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

This booklet constitutes the joint refereed lawsuits of the 4th overseas Workshop on Approximation Algorithms for Optimization difficulties, APPROX 2001 and of the fifth foreign Workshop on Ranomization and Approximation options in desktop technology, RANDOM 2001, held in Berkeley, California, united states in August 2001. The 26 revised complete papers provided 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 periods, randomized complexity idea, scheduling, routing, coloring, partitioning, packing, masking, computational geometry, community layout, and functions in quite a few fields.

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**Extra resources for Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques: 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2001 and 5th International Workshop on Randomization and Approx**

**Example text**

T. F x ← LRmin(p − δ) Return x Theorem 3. Algorithm LRmin outputs an r-approximate solution. 4 Primal-Dual In [15] Goemans and Williamson presented a generic algorithm based on the hitting set problem which is deﬁned as follows: Given subsets T1 , . . , Tq ⊆ E Primal-Dual Schema and Local-Ratio Technique 29 and a non-negative cost ce for every element e ∈ E, ﬁnd a minimum-cost subset x ⊆ E such that x∩Ti = ∅ for every i ∈ {1, . . , q}. In turns out that many known problems are special cases of this problem.

Am , bm ) be the sequence of all intervals in B obtained by sorting them by increasing end index, where intervals with the same end index are sorted by increasing start index breaking ties arbitrarily. One can easily verify that in an optimal schedule for B, stall times occur at the end of intervals, the fetch in (a1 , b1 ) is started at the latest point in time (i. e. immediately before request a2 if b1 = a1 and after a1 otherwise) whereas the fetches in (ai , bi ), i ≥ 2, are started at the earliest point in time.

A 2-approximation algorithm for the undirected feedback vertex set problem. SIAM J. on Disc. , 12(3):289–297, 1999. 2. A. Bar-Noy, R. Bar-Yehuda, A. Freund, J. Naor, and B. Shieber. A uniﬁed approach to approximating resource allocation and scheduling. In 32nd ACM Symposium on the Theory of Computing, 2000. 3. R. Bar-Yehuda. One for the price of two: A uniﬁed approach for approximating covering problems. Algorithmica, 27(2):131–144, 2000. 4. R. Bar-Yehuda and S. Even. A linear time approximation algorithm for the weighted vertex cover problem.