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We give deterministic distributed algorithms that given δ > 0 find in a planar graph G, (1 ± δ)-approximations of a maximum independent set, a maximum matching, and a minimum dominating set. The algorithms run in O(log * |G|) rounds. In addition, we prove that no faster deterministic approximation is possible and show that if randomization is allowed it is… (More)

We present a distributed approximation algorithm that computes in every graph G a matching M of size at least 2 3 β(G), where β(G) is the size of a maximum matching in G. The algorithm runs in O(log 4 |V (G)|) rounds in the synchronous, message passing model of computation and matches the best known asymptotic complexity for computing a maximal matching in… (More)

We study distributed algorithms for three graph-theoretic problems in weighted trees and weighted planar graphs. For trees, we present an efficient deterministic distributed algorithm which finds an almost exact approximation of a maximum-weight matching. In addition, in the case of trees, we show how to approximately solve the minimum-weight dominating set… (More)

We present a distributed algorithm that finds a matching M of size which is at least 2/3|M * | where M * is a maximum matching in a graph. The algorithm runs in O(log 6 n) steps.

We show that maximal matchings can be computed deterministically in O(log4 n) rounds in the synchronous, message-passing model of computation. This improves on an earlier result by three log-factors.

We will give distributed approximation schemes for the maximum matching problem and the minimum connected dominating set problem in unit-disk graphs. The algorithms are deterministic, run in a poly-logarithmic number of rounds in the message passing model and the approximation error can be made O(1/ log k |G|) where |G| is the order of the graph and k is a… (More)

Let G be a graph on n vertices that does not have odd cycles of lengths 3,. .. , 2k − 1 with k ≥ 2. We give a deterministic distributed algorithm which finds in a poly-logarithmic (in n) number of rounds a matching M , such that |M | ≥ (1−α)m(G), where m(G) is the size of a maximum matching in G and α = 1 k+1 .

We give efficient deterministic distributed algorithms which given a graph G from a proper minor-closed family C find an approximation of a minimum dominating set in G and a minimum connected dominating set in G. The algorithms are deterministic and run in a poly-logarithmic number of rounds. The approximation accomplished differs from an optimal by a… (More)

In this paper we construct two distributed algorithms for computing approximations of a largest matching and a minimum dominating set in planar graphs on n vertices. The approximation ratio in both cases approaches one with n tending to infinity and the number of synchronous communication rounds is poly-logarithmic in n. Our algorithms are purely… (More)