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We give the first O(1)-speed O(1)-approximation polynomial-time algorithms for several nonpreemptive minsum scheduling problems where jobs arrive over time and must be processed on one machine. More precisely, we give the first O(1)-speed O(1)-approximations for the nonpreemptive scheduling problems and an O(1)-machine, O(1)-speed O(1)-approximation for Our main contribution is an integer programming formulation whose relaxation is sufficiently close to the integer optimum, and which can be transformed to a schedule on a faster machine.doi:10.1109/focs.2007.11 dblp:conf/focs/FischerMS07 fatcat:7tbgzvw4o5hohgrjxsdwbiffle