236605 Advanced Topics Spring Semester, 2000 2 the Approximation Scheme 2.1 Approximation for a Constant Range of Ratios Claim 2.1 Let S Be a Schedule for Which W J
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چکیده
1 Background In the previous lecture we saw a PTAS for the problem PkM 2 i. Recall that M i is the completion time of machine i. In this lecture we present a PTAS for the problem Pk P c j w j , due to Skutella and Woeginger (1999). Some known results for related problems: 1k P w j c j-can be solved in polynomial time using Smith's Ratio Rule. Pk P c j-can be solved in polynomial time using SPT Rule. Pmk P w j c j-is weakly NP-hard and has a FPTAS 1] Rk P c j-can be solved in polynomial time. 4], 5] Rk P w j c j-does not have a PTAS unless P=NP. Pjr j j P w j c j-has a PTAS which is also applicable for Rmjr j j P w j c j. Qjr j j P w j c j-this problem is still open.
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