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By Yair (il-hebr-c) Byers and John W. (-bost-c) Raz


Fast, distributed approximation algorithms for positive linear programming with applications to flow control. (English summary) SIAM J. Comput. 33 (2004), no. 6, 1261–1279 (electronic). The authors study combinatorial optimization problems in which a set of distributed agents must achieve a global objective using only local information. More precisely, the authors consider the problem of having distributed decision-makers assign values to a set of variables in a linear program (LP) where the agents have limited information. In one scenario, each agent, acting in isolation, must set the value of a single primal variable, knowing only the constraints affecting that variable in the LP. In the model used, each agent can communicate a fixed-size message to its immediate neighbors, where agents are neighbors if and only if they share one or more constraints in the LP. The authors mainly offer a parameterized algorithm for approximately solving a positive LP in normalized form by relating the quality of the approximation to the running time. More precisely,)) time. For any 1 < ε ≤ ln(γ ×m), the authors propose a (1+ε)-approximation in time O ( n×m×ln2 (γ×m) ε Finally, the authors propose an application of their results to flow control

Year: 2010
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