Wojciech Wawrzyniak

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.

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 strengthened analysis of a local algorithm for the minimum dominating set problem in planar graphs

{d_M(v) +1\choose 2}

Brief announcement: a local approximation algorithm for MDS problem in anonymous planar networks

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

Brief announcement: distributed approximations for the semi-matching problem

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

Distributed packing in planar graphs

-approximation (where

Improved distributed local approximation algorithm for minimum 2-dominating set in planar graphs

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

Distributed Local Approximation of the Minimum k-Tuple Dominating Set in Planar Graphs

) and has time complexity

Distributed CONGESTBC constant approximation of MDS in bounded genus graphs

O\left(\Delta^5\right),

On the distributed complexity of the semi-matching problem

where Δ is the maximum degree of a vertex in V. In particular, for Δ=O(1) it gives constant approximation with constant time complexity. We also give a fast algorithm for the case when Δ is large and the degrees in V and U satisfy some additional properties. Both algorithms are deterministic.