Andrzej Czygrinow

Fast Distributed Approximations in Planar Graphs

We give deterministic distributed algorithms that given i¾?> 0 find in a planar graph G, (1±i¾?)-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 possible to beat the lower bound for deterministic algorithms.

An Algorithmic Regularity Lemma for Hypergraphs

In this paper, we will consider the problem of designing an efficient algorithm that finds an

Constructive Quasi-Ramsey Numbers and Tournament Ranking

\epsilon

Distributed algorithm for approximating the maximum matching

-regular partition of an l-uniform hypergraph.

Distributed algorithm for better approximation of the maximum matching

A constructive lower bound on the quasi-Ramsey numbers and the tournament ranking function was obtained in [S. Poljak, V. Rodl, and J. Spencer, SIAM J. Discrete Math., (1) 1988, pp. 372--376]. We consider the weighted versions of both problems. Our method yields a polynomial time heuristic with guaranteed lower bound for the linear ordering problem.

Tight Codegree Condition for the Existence of Loose Hamilton Cycles in 3-Graphs

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(log6 n) steps.

Distributed 2-approximation algorithm for the semi-matching problem

Let G be a graph on n vertices that does not have odd cycles of lengths 3, ..., 2k - 1. We present an efficient distributed algorithm that finds in O(logD n) steps (D = D(k)) matching M, such that |M| ≥ (1 - α)|M*|, where M* is a maximum matching in G, α = 1/k+1.

A note on graph pebbling

In 2006, Kuhn and Osthus [J. Combin. Theory Ser. B, 96 (2006), pp. 767--821] showed that if a 3-graph

On pebbling threshold functions for graph sequences

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Tiling 3‐Uniform Hypergraphs With K43−2e

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