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

ISBN-10: 3642380158

ISBN-13: 9783642380150

ISBN-10: 3642380166

ISBN-13: 9783642380167

This ebook constitutes the completely refereed publish workshop complaints of the tenth foreign 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 components reminiscent of geometric difficulties, on-line algorithms, scheduling, algorithmic video game idea, and approximation algorithms.

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The paper is organized as follows. In Section 2 we describe our local search approximation algorithm. The analysis of the performance guarantee of the algorithm consitutes the main body of this work and is presented in Section 3. Finally, we make some observations concerning the tightness of our analysis in Section 4. 2 Algorithm As pointed out above every spanning tree of the input graph is already a 1/2approximation since at least one half of the nodes in a tree have degree 1 or 2. The worst case of ratio 1/2 occurs when the considered spanning tree consists of only leaves and cubic nodes (nodes with degree 3) while the optimum is a Hamiltonian path or a star with a single high-degree node.

OPT |P | + |C ∪ H| |P | + 5/6|P | 11 (1) It remains how to show the existence of at least 1/5 · |C ∪ H| supplementary leaves or forward nodes in T . We consider the following coin transfer scheme: Initially, each node in C ∪ H receives one coin. In three stages, described in detail below, each node in C transfers its coin either to a forward node or to a high-degree node in T . In doing so, we ensure that the following conditions hold after the transfer scheme: (P1) Only nodes in F ∪ H hold coins, (P2) each node in F holds at most five coins, and (P3) each node v ∈ H holds at most deg(v) + 1 coins.

Even and M. t input sequence σ = {rj }j . Definition 3. An mcf F = (f1 , f2 , . ) is (α, β)-competitive with respect to a sequence {rj }j of requests if for every j: (i) F is α-competitive: benefitj (F ) ≥ 1 ∗ (j) (e) ≤ β · ce . α · benefitj (F ). (ii) F is β-feasible: for every e ∈ E, F Definition 4. An mcf F = (f1 , f2 , . , |fj | ∈ {0, dj }). 2 Description Upon arrival of a request rj , if the request is not feasible, then the algorithm rejects it upfront. Otherwise, if the request is feasible, then alg invokes a tricriteria oracle.

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Approximation and Online Algorithms: 10th International Workshop, WAOA 2012, Ljubljana, Slovenia, September 13-14, 2012, Revised Selected Papers by Nikhil Bansal (auth.), Thomas Erlebach, Giuseppe Persiano (eds.)

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