Michal Hanckowiak

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.

A faster distributed algorithm for computing maximal matchings deterministically

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.

Distributed algorithm for approximating the maximum matching

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 algorithm for better approximation of the maximum matching

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.

Distributed 2-approximation algorithm for the semi-matching problem

In this paper we consider the problem of matching clients with servers, each of which can process a subset of clients. It is known as the semi-matching or load balancing problem in a bipartite graph G=(V,U,E), where U corresponds to the clients, V to the servers, and E is the set of available connections between them. The goal is to find a set of edges M⊆E such that every vertex in U is incident to exactly one edge in M. The load of a server v∈V is defined as

A Fast Distributed Algorithm for Approximating the Maximum Matching

{d_M(v) +1\choose 2}

Distributed algorithms for weighted problems in sparse graphs

where dM(v) is the degree of v in M, and the problem is to find an optimal semi-matching, i.e. a semi-matching that minimizes the sum of the loads of the servers. An optimal solution can be found sequentially in polynomial time but the distributed complexity is not well understood. Our algorithm yields

Distributed almost exact approximations for minor-closed families

(1+\frac{1}{\alpha})

Brief announcement: distributed approximations for the semi-matching problem

-approximation (where

Distributed packing in planar graphs

\alpha=\max\left\{1, \frac 12\left(\frac{|U|}{|V|} +1\right)\right\}