Scheduling to minimize gaps and power consumption

This paper considers scheduling tasks while minimizing the power consumption of one or more processors, each of which can go to sleep at a fixed cost α . There are two natural versions of this problem, both considered extensively in recent work: minimize the total power consumption (including computation time), or minimize the number of “gaps” in execution. For both versions in a multiprocessor system, we develop a polynomial-time algorithm based on sophisticated dynamic programming. In a generalization of the power-saving problem, where each task can execute in any of a specified set of time intervals, we develop a (1+23α) -approximation, and show that dependence on α is necessary. In contrast, the analogous multi-interval gap scheduling problem is set-cover hard (and thus not o(lgn) -approximable), even in the special cases of just two intervals per job or just three unit intervals per job. We also prove several other hardness-of-approximation results. Finally, we give an O(n√) -approximation for maximizing throughput given a hard upper bound on the number of gaps.Institute for Research in Fundamental Sciences (Iran) (Grant Number CS1385-2-01)Institute for Research in Fundamental Sciences (Iran) (Grant Number CS1384-6-01

ABSTRACT

This paper considers scheduling tasks while minimizing the power consumption of one or more processors, each of which can go to sleep at a fixed cost α. There are two natural versions of this problem, both considered extensively in recent work: minimize the total power consumption (including computation time), or minimize the number of “gaps” in execution. For both versions in a multiprocessor system, we develop a polynomial-time algorithm based on sophisticated dynamic programming. In a generalization of the power-saving problem, where each task can execute in any of a specified set of time intervals, we develop a (1 + 2 3 α)approximation, and show that dependence on α is necessary. In contrast, the analogous multi-interval gap scheduling problem is set-cover hard (and thus not o(lg n)-approximable), even in the special cases of just two intervals per job or just three unit intervals per job. We also prove several other hardness-of-approximation results. Finally, we give an O ( √ n)-approximation for maximizing throughput given a hard upper bound on the number of gaps

Minimizing Movement

We give approximation algorithms and inapproximability results for a class of movement problems. In general, these problems involve planning the coordinated motion of a large collection of objects (representing anything from a robot swarm or firefighter team to map labels or network messages) to achieve a global property of the network while minimizing the maximum or average movement. In particular, we consider the goals of achieving connectivity (undirected and directed), achieving connectivity between a given pair of vertices, achieving independence (a dispersion problem), and achieving a perfect matching (with applications to multicasting). This general family of movement problems encompass an intriguing range of graph and geometric algorithms, with several real-world applications and a surprising range of approximability. In some cases, we obtain tight approximation and inapproximability results using direct techniques (without use of PCP), assuming just that P != NP

Scheduling to minimize gaps and power consumption

This paper considers scheduling tasks while minimizing the power consumptionof one or more processors, each of which can go to sleep at a fixed cost α. There are two natural versions of this problem, both considered extensively in recent work: minimize the total power consumption (including computation time), or minimize the number of “gaps” in execution. For both versions in a multiprocessor system, we develop a polynomial-time algorithm based on sophisticated dynamic programming. In a generalization of the power-saving problem, where each task can execute in any of a specified set of time intervals, we develop a (1 + 2 3 α)approximation, and show that dependence on α is necessary. In contrast, the analogous multi-interval gap scheduling problem is set-cover hard (and thus not o(lg n)-approximable), even in the special cases of just two intervals per job or just three unit intervals per job. We also prove several other hardness-of-approximation results. Finally, we give an O ( √ n)-approximation for maximizing throughput given ahardupperboundonthenumberofgaps