Abstract

In this paper, we develop algorithmic optimizations to improve the cache performance of four fundamental graph algorithms. We present a cache-oblivious implementation of the Floyd-Warshall Algorithm for the fundamental graph problem of all-pairs shortest paths by relaxing some dependencies in the iterative version. We show that this implementation achieves the lower bound on processor-memory traffic of Ω(N 3 / C), where N and C are the problem size and cache size respectively. Experimental results show that this cache-oblivious implementation shows more than 6× improvement in real execution time over that of the iterative implementation with the usual row major data layout, on three state-of-the-art architectures. Secondly, we address Dijkstra's algorithm for the single-source shortest paths problem and Prim's algorithm for Minimum Spanning Tree. For these algorithms, we demonstrate up to 2 × improvement in real execution time by using a simple cachefriendly graph representation, namely adjacency arrays. Finally, we address the matching algorithm for bipartite graphs. We show performance improvements of 2 ×- 3 × in real execution time by using the technique of making the algorithm initially work on sub-problems to generate a sub-optimal solution and then solving the whole problem using the sub-optimal solution as a starting point.

Citations