{"id":700834,"date":"2020-10-23T13:39:04","date_gmt":"2020-10-23T20:39:04","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=700834"},"modified":"2021-06-11T06:36:16","modified_gmt":"2021-06-11T13:36:16","slug":"scheduling-with-communication-delays-via-lp-hierarchies-and-clustering","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/scheduling-with-communication-delays-via-lp-hierarchies-and-clustering\/","title":{"rendered":"Scheduling with Communication Delays via LP Hierarchies and Clustering"},"content":{"rendered":"

We consider the classic problem of scheduling jobs with precedence constraints on identical machines to minimize makespan, in the presence of communication delays. In this setting, denoted by P | prec, c<\/em> | C<\/em>max, if two dependent jobs are scheduled on different machines, then at least c units of time must pass between their executions. Despite its relevance to many applications, this model remains one of the most poorly understood in scheduling theory. Even for a special case where an unlimited number of machines is available, the best known approximation ratio is 2\/3 \u00b7(c<\/em> + 1), whereas Graham\u2019s greedy list scheduling algorithm already gives a (c<\/em> + 1)- approximation in that setting. An outstanding open problem in the top-10 list by Schuurman and Woeginger and its recent update by Bansal asks whether there exists a constant-factor approximation algorithm.<\/p>\n

In this work we give a polynomial-time O<\/em>(log c<\/em> \u00b7 log m<\/em>)-approximation algorithm for this problem, where m<\/em> is the number of machines and c<\/em> is the communication delay. Our approach is based on a Sherali-Adams lift of a linear programming relaxation and a randomized clustering of the semimetric space induced by this lift.<\/p>\n","protected":false},"excerpt":{"rendered":"

We consider the classic problem of scheduling jobs with precedence constraints on identical machines to minimize makespan, in the presence of communication delays. In this setting, denoted by P | prec, c | Cmax, if two dependent jobs are scheduled on different machines, then at least c units of time must pass between their executions. 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Davies","user_id":0,"rest_url":false},{"type":"user_nicename","value":"Janardhan Kulkarni","user_id":32147,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Janardhan Kulkarni"},{"type":"text","value":"Thomas Rothvoss","user_id":0,"rest_url":false},{"type":"user_nicename","value":"Jakub Tarnawski","user_id":38820,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Jakub Tarnawski"},{"type":"text","value":"Yihao 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