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

This ebook constitutes the completely refereed post-proceedings of the 4th foreign 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 awarded have been conscientiously reviewed and chosen from sixty two submissions. subject matters addressed via the workshop are algorithmic video game conception, approximation periods, coloring and partitioning, aggressive research, computational finance, cuts and connectivity, geometric difficulties, inapproximability effects, mechanism layout, community layout, packing and masking, paradigms, randomization ideas, real-world purposes, 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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38 D. Amzallag, J. Naor, and D. Raz Algorithm 2 [cycle canceling with interference]. As long as there are cycles in GΔ , pick a cycle C = (v1 , . . , vk = v1 ) where odd vertices represent base stations. As before, every edge ei = (vi , vi+1 ) on the cycle has a weight w(vi , vi+1 ) associated with it, representing the amount of demand supplied by the base-station-vertex in ei to the client-vertex in ei . For simplicity, let di denote this value. We recursively define a sequence of weights {yi }k−1 i=1 , with alternating signs which represent a shift in the demand supply of base stations to clients along the cycle.

Amzallag, J. Naor, and D. Raz Maximizing Submodular Set Functions Let U = {1, . . , n}, let cu , u ∈ U be a set of nonnegative weights, and let B be a nonnegative budget. The problem of maximizing nondecreasing submodular set function with budget constraint is cu ≤ B max f (S) : S⊆U , u∈S where f (S) is a nonnegative nondecreasing submodular polynomially computable set function (a set function is submodular if f (S) + f (T ) ≥ f (S ∪ T ) + f (S ∩ T ) for all S, T ⊆ U and nondecreasing if f (S) ≤ f (T ) for all S ⊆ T ).

9. : Microeconomic Theory. il Abstract. Cell planning includes planning a network of base stations providing a coverage of the service area with respect to current and future traffic requirements, available capacities, interference, and the desired quality-of-service. This paper studies cell planning under budget constraints through a very close-to-practice model. This problem generalizes several problems such as budgeted maximum coverage, budgeted unique coverage, and the budgeted version of the facility location problem.

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