Fast distributed approximation algorithms for vertex cover and set cover in anonymous networks

We present a distributed algorithm that finds a maximal edge packing in O(Δ + log* W) synchronous communication rounds in a weighted graph, independent of the number of nodes in the network; here Δ is the maximum degree of the graph and W is the maximum weight. As a direct application, we have a distributed 2-approximation algorithm for minimum-weight vertex cover, with the same running time. We also show how to find an f-approximation of minimum-weight set cover in O(f2k2 + fk log* W) rounds; here k is the maximum size of a subset in the set cover instance, f is the maximum frequency of an element, and W is the maximum weight of a subset. The algorithms are deterministic, and they can be applied in anonymous networks.

A local 2-approximation algorithm for the vertex cover problem

We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (Δ + 1)2 synchronous communication rounds, where Δ is the maximum degree of the graph. For Δ = 3, we give a 2-approximation algorithm also for the weighted version of the problem.

A simple local 3-approximation algorithm for vertex cover

We present a local algorithm (constant-time distributed algorithm) for finding a 3-approximate vertex cover in bounded-degree graphs. The algorithm is deterministic, and no auxiliary information besides port numbering is required. (c) 2009 Elsevier B.V. All rights reserved.

A local 2-approximation algorithm for the vertex cover problem

We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (Δ + 1)2 synchronous communication rounds, where Δ is the maximum degree of the graph. For Δ = 3, we give a 2-approximation algorithm also for the weighted version of the problem.

Finite-State Spell-Checking with Weighted Language and Error Models

In this paper we present simple methods for construction and evaluation of finite-state spell-checking tools using an existing finite-state lexical automaton, freely available finite-state tools and Internet corpora acquired from projects such as Wikipedia. As an example, we use a freely available open-source implementation of Finnish morphology, made with traditional finite-state morphology tools, and demonstrate rapid building of Northern Sámi and English spell checkers from tools and resources available from the Internet.