Maintaining Shortest Path Tree in Dynamic Digraphs Having Negative Edge-Weights

Given a directed graph G, a source vertex s and shortest path tree (SPT). T(s) rooted at 8 in G, the dynamic shortest path problem is to find the new SPT, T'(s) in G from T(s) when update(s) on edge weight(s) are performed. Previous works focus either on single edge weight update at a time or, process a set of updates together with the constraint that edge weights remain positive. In this paper we propose two semi-dynamic algorithms (one for increase only and the other for decrease only case) for maintaining SPT in a directed graph, even when some of edge weights assume negative values. Our algorithms process multiple edge weight updates simultaneously and also able to detect presence of negative weight cycle if introduced during update, to assert that no real SPT exists. From experiments conducted, we observe that dynamic algorithms perform better than the static algorithm when the percentage of updated edges is smaller than a certain threshold.