Performance Study of Parallel Shortest Path Algorithms: Characteristics of Good Decompositions

Shortest path algorithms are a key component of many applications such as VLSI and transportation algorithms. The solution for shortest paths is very computationally intensive; therefore, using parallel processing is advantageous. The performance of parallel shortest path depends on how the data is partitioned among the processors. In this paper, we investigate how the decomposition aaects performance and identify characteristics of a good decomposition. We consider ve decomposition characteristics: number of boundary nodes, number of interfaces, number of boundary nodes per interface, subnetwork connectivity and subnetwork diameter. Through an extensive statistical analysis we determine that a good decomposition has a small number of interfaces and connected components and a small diameter, but a large number of boundary nodes per interface. Furthermore, the eeectiveness of a decomposition depends on all the characteristics, not on just one.