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

ISBN-10: 3540210792

ISBN-13: 9783540210795

The Workshop on Approximation and on-line Algorithms (WAOA 2003) thinking about the layout and research of algorithms for on-line and computationally difficult difficulties. either types of difficulties have numerous purposes ar- ing from various ?elds. The workshop additionally coated experimental study on approximation and on-line algorithms. WAOA 2003 came about in Budapest, Hungary, from September sixteen to September 18. The workshop used to be 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 masking, geometric pr- lems, community layout, and functions to video game thought and ?nancial difficulties. according to our demand papers we bought forty-one submissions. every one submission was once reviewed through at the least three referees, who judged the papers on originality, caliber, and consistency with the themes of the convention. in response to those experiences this system committee chosen 19 papers for presentation on the workshop and for book during this lawsuits. This quantity includes the nineteen chosen papers and five invited abstracts from an ARACNE minisymposium which happened as a part of WAOA.

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Additional resources for Approximation and Online Algorithms: First International Workshop, WAOA 2003, Budapest, Hungary, September 16-18, 2003. Revised Papers

Example text

Such that their total length is at most 9), it should be shown that there exists a schedule for that machine in which each i-job is assigned to one of its allowed locations. Define a set Li of allowed locations for each i ∈ {2, . . , 9} as follows: L9 = {[0, 9]}, L8 = {[1, 9]}, L7 = {[2, 9]}, L6 = {[3, 9]}, L5 = {[4, 9]}, L4 = {[0, 4], [4, 8]}, L3 = {[0, 3], [3, 6], [6, 9]}, L2 = {[0, 2], [2, 4], [4, 6], [6, 8]} (clearly, 1-jobs may be scheduled arbitrarily). It can be easily checked that, given a family of jobs {J1 , .

The desired (1 + ε)-approximation can be easily attained in the case that dmax ≤ ε · max : a simple greedy algorithm [13] finds a schedule S with makespan Cmax (S) ≤ max + dmax ≤ (1 + ε) max ≤ (1 + ε)OP T in time O(m2 n). The running time can be reduced to O(nm + C(m, ε)), if we first apply the following Second gluing procedure with d = ε · max . Given a lower threshold d on lengths of jobs, we scan the list of jobs, gluing two jobs Open Block Scheduling in Optical Communication Networks 25 together each time that the maximum of their lengths is no greater than d/2.

In the case dmax > ε · max we divide the set of jobs J into three subsets L, M, S of large, medium, and small jobs, respectively: L = {Jj ∈ J | dj ≥ α max }, M = {Jj ∈ J | α max ≤ dj < α max }, S = {Jj ∈ J | dj < α max }. The values of α and α are chosen with respect to the value of ε so that: (a) the number |L| of large jobs was bounded above by a constant; (b) the total length of medium jobs was at most ε · max ; (c) the ratio α /α was small enough, so as to meet α + α + α |L| ≤ ε. As proved in [13], the numbers α and α with the above properties exist, .

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Approximation and Online Algorithms: First International Workshop, WAOA 2003, Budapest, Hungary, September 16-18, 2003. Revised Papers by Udo Adamy, Thomas Erlebach (auth.), Roberto Solis-Oba, Klaus Jansen (eds.)

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