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By Alexander A. Ageev, Alexander V. Kononov (auth.), Thomas Erlebach, Christos Kaklamanis (eds.)

This booklet constitutes the completely refereed post-proceedings of the 4th overseas Workshop on Approximation and on-line Algorithms, WAOA 2006, held in Zurich, Switzerland in September 2006 as a part of the ALGO 2006 convention event.

The 26 revised complete papers provided have been conscientiously reviewed and chosen from sixty two submissions. themes addressed through the workshop are algorithmic online game concept, approximation sessions, coloring and partitioning, aggressive research, computational finance, cuts and connectivity, geometric difficulties, inapproximability effects, mechanism layout, community layout, packing and protecting, paradigms, randomization strategies, real-world functions, and scheduling problems.

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Extra info for Approximation and Online Algorithms: 4th International Workshop, WAOA 2006, Zurich, Switzerland, September 14-15, 2006. Revised Papers

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The following lemma is a key component in the analysis of our approximation algorithm. Lemma 1. Every solution to the k4k-budgeted cell planning problem can be transformed to a solution in which the number of clients that are covered by more than one base station is at most the number of opened base stations. Moreover, this transformation leaves the number of fully satisfied clients as well as the solution cost unchanged. Proof. Consider a solution Δ = {I , J , x} to the k4k-BCPP , where I ⊆ I is the set of base stations selected for opening, J ⊆ J is the set of fully satisfied clients, xij ’s are the base station-client coverage rates, and J ⊆ J is the set of clients that are satisfied by more than one base station.

In Proceedings of the Conference on Integer Programming and Combinatorial Optimization, volume 1610 of Lecture Notes in Computer Science, pages 17–30. Springer-Verlag, Berlin, 1999. 2. D. Amzallag, R. Engelberg, J. Naor, and D. Raz. Approximation algorithms for cell planning problems. Manuscript, 2006. 3. D. Amzallag, M. Livschitz, J. Naor, and D. Raz. Cell planning of 4G cellular networks: Algorithmic techniques, and results. In Proceedings of the 6th IEE International Conference on 3G & Beyond (3G’2005), pages 501–506, 2005.

However, one can assume for optimal solutions that these cases do not occur (as the solution could be transformed into an equivalent solution where such edges have w(vi , vi+1 ) = 0). To demonstrate the idea of canceling cycles when interferences exist let us assume, for simplicity, that there is only a single base station which is not on the cycle, denoted by vo , which participates in the coverage of client vi , and the interference model is assumed to be the one in (4). Then, the total contribution of base stations vi−1 , vi+1 , and vo to the coverage of client vi is, by (1), δ(vi ) = Q(v0 , vi ) + Q(vi+1 , vi ) + Q(vi−1 , vi ).

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