By Nikhil Bansal (auth.), Thomas Erlebach, Giuseppe Persiano (eds.)

This e-book constitutes the completely refereed publish workshop complaints of the tenth overseas Workshop on Approximation and on-line Algorithms, WAOA 2012, held in Ljubljana, Slovenia, in September 2012 as a part of the ALGO 2012 convention occasion. The 22 revised complete papers awarded including invited speak have been rigorously reviewed and chosen from 60 submissions. The workshop coated parts corresponding to geometric difficulties, on-line algorithms, scheduling, algorithmic video game conception, and approximation algorithms.

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Extra info for Approximation and Online Algorithms: 10th International Workshop, WAOA 2012, Ljubljana, Slovenia, September 13-14, 2012, Revised Selected Papers

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One can apply a tri-criteria oracle with granularity O(n−2 ), to obtain an (O(1), O(log(nT )))-competitive ratio for known durations even with high demands. All-or-Nothing Machine Scheduling. A simple application of our algorithm is the case of maximizing throughput in an online job all-or-nothing scheduling problem on unrelated machines. The variant in which the objective is to minimize the load was studied by Aspnes et al. [4]. We, on the other hand, focus on maximizing the throughput. Jobs arrive online, and may be assigned to multiple machines immediately upon arrival.

Chimani and J. Spoerhase Figure 1(b) shows an instance (in fact, a repetitive pattern) which requires branch nodes. Each pattern has 12 nodes, the figure shows three repetitions. A final instance would consist of k repetitions, with some constant size “caps” on the left and right end of the graph structure. The optimum solution requires 2 branch nodes and hence allows 10 path nodes per pattern, whereas the algorithm may terminate with only 7 path nodes (5 branch nodes) per pattern. Hence, this example would result in a ratio of (asymptotically) 7/10.

For two clients to be able to communicate in the network, the regenerators must be placed such that lightpaths can be formed between them such that there is at least one regenerator in every d consecutive vertices of each path. A regenerator can serve only one lightpath. Regenerators are rather expensive equipment, and much research has been conducted, concerning minimizing their usage while satisfying all or most of the communication requirements posed by clients. The cost of regenerators in a network is measured in two main ways: – The number of regenerators placed in the network.

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