By Michel Goemans, Klaus Jansen, Jose D.P. Rolim, Luca Trevisan

This e-book constitutes the joint refereed complaints of the 4th overseas Workshop on Approximation Algorithms for Optimization difficulties, APPROX 2001 and of the fifth foreign Workshop on Ranomization and Approximation concepts in desktop technology, RANDOM 2001, held in Berkeley, California, united states in August 2001. The 26 revised complete papers awarded have been rigorously reviewed and chosen from a complete of fifty four submissions. one of the matters addressed are layout and research of approximation algorithms, inapproximability effects, online difficulties, randomization, de-randomization, average-case research, approximation sessions, randomized complexity concept, scheduling, routing, coloring, partitioning, packing, protecting, computational geometry, community layout, and purposes in numerous fields.

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Palmon, and S. Plotkin. Fast approximation algorithm for minimum cost multicommodity ﬂow. In Proc. 6th Annual ACM-SIAM Symp. on Discrete Algorithms, pages 493–501, 1995. 7. R. Karlin and T. Kimbrel. Near-optimal parallel prefetching and caching. In Proc. 37th Annual Symp. on Foundations of Computer Science, pages 540–549. IEEE Society, 1996. il Abstract. We discuss two approximation approaches, the primal-dual schema and the local-ratio technique. We present two relatively simple frameworks, one for each approach, which extend known frameworks for covering problems.

This means, in primal-dual terms, that in the maximization case the dual solution is initially not feasible, and that it becomes feasible at the end of the algorithm. The negative coordinates of the proﬁt vector correspond to the non-tight constraints. In the interval scheduling problem we are given a set of activities, each requiring the utilization of a given resource. The activities are speciﬁed as a collection of sets A1 , . . , Am . Each set represents a single activity: it consists of all possible instances of that activity.

Using techniques from [1], we can convert a fractional solution to the extended LP with cost C to an integral prefetching/caching schedule with stall time C if D −1 extra memory locations in cache are available. Thus we obtain an approximation algorithm of factor 2D/z. Theorem 10. There is a polynomial p(n) such that for each z ∈ {1, . . ) that computes a 2D/z-approximation for IPC provided that D − 1 extra memory locations are available in cache. Finally, for D = 2 the extended linear program does not seem to give an improved approximation.