Advances in Randomized Parallel Computing pp 113-132 | Cite as

# Ultrafast Randomized Parallel Construction- and Approximation Algorithms for Spanning Forests in Dense Graphs

## Abstract

This chapter contains new results, in the form of two algorithms, on the construction of a spanning forest in a dense graph. In this introduction the model of a shared memory Parallel Random Access Machine is described and the spanning forest problem is shortly overviewed. Our new algorithms belong to the so called *ultrafast* algorithms which we shortly survey in Section 6.2. The denseness property of graphs, which is crucial for our algorithms and very interesting in itself, is discussed in Section 6.3. Our two new algorithms are presented in detail in Section 6.4. An interested reader can find a short list of related open problems at the end of the chapter.

## Keywords

Span Tree Parallel Algorithm Hamiltonian Cycle Dense Graph Span Forest## Preview

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