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Priority Algorithms for Makespan Minimization in the Subset Mo del Oded Regev  February 14, 2002 Keywords: algorithmical approximation, scheduling Abstract We continue the recent study of priority algorithms initiated by Boro din et al. [3]. The de nition of a priority algorithm nicely cap- tures the idea of a \greedy-like typ e algorithm. While priority algo- rithms are applicable to many optimization problems, in this pap er we consider the problem of makespan minimization in scheduling in the subset mo del. We show that by using a xed priority algorithm e a considerable improvement over the approxima- one cannot achiev tion ratio given by the online greedy algorithm. Namely, we present an ( log m ) lower b ound on the approximation ratio of any xed log log m priority algorithm where m is the numb er of machines. 1 Intro duction In a recent pap er [3], Boro din et al. de ned the notion of a \greedy-like algorithm. The de nition is based on the observation that greedy-like al- gorithms satisfy the prop erty that the output is constructed incrementally with each input item b eing considered once. Following this observation, they de ne a Fixed Priority algorithm as an algorithm that determines a total ordering on all p ossible input items without actually seeing the input items. Then the algorithm pro ceeds with pro cessing one element of the input at a time following this order. It is imp ortant to note that the decisions taken  Institute for Advanced Study, Princeton, NJ. E-Mail: o de