A Simple Yet Effective Algorithm to Compute Incremental All-Pairs Shortest Distances

Abstract

Many activities of modern day living operate on the basis of graph structures that change over time (e.g. social networks, city traffic navigation, disease transmission paths). Hence, the problem of dynamically maintaining properties of such structures after modifying one of its edges (or links), specially for large-scale graphs, has received a great amount of attention in recent years. We address the particular case of updating all-pairs shortest distances upon incremental changes, i.e. re-computing shortest distances among all the nodes of a graph when a new or smaller shortcut between two nodes arises. We build upon the naive algorithm that visits all pairs of nodes comparing if the new shortcut shortens the distances, and propose a simple variation that instead chooses pairs of source and target nodes, only from the affected shortest paths. The new algorithm works with an optimal data structure, constant query time and worst-case $O(n^2)$ update cost, although our results on synthetic datasets hints at its practicality when compared with state-of-the-art approaches.