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1 Introduction One of the fascinating questions of computer science is whether and to what extent randomization increases the power of algorithmic procedures. It is well-known that, in general, randomization makes distributed algorithms more powerful, for there are examples of basic coordination tasks in asynchronous systems which cannot be solved by… (More)

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 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 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 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)