By Udo Adamy, Thomas Erlebach (auth.), Roberto Solis-Oba, Klaus Jansen (eds.)

The Workshop on Approximation and on-line Algorithms (WAOA 2003) occupied with the layout and research of algorithms for on-line and computationally challenging difficulties. either forms of difficulties have lots of functions ar- ing from numerous ?elds. The workshop additionally lined experimental study on approximation and on-line algorithms. WAOA 2003 happened in Budapest, Hungary, from September sixteen to September 18. The workshop was once a part of the ALGO 2003 occasion, which additionally hosted ESA 2003, WABI 2003, and ATMOS 2003. TopicsofinterestforWAOA2003were:competitiveanalysis,inapproximab- ityresults,randomizationtechniques,approximationclasses,scheduling,coloring and partitioning, cuts and connectivity, packing and protecting, geometric pr- lems, community layout, and functions to online game idea and ?nancial difficulties. based on our demand papers we got forty-one submissions. each one submission was once reviewed through at the very least three referees, who judged the papers on originality, caliber, and consistency with the subjects of the convention. in line with those reports this system committee chosen 19 papers for presentation on the workshop and for ebook during this complaints. This quantity includes the nineteen chosen papers and five invited abstracts from an ARACNE minisymposium which came about as a part of WAOA.

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To prove that the decision problem is NP-complete, we construct a reduction from the Modiff-4Sat problem. The technique used in our 22 Alexander A. Ageev et al. reduction diﬀers from the one used in Williamson et. al. [15] in the following: instead of associating jobs and machines with literals (which obliges one to synchronize the jobs corresponding to literals of the same variable), we associate them with variables. As a straightforward corollary of the above theorem, we obtain Theorem 7. For the OB-problem with a variable number of machines and for any ρ < 11/10, there is no polynomial time ρ-approximation algorithm, unless P = NP.

Thus, we come to the following algorithm Aε in the case dmax > ε · max . Algorithm Aε (in the case dmax > ε · max ): Step 1. 25 · 2−m/ε · max . Number the jobs with dj > d in nonincreasing order of dj . Step 2. Find a partition of the job set into subsets L, M , and S satisfying (a)–(c). Step 3. Construct an optimal schedule OP T (L) for the jobs in L. Step 4. Use the greedy algorithm [13] to place the jobs of M and S into OP T (L). Similar to [13], the following result can be proved. Theorem 10.

22. M. Mahdian, J. Ye, and J. Zhang. 52-approximation algorithm for the uncapacitated facility location problem. In Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, pages 229–242, 2002. 23. R. R. Mettu and C. G. Plaxton. The online median problem. In Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science, pages 339–348, 2000. 24. A. Meyerson. Online facility location. In Proceedings of the 42nd Annual IEEE Symposium on Foundations of Computer Science, pages 426–431, 2001.