Abstract
In this paper, Label Setting Algorithm and Dynamic Programming Algorithm had been critically examined in determining the shortest path from one source to a destination. Shortest path problems are for finding a path with minimum cost from one or more origin (s) to one or more destination(s) through a connected network. A network of ten (10) cities (nodes) was employed as a numerical example to compare the performance of the two algorithms. Both algorithms arrived at the optimal distance of 11 km, which corresponds to the paths 1→4→5→8→10 ,1→3→5→8→10 , 1→2→6→9→10  and  1→4→6→9→10 . Thus, the problem has multiple shortest paths. The computational results evince the outperformance of Dynamic Programming Algorithm, in terms of time efficiency, over the Label Setting Algorithm. Therefore, to save time, it is recommended to apply Dynamic Programming Algorithm to shortest paths and other applicable problems over the Label-Setting Algorithm.
Highlights
A network is a collection of entities connected by some relationship, which can be represented as a graph
We present the discussion of the results obtained from the Dijkstra’s algorithm and that of the Dynamic Programming algorithm
Albeit the fact that Hillier and Lieberman (2005) cited an inherent flaw of Dynamic Programming method in respect of its impromptu nature and the fact that it is designed to fit a particular problem rather than a variety of applications, it involves fewer iterations leading to fewer computational steps, thereby making it time efficient in relation to the Dijkstra’s (Label-Setting) algorithm
Summary
A network is a collection of entities connected by some relationship, which can be represented as a graph. The Shortest Path Problems (SPP) are concerned with finding a path with minimum distance from one or more origins to one or more destinations through a network (Yongtaek & Sungmo, 2010; Paraveen & Neha, 2013). Classical examples of Shortest Path Network Problems are Travelling Salesman Problem (TSP), Knapsack Problem (KP) and Capacitated Vehicle Routing Problem (CVRP). With the increasing application of Shortest Path Network Problems in human life, researchers in algorithms for solving shortest path network problems have been compelled to look outside the traditional algorithms such as Label Setting and Label Correcting, which have some deficits to novel algorithm such as Dynamic Programming. This paper makes a comparative analysis between Label Setting Algorithm and Dynamic Programming Algorithm using a network of ten (10) nodes network problems
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