Summary The Dagstuhl seminar on Combinatorial Approximation Algorithms brought together 54 researchers with affiliations in Austria List of Participants Abstracts Minimizing Service and Operation Costs of Periodic Scheduling Approximating the permanent of a non-negative matrix Dagstuhl-Seminar 9734

Yuval Rabani, David Shmoys, Gerhard Woeginger, Karen Aardal, Yossi Azar, Reuven Bar-Yehuda, Technion Yair Bartal, Berkeley Barvinok, Martin Dyer, David Karger, Howard Karloff, Marek Karpinski (+35 others)
unpublished
In 35 talks the participants presented their latest results on approximation algorithms, covering a wide range of topics. The abstracts of most of these talks can be found in this report. Moreover, there is a list of open problems that were stated in the open problem session. Special events were a hiking tour on Wednesday afternoon and an open problems session held on Thursday evening. In the open problem session, Mark Jerrum, Dorrit Hochbaum, David Shmoys, Vijay Vazirani, and David Williamson
more » ... resented lists with their favorite open problems. Following the example of Paul Erdös, David Williamson offered money rewards for solutions to his open problems; Sanjeev Arora. and Luca Trevisan managed to solve one of his problems (on the Rectilinear Steiner Arborescence problem) by Friday morning. Due to the outstanding local organization and the pleasant atmosphere, this seminar was a most enjoyable and memorable event. We study the problem of scheduling activities of several types under the constraint that at most a fixed number of activities can be scheduled in any single period. Any given activity type is associated with a.service cost, and an operating cost that increases linearly with the number of periods since the last service of this type. The problem is to find an optimal schedule that minimizes the long-runaverage cost per period. Applications of such a model are the scheduling of maintenance service to ma­ chines, multi-item replenishment of stock, and minimizing the mean response time in broadcast disks. Broadcast disks gained a lot of attention recently, since they are used to model backbone communications in wireless systems7 Teletext systems, and web caching in satellite systems. The first contribution of our work is the definition of a general model that com­ bines into one several important previous models. We prove that an optimal cyclic schedule for the general problem exists and establish the NP-hardnessof the prob­ lem. Next we show a lower bound on the cost achieved by an optimal solution. Using this bound we analyze several approximation algorithms. Next, we give a non-trivial 9/8-approximation for a variant of the problem that models the broadcast disks application. The algorithm uses some properties of "Fibonacci sequences". Using this sequence we present a 1.57-approximation algorithm for the general problem. Fi­ nally, we describe a simple randomized algorithm and a. simple deterministic greedy algorithm for the problem, and prove that both achieve approximation factor of 2. To the best of our knowledge this is the first worst case analysis of a widely used greedy heuristic for this problem. Joint work with Randeep Bhatia, Seffi Naor, and Baruch Schieber. A full version of the paper can be found in: Let A = (a,-j) be a non-negative n x n matrix. Let us consider the following algorithm for approximating the permanent of A (Gaussian version of the Godsil-Gutmanesti­ mator). Sample n2 variables Uij at random from the standard Gaussian distribution in R with the density ¢($) = (l/x/2-1r)exp{-rt2/2}.Compute an n X n matrix B = (bij) as follows: b,] = ask-Es Compute 01= (det B)? Output a. It is easy to show that the expectation of ozis the permanent of A, and, therefore,
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