By Raimund Seidel (auth.), Lars Arge, Rusins Freivalds (eds.)

ISBN-10: 354035753X

ISBN-13: 9783540357537

This ebook constitutes the refereed court cases of the tenth Scandinavian Workshop on set of rules concept, SWAT 2006, held in Riga, Latvia, in July 2006.

The complaints comprises 36 revised complete papers awarded including three invited papers, addressing problems with theoretical algorithmics and purposes in a variety of fields together with graph algorithms, computational geometry, scheduling, approximation algorithms, community algorithms, information garage and manipulation, combinatorics, sorting, looking out, on-line algorithms, optimization, amd more.

**Read or Download Algorithm Theory – SWAT 2006: 10th Scandinavian Workshop on Algorithm Theory, Riga, Latvia, July 6-8, 2006. Proceedings PDF**

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**Additional resources for Algorithm Theory – SWAT 2006: 10th Scandinavian Workshop on Algorithm Theory, Riga, Latvia, July 6-8, 2006. Proceedings**

**Example text**

X as well as the sequence b(x0 ), . . , b(x ) of bins. For any chain of items, x0 , x1 , . . , x , we let b (x0 ) = bo (x ) denote the bin where OPT places the last item of the chain. Note that b (x0 ) is not part of the chain. We now deﬁne one more set of bins: L: the set of bins which are b (x) for some x ∈ F < . The main ideas of the proof are that all chains are well deﬁned, the total size of bins in F < \ F < is small, the items packed in F < all ﬁt in L, and most bins in L are ﬁlled to at least α full.

Epstein, T. Erlebach, and A. Levin Adamy and Erlebach [1] introduced the interval coloring with bandwidth problem and presented a 195-competitive algorithm. In this problem each interval has a bandwidth requirement in (0, 1]. The intervals are to be colored so that at each point, the sum of bandwidths of intervals colored by a certain color does not exceed 1. 2609. We study a variant of this problem, where colors are not necessarily of capacity 1 as in [1]. The input arrives as in this model, but an algorithm may use colors of arbitrary capacity.

Before we construct the lower bound we note that we assume for ease of presentation that bandwidth requirements can be numbers larger than 1. Clearly, the unbounded model is equivalent to any model where the bandwidths are bounded by some constant (not necessarily 1). Before presenting the sequence, we can compute a bound on the largest bandwidth needed for the proof, and thus our lower bound satisﬁes the model. Our construction of the lower bound for the unbounded model is based on instances in which OPT equals the maximum load, whereas the algorithm tries to guess an upper bound on the maximum load, and pays the sum of all its guesses.

### Algorithm Theory – SWAT 2006: 10th Scandinavian Workshop on Algorithm Theory, Riga, Latvia, July 6-8, 2006. Proceedings by Raimund Seidel (auth.), Lars Arge, Rusins Freivalds (eds.)

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