Improved Approximation Algorithms for Shop Scheduling Problems
SIAM Journal on Computing
Improved bounds for acyclic job shop scheduling (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Better approximation guarantees for job-shop scheduling
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Universal Routing Strategies for Interconnection Networks
Universal Routing Strategies for Interconnection Networks
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We consider the job shop scheduling problem unit-Jm, where each job is processed once on each of m given machines. The execution of anyt ask on its corresponding machine takes exactly one time unit. The objective is to minimize the overall completion time, called makespan. The contribution of this paper are the following results: (i) For anyi nput instance of unit-Jmwith d jobs, the makespan of an optimum schedule is at most m+o(m), for d = o(m1/2). For d = o(m1/2), this improves on the upper bound O(m+d) given in [LMR99] with a constant equal to two as shown in [S98]. For d = 2 the upper bound is improved to m + 驴驴m驴. (ii) There exist input instances of unit-Jm with d = 2 such that the makespan of an optimum schedule is at least m+驴驴m驴, i.e., the result (i) cannot be improved for d = 2. (iii) We present a randomized on-line approximation algorithm for unit-Jmwith the best known approximation ratio for d = o(m1/2). (iv) A deterministic approximation algorithm for unit-Jm is described that works in quadratic time for constant d and has an approximation ratio of 1 + 2d/驴驴m驴 for d 驴 2 log2m.