An efficient parallel algorithm for planarity

An Efficient Parallel Algorithm for Planarity by Philip

We describe a parallel algorithm for testing a graph for planarity, and for finding an embedding of a planar graph. For a graph on n vertices, the algorithm runs in O(log2 n) steps on n processors of a parallel RAM. The previous best algorithm for planarity testing in parallel polylog time ([Ja'Ja' and Simon, 82]) used a reduction to solving linear systems, and hence required fl(n2 49 ) process...

A New Parallel Algorithm for Planarity Testing

This paper presents a new parallel algorithm for planarity testing based upon the work of Klein and Reif [14]. Our new approach gives correct answers on instances that provoke false positive and false negative results using Klein and Reif’s algorithm. The new algorithm has the same complexity bounds as Klein and Reif’s algorithm and runs in O ( n log n p ) time for any number p ≤ n processors o...

A New Parallel Algorithm for Planarity Testing

Determining whether a graph is planar is both theoretically and practically interesting. Although several sequential algorithms have been introduced which accomplish planarity testing in O(V ) time for graphs with V vertices, very few of these have been parallelized. In a recent comparison of sequential planarity testing algorithms, the newest algorithms were found to be fastest; however, these...

An Efficient Parallel Biconnectivity Algorithm

An Efficient Parallel Block-Reduction Algorithm

In this paper, we present a new parallel block-reduction algorithm for reducing lattice bases which allows the use of an arbitrarily chosen block-size between two and n where n denotes the dimension of the lattice. Thus, we are building a hierarchy of parallel lattice basis reduction algorithms between the known parallel all-swap algorithm which is a parallelization for block-size two and the r...