volume-title":"Proceedings of the 11th Annual ACM-SIAM Symposium on Discrete. 106--115","author":"Carr R. 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