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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 provided have been conscientiously reviewed and chosen from sixty two submissions. issues addressed via the workshop are algorithmic online game concept, 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 thoughts, real-world functions, and scheduling problems.

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

Example text

In this problem we are given a set I = {1, 2, . . , m} of base stations that are already opened, a set J = {1, 2, . . , n} of clients. Each base station i ∈ I has capacity wi , and every client j ∈ J has a profit pj and a demand dj which is allowed to be simultaneously satisfied by more than one base station. Each base station i has a coverage area represented by a set Si ⊆ J of clients admissible to be covered (or satisfied) by it. Let P be an m × m × n matrix of interference for satisfying a client by several base stations, as in BCPP.

J|}. Here Qik denotes the first k clients in a linear order with nondecreasing cij . Clearly, other stars cannot be more effective. Hence, we get the same approximation ratio as the budgeted maximum coverage problem. Moreover, since the budgeted maximum coverage can be described, by a simple reduction, as a special case of the budgeted facility location, the best we can hope for the budgeted facility location problem is the same approximation factor as the budgeted maximum coverage problem. 5 D.

This would prove (a) and (b) above. The chain. To show that the bids are indeed decreasing, and to show (c), it turns out that we need to prove some technical lemmas about the difference between Θ and Θ−i for some arbitrary bidder i. In Θ−i , some bidder i takes the place of i (unless i is in the last slot, in which case perhaps no bidder takes this slot). , until either the vacated slot is the bottom slot k, or some previously unassigned bidder is introduced into the solution. We call this sequence of bidder movements ending at slot i the “chain” of moves of Θ−i .

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