{"id":168291,"date":"2014-05-01T00:00:00","date_gmt":"2014-05-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/cluster-before-you-hallucinate-approximating-node-capacitated-network-design-and-energy-efficient-routing\/"},"modified":"2018-10-16T20:13:25","modified_gmt":"2018-10-17T03:13:25","slug":"cluster-before-you-hallucinate-approximating-node-capacitated-network-design-and-energy-efficient-routing","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/cluster-before-you-hallucinate-approximating-node-capacitated-network-design-and-energy-efficient-routing\/","title":{"rendered":"Cluster Before You Hallucinate: Approximating Node-capacitated Network Design and Energy Efficient Routing"},"content":{"rendered":"<p>We consider circuit routing with an objective of minimizing energy, in a network of routers that are speed scalable and that may be shutdown when idle. It is known that this energy minimization problem can be reduced to a capacitated flow network design problem, where vertices have a common capacity but arbitrary costs, and the goal is to choose a minimum cost collection of vertices whose induced subgraph will support the specified flow requirements. For the multicast (single-sink) capacitated design problem we give a polynomial-time algorithm that is <i>O<\/i>(log<sup>3<\/sup> <i>n<\/i>)- approximate with <i>O<\/i>(log<sup>4<\/sup> <i>n<\/i>) congestion. This translates back to a <i>O<\/i>(log<sup>4\u03b1+3<\/sup> <i>n<\/i>)-approximation for the multicast energy-minimization routing problem, where \u03b1 is the polynomial exponent in the dynamic power used by a router. For the unicast (multicommodity) capacitated design problem we give a polynomial-time algorithm that is <i>O<\/i>(log<sup>5<\/sup> <i>n<\/i>)-approximate with <i>O<\/i>(log<sup>12<\/sup> <i>n<\/i>) congestion, which translates back to a <i>O<\/i>(log<sup>12\u03b1+5<\/sup> <i>n<\/i>)-approximation for the unicast energy-minimization routing problem.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We consider circuit routing with an objective of minimizing energy, in a network of routers that are speed scalable and that may be shutdown when idle. It is known that this energy minimization problem can be reduced to a capacitated flow network design problem, where vertices have a common capacity but arbitrary costs, and the [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"ACM","msr_publisher_other":"","msr_booktitle":"Proceedings of the 46th Annual ACM Symposium on Theory of Computing","msr_chapter":"","msr_edition":"Proceedings of the 46th Annual ACM Symposium on Theory of Computing","msr_editors":"","msr_how_published":"","msr_isbn":"978-1-4503-2710-7","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"734\u2013743","msr_page_range_start":"734","msr_page_range_end":"743","msr_series":"STOC '14","msr_volume":"","msr_copyright":"","msr_conference_name":"Proceedings of 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