Abstract
Abstract. minimum spanning tree (MST) of a connected, undirected and weighted network is a tree of that network consisting of all its nodes and the sum of weights of all its edges is minimum among all such possible spanning trees of the same network. In this study, we have developed a new GIS tool using most commonly known rudimentary algorithm called Prim’s algorithm to construct the minimum spanning tree of a connected, undirected and weighted road network. This algorithm is based on the weight (adjacency) matrix of a weighted network and helps to solve complex network MST problem easily, efficiently and effectively. The selection of the appropriate algorithm is very essential otherwise it will be very hard to get an optimal result. In case of Road Transportation Network, it is very essential to find the optimal results by considering all the necessary points based on cost factor (time or distance). This paper is based on solving the Minimum Spanning Tree (MST) problem of a road network by finding it’s minimum span by considering all the important network junction point. GIS technology is usually used to solve the network related problems like the optimal path problem, travelling salesman problem, vehicle routing problems, location-allocation problems etc. Therefore, in this study we have developed a customized GIS tool using Python script in ArcGIS software for the solution of MST problem for a Road Transportation Network of Dehradun city by considering distance and time as the impedance (cost) factors. It has a number of advantages like the users do not need a greater knowledge of the subject as the tool is user-friendly and that allows to access information varied and adapted the needs of the users. This GIS tool for MST can be applied for a nationwide plan called Prime Minister Gram Sadak Yojana in India to provide optimal all weather road connectivity to unconnected villages (points). This tool is also useful for constructing highways or railways spanning several cities optimally or connecting all cities with minimum total road length.
Highlights
In most scientific disciplines, software plays an important role for the solution of any transportation related problem like optimal routing, time analysis, services area analysis, closest facilities analysis, travelling sales man problem, vehicle routing problem, postman problem, supply-demand problem etc
A customized Geographic Information System (GIS) tool helps users in their specific domain of work leads to the usage of recent software technologies according to their interest
The main objectives of this study are i) to create the digital database consisting of roads and junctions feature classes in GIS environment and assigning attribute information to all the features for performing the solution of minimum spanning tree (MST), ii) Development of GIS tool for the solution of MST using Prim’s Algorithm in Python Shell, iii) Linking of digital database with MST tool and performing the solution
Summary
Software plays an important role for the solution of any transportation related problem like optimal routing, time analysis, services area analysis, closest facilities analysis (for emergency services), travelling sales man problem, vehicle routing problem, postman problem, supply-demand problem etc. A graph (network) can be defined as G = G (E, V) where E is a set of edges and V is a set of vertices (nodes). A road transportation network is an interconnected linear system of nodes (junctions or vertices) and edges (lines or arcs) through which resources flow. Transportation is emerging as one of the biggest concerns for the people and congestion and lack of information cause delay in reaching destination. It is a demand of today that everyone wants to reach at the destination within a reasonable travel time or distance from the original place. In this study we are trying to find out the solution within these limits
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