@inbook{864dbe2abacf4aa5ac14ca0aba51bcfc,

title = "On dynamic shortest paths problems",

abstract = "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 {\~O}(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.",

author = "Liam Roditty and Uri Zwick",

year = "2004",

doi = "10.1007/978-3-540-30140-0_52",

language = "אנגלית",

isbn = "3540230254",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "580--591",

editor = "Susanne Albers and Tomasz Radzik",

booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

address = "גרמניה",

}