By Nikhil Bansal (auth.), Thomas Erlebach, Giuseppe Persiano (eds.)
This e-book constitutes the completely refereed publish workshop lawsuits 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 conscientiously reviewed and chosen from 60 submissions. The workshop lined parts comparable to geometric difficulties, on-line algorithms, scheduling, algorithmic online game concept, and approximation algorithms.
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Extra resources for Approximation and Online Algorithms: 10th International Workshop, WAOA 2012, Ljubljana, Slovenia, September 13-14, 2012, Revised Selected Papers
The proof for the case of small demands appears in . The augmentation of the capacities are determined by the oracle with the “worst” parameters. Because the exact oracle is (1, 1, 1)-criteria, it is also (λ, μ, )-criteria. Thus, the augmentation factor β is determined by the approximate oracle. 7 Further Extensions Requests with known durations. The algorithm can be extended to deal with ﬂow requests with known durations. For the sake of simplicity, the ﬂow requests Online Multi-Commodity Flow with High Demands 27 in this paper are permanent, namely, after arrival, a request stays forever.
It was proven in  that RLPpath is polynomial-time solvable in tree and ring networks. The problems RLPpath and RLPreq are identical in trees, and therefore RLPreq is also polynomial-time solvable in this topology. We show that RLPreq is polynomialtime solvable in ring networks. We consider the treewidth of the network as one main parameter. The treewidth tw(G) of a network G is a measure for its structure, resembling the network’s level of similarity to a tree. 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.
If the cost of the oracles’s ﬂow is “small enough”, then the request is accepted as follows: (1) the ﬂow F is updated by adding the oracle’s unit-ﬂow fj times the required demand dj , (2) the primal variables xe , for every edge e that the ﬂow fj traverses, are updated. If the ﬂow is “too expensive”, then the request is rejected and no updates are made to the primal variables and to the mcf F . The listing of the online algorithm alg appears in Algorithm 1. Algorithm 1 alg: Online multi-commodity ﬂow algorithm.
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.)