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We propose a new solution for the fully dynamic single source shortest paths problem in a directed graph G=(N,A) with arbitrary arc weights, that works for any digraph and has optimal space requirements and query time. If a negative-length cycle is introduced in the subgraph of G reachable from the source during an update operation, then it is detected by the algorithm. Zero-length cycles are explicitly...
We propose fully dynamic algorithms for maintaining the distances and the shortest paths from a single source in either a directed or an undirected graph with positive real edge weights, handling insertions, deletions, and weight updates of edges. The algorithms require linear space and optimal query time. The cost of the update operations depends on the class of the considered graph and on the number...
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