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37. 38. 39. 40. 41. 42. 43. 44. 45. editor, Approximation Algorithms for NP-hard problems, pages 482-520. PWS, Boston, 1995. M. Jerrum, L. Valiant, and V. Vazirani. Random generation of combinatorial structures from a uniform distribution. Theoretical Computer Science, 43:169-188, 1986. R. Karp and M. Luby. Monte-Carlo algorithms for enumeration and realiability problems. In 24th. IEEE Symposium on Foundations of Computer Science, pages 56-64, 1983. P. Kasteley. Dimer statistics and phase transitions.
Improved approximation algorithms for shop scheduling problems. SIAM Journal on Computing 23 (1994), 617-632. 70. B. Sidney. Decomposition algorithms for single-machine sequencing with precedence relations and deferral costs. Operations Research 23 (1975), 283-298. 71. M. Skutella. Semidefinite relaxations for parallel machine scheduling. Proceedings of the 39th Annual IEEE Symposium on Foundations of Computer Science (FOCS'1998), 472-481. Journal version in Journal of the ACM 48, 2001, 206-242.
4 Makespan Minimization on Unrelated Machines In the preceding section we discussed P\ | C m a x , makespan minimization on identical parallel machines. One generalization of this identical machine environment are so-called uniform machines that run at different speeds. Every job Jj has a processing requirement pj: and every machine Mj has a speed Sj. The processing time of job Jj on machine Mj equals Pj/si. Uniform machines are indicated by an entry 'Q' in the a-field. Another generalization are unrelated machines (indicated by an entry lR' in the a-field).