We obtain the following results related to dynamic versions of the shortest-paths problem: (i) Reductions that show that the incremental and dceremental singlesource shortest-paths problems, for weighted directed or undirected graphs, are, in a strong sense, at least as hard as the static all-pairs shortest-paths problem. We also obtain slightly weaker results for the corresponding unweighted problems. (ii) A randomized fully-dynamic algorithm for the all-pairs shortestpaths problem in directed unweighted graphs with an amortized update time of Õ(m√n) and a worst case query time is O(n3/4). (iii) A deterministic O(n2log n) time algorithm for constructing a (log n)-spanner with O(n) edges for any weighted undirected graph on n vertices. The algorithm uses a simple algorithm for incrementally maintaining single-source shortest-paths tree up to a given distance. © Springer-Verlag 2004.
CITATION STYLE
Roditty, L., & Zwick, U. (2004). On dynamic shortest paths problems. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 3221, 580–591. https://doi.org/10.1007/978-3-540-30140-0_52
Mendeley helps you to discover research relevant for your work.