An all-pairs shortest path algorithm for bipartite graphs

Abstract

Bipartite graphs are widely used for modeling of complex structures in biology, engineering, and computer science. The search for shortest paths in such structures is a highly demanded procedure that requires optimization. This paper presents a variant of the all-pairs shortest path algorithm for bipartite graphs. The method is based on the distance matrix product and improves the general algorithm by exploiting the graph topology. The space complexity is reduced by a factor of at least four and the time complexity decreased by almost an order of magnitude when compared with the basic APSP algorithm.

Accelerating all-pairs shortest path algorithms for bipartite graphs on graphics processing units

“…The reason is that each acyclic path consists of an alternating sequence of vertices in V 1 and V 2 . Thus the 2m 1 -th tropical power of weight matrix Q provides the solution of the APSP problem for bipartite graphs [42]:…”

“…Torgasin and Zimmermann have further optimized the solution of the APSP problem by considering properties of bipartite graphs [42]. TORGASINZIMMERMANN algorithm takes weight matrix blocks Q 1 and Q 2 as input.…”

“…For example, Chin-Wen and Chang [10] and Chen [9] proposed the solution of the shortest path problem for unweighted chordal and unweighted permutation bipartite graphs, respectively. Torgasin and Zimmermann proposed an tropical-algebra based approach to solve the APSP problem for bipartite graphs [42]. However, computational complexity is a major concern for large bipartite graphs.…”

Multiple Object Tracking for Occluded Particles

“…The graph model [17] is made up of nodes and edges, with each node representing one or a group of variables and the edge bearing the contact information between nodes representing the bridge between connecting nodes. In the case of particle tracking, the object detected in successive frames can be regarded as the nodes of the graph model.…”

Comparative Analysis of Algorithms to Discover Shortest Path in Social Networks

“…Four blocks of weight matrix are calculated by multiplying matrix D with itself n1-1 times. The computational complexity of this algorithm is O ((n 3 ) log 2 (n)).This algorithm is at least eight times quicker and needs four times less space in worst case when compared with Floyd-Warshall algorithm [20]. Later on, this algorithm was implemented on GPU [21].…”