Modified Dijkstra Algorithm with Invention Hierarchies Applied to a Conic Graph

TL;DR

This paper introduces a modified Dijkstra algorithm utilizing invention hierarchies and contraction techniques to efficiently find minimum paths in conic graphs, demonstrated in a hospital locator system.

Contribution

It presents a novel algorithm that automatically invents new paths and extends multi-source multi-destination pathfinding in specialized graph structures.

Findings

Effective in finding minimum paths in conic graphs

Automatically invents new paths with O(n) complexity

Successfully applied to hospital locator system

Abstract

A modified version of the Dijkstra algorithm using an inventive contraction hierarchy is proposed. The algorithm considers a directed acyclic graph with a conical or semi-circular structure for which a pair of edges is chosen iteratively from multi-sources. The algorithm obtains minimum paths by using a comparison process. The comparison process follows a mathematical construction routine that considers a forward and backward check such that only paths with minimum lengths are selected. In addition, the algorithm automatically invents a new path by computing the absolute edge difference for the minimum edge pair and its succeeding neighbour in O (n) time. The invented path is approximated to the hidden path using a fitness criterion. The proposed algorithm extends the multi-source multi-destination problem to include those paths for which a path mining redirection from multi-sources to multi-destinations is a minimum. The algorithm has been applied to a hospital locator path finding system and the results were quite satisfactory.