Approximation and Online Algorithms: 10th International by Nikhil Bansal (auth.), Thomas Erlebach, Giuseppe Persiano PDF

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 submit 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 offered including invited speak have been conscientiously reviewed and chosen from 60 submissions. The workshop lined parts akin to geometric difficulties, on-line algorithms, scheduling, algorithmic online 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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46 I. Hartstein, M. Shalom, and S. Zaks Two Fundamental Problems. We mention here two fundamental problems used in this work: the 3Sat problem and the Vertex Cover problem. An instance (X, φ) of 3Sat (or any of its variants that we use in this work) is a set φ = {φi | 1 ≤ i ≤ m} of clauses over a set of boolean variables X = ¯ = {x¯j | 1 ≤ j ≤ n} is the set of all negative literals over X. {xj | 1 ≤ j ≤ n}. X ¯ The Each clause φi = i,1 ∨ i,2 ∨ i,3 is a conjunction of 3 literals from X ∪ X. e. at for least one literal i,k (k ∈ {1, 2, 3}) either i,k = xj ∧ f (xj ) = 1 for some 1 ≤ j ≤ n or i,k = x¯j ∧ f (xj ) = 0 for some 1 ≤ j ≤ n.

We show that: (1) RLPreq is NP-hard for any fixed value of d and for any fixed value of tw(G) at least 3, (2) RLPpath is fixed parameter tractable for d = 2 with the treewidth tw(G) of the graph as 44 I. Hartstein, M. Shalom, and S. Zaks the parameter, and (3) RLPpath is NP-hard for any fixed value d ≥ 5 and for graphs of any fixed treewidth at least 2. Next, we introduce the vertex load parameter for the problem RLPpath . The vertex load of a path set P, Lv (P), is the maximum number of paths which share the same common vertex.

We say that request rk is feasible if Πk = ∅. Note that a request rj is μ-feasible if and only if the capacity of the minimum cut that separates sk from tk is at least dμk . In particular, a request rj may be feasible even if dj > maxe ce . 2 Packing and Covering Formulation For every prefix of requests {rk }jk=1 we define a primal linear program p-lp(j) and a dual linear program d-lp(j). The LP’s appear in Figure 1. The packing program d-lp(j) has a variable yf for every flow f ∈ k V (Πk ) and two types of constraints: demand constraints and capacity constraints.

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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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