Abstract
In this paper we propose an experimental study model S3P2 of a fast fully dynamic programming algorithm design technique in finite directed graphs with few distinct nonnegative real edge weights. The Bellman-Ford’s approach for shortest path problems has come out in various implementations. In this paper the approach once again is re-investigated with adjacency matrix selection in associate least running time. The model tests proposed algorithm against arbitrarily but positive valued weighted digraphs introducing notion of Prograph that speeds up finding the shortest path over previous implementations. Our experiments have established abstract results with the intention that the proposed algorithm can consistently dominate other existing algorithms for Single Source Shortest Path Problems. A comparison study is also shown among Dijkstra’s algorithm, Bellman-Ford algorithm, and our algorithm.
Highlights
Computation of Shortest Path (SP) is one of the most fundamental problems in graph theory
Many optimization problems solved by dynamic programming or more complicated matrix searching techniques, such as the 0/1 knapsack problem, construction of optimal inscribed polygons, sequence alignment in molecular biology, length-limited Huffman coding etc, are expressed as shortest path problems
A directed Shortest Path Length (SPL) from a given source vertex s to each other vertex v in G can be defined in (1) as: SPL(s, v) = min(W( p):s p→v), if ∃ a path from s to v (1)
Summary
Computation of Shortest Path (SP) is one of the most fundamental problems in graph theory. Many optimization problems solved by dynamic programming or more complicated matrix searching techniques, such as the 0/1 knapsack problem, construction of optimal inscribed polygons, sequence alignment in molecular biology, length-limited Huffman coding etc, are expressed as shortest path problems. These include scheduling problems such as critical path computation in PERT [3] charts. With the rapid advancements and developments in communication, computer science and transportation systems, more variants of the SPPs have appeared Some of these are the traveling salesman problem, K-shortest paths, constrained shortest-path problem, multi-objective shortest path problem, network flow problems, and so forth including our key SSSPP [2, 4, 8]. Bhowmik and ag Chowdhury: Prograph Based Analysis of SSSPPs with Few Distinct Positive Lengths study is shown among Dijkstra’s algorithm, Bellman-Ford algorithm and our algorithm
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