An Experimental Comparison of Parallel Algorithms for Ear Decomposition of Graphs using Two Leading Paradigms

Graph decomposition is an important and necessary operation when solving graph-theoretic problems on parallel computers, for instance, from computational fluid dynamics, mechanics, and astrophysics. In this paper, we design and analyze message-passing and shared-memory parallel algorithms that efficiently decompose a planar graph into a number of ears, known as the Ear Decomposition. This decomposition provides a general framework for solving graph problems efficiently in parallel. Our study includes both theoretical analysis and confirmation of the complexity cost using two leading parallel programming paradigms, namely, message-passing (MPI) and shared-memory (SMP) implementations. A catalog of both regular and irregular input graphs are provided to benchmark these algorithms in our empirical study.