Applications of Ear Decomposition to Efficient Heterogeneous Algorithms for Shortest Path/Cycle Problems

Abstract

Graph algorithms play an important role in several fields of sciences and engineering. Prominent among them are the All-Pairs-Shortest-Paths (APSP) and related problems. Indeed there are several efficient implementations for such problems on a variety of modern multi-and manycore architectures.It can be noticed that for several graph problems, parallelism offers only a limited success as current parallel architectures have severe short-comings when deployed for most graph algorithms. At the same time, some of these graphs exhibit clear structural properties due to their sparsity. This calls for particular solution strategies aimed at scalable processing of large, sparse graphs on modern parallel architectures.In this paper, we study the applicability of an ear decomposition of graphs to problems such as all-pairs-shortest-paths and minimum cost cycle basis. Through experimentation, we show that the resulting solutions are scalable in terms of both memory usage and also their speedup over best known current implementations. We believe that our techniques have the potential to be relevant for designing scalable solutions for other computations on large sparse graphs.

Sparse Pose Graph Optimization in Cycle Space

“…Reconstruct MCB for G [81]. APSP is required to construct the Horton set, and a consistent APSP for the isometric set.…”

“…The vertices of degree two can also be pruned out using the ear decomposition [86], which requires the graph to be 2-edge connected. A minimum cycle basis algorithm exploiting ear decomposition is provided in [81]. The algorithm in [81] exploiting the idea of feedback vertices to reduce the Horton set, which is encompassed in the concept of isometric cycles [79].…”

“…A minimum cycle basis algorithm exploiting ear decomposition is provided in [81]. The algorithm in [81] exploiting the idea of feedback vertices to reduce the Horton set, which is encompassed in the concept of isometric cycles [79]. Nevertheless, the set of isometric cycles are much smaller than the set of cycles exploiting the idea of feedback vertices [79].…”

“…However, the code is not maintained anymore for recent LEDA versions, or Ubuntu systems. The other competitive implementations, for example [79], [81], are not available in open-source. In contrast, our implementation is freely available to the research community, and can be easily used in other MCB related problems.…”