A Study on New Algorithm for K Shortest Paths Problem

복수최단경로의 새로운 해법 연구

This article presents a new algorithm for the K Shortest Paths Problem which develops initial K shortest paths, and repeal to expose hidden shortest paths with dual approach and to replace the longest path in the present K paths. The initial solution which comprises K shortest paths among shortest paths to traverse each arc is made from bidirectional Dijkstra algorithm. When a crossing node that have two or more inward arcs is found at least three time by turns in this K shortest paths, one inward arc of this crossing node, which has minimum detouring distance, is chosen, and a new path is exposed with joining a detouring subpath from source to this inward arc and a spur of a feasible path from this crossing node to sink. This algorithm, requires worst case time complexity of $O(Kn^2),\;and\;O(n^2)$ in the case $K{\leq}3$.