Hammock-on-Ears Decomposition: A Technique for the Efficient Parallel Solution of Shortest Paths and Other Problems

Dimitris J. Kavvadias, Grammati E. Pantziou, Paul G. Spirakis, Christos D. Zaroliagis

Abstract: We show how to decompose efficiently in parallel any graph into a number, \(\tilde \gamma\), of outerplanar subgraphs (called hammocks) satisfying certain separator properties. We achieve this decomposition in O(log n log log n) time using O(n + m) CREW PRAM processors, for an n-vertex, m-edge graph. This decomposition provides a general framework for solving graph problems efficiently in parallel. Its value is demonstrated by using it to improve previous bounds for shortest paths and related problems in the class of sparse graphs (which includes planar and bounded genus graphs).