On the Configuration-LP of the Restricted Assignment Problem
On the Configuration-LP of the Restricted Assignment Problem
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DOI：
10.1137/1.9781611974782.176
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发表时间：
2016-11
期刊：
影响因子：
--
通讯作者：
K. Jansen;Lars Rohwedder
中科院分区：
文献类型：
--
作者：
K. Jansen;Lars Rohwedder
We consider the classical problem of S cheduling on U nrelated M achines . In this problem a set of jobs is to be distributed among a set of machines and the maximum load (makespan) is to be minimized. The processing time pij of a job j depends on the machine i it is assigned to. Lenstra, Shmoys and Tardos gave a polynomial time 2-approximation for this problem [8]. In this paper we focus on a prominent special case, the R estricted A ssignment problem, in which pij ∈ {pj, ∞}. The configuration-LP is a linear programming relaxation for the R estricted A ssignment problem. It was shown by Svensson that the multiplicative gap between integral and fractional solution, the integrality gap, is at most 2 − 1/17 ≈ 1.9412 [11]. In this paper we significantly simplify his proof and achieve a bound of 2 − 1/6 ≈ 1.8333. As a direct consequence this provides a polynomial (2 − 1/6 + ϵ)-estimation algorithm for the R estricted A ssignment problem by approximating the configuration-LP. The best lower bound known for the integrality gap is 1.5 and no estimation algorithm with a guarantee better than 1.5 exists unless P = NP.
