On Dynamic Shortest Paths Problems

We obtain the following results related to dynamic versions of the shortest-paths problem: Reductions that show that the incremental and decremental single-source shortest-paths problems, for weighted directed or undirected graphs, are, in a strong sense, at least as hard as the static all-pairs sho...

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Published in:	Algorithmica Vol. 61; no. 2; pp. 389 - 401
Main Authors:	Roditty, Liam, Zwick, Uri
Format:	Journal Article
Language:	English
Published:	New York Springer-Verlag 01.10.2011 Springer
Subjects:	Algorithm Analysis and Problem Complexity Algorithms Applied sciences Computer Science Computer science; control theory; systems Computer Systems Organization and Communication Networks Data Structures and Information Theory Exact sciences and technology Information retrieval. Graph Mathematics of Computing Theoretical computing Theory of Computation Spanners Dynamic algorithms Graph Shortest paths Tree(graph) Logarithmic function Worst case method Shortest path Updating Routing Randomized algorithm Weighted graph Direct problem Spanning tree Digraph Deterministic approach Non directed graph
ISSN:	0178-4617, 1432-0541
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Abstract	We obtain the following results related to dynamic versions of the shortest-paths problem: Reductions that show that the incremental and decremental single-source 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. A randomized fully-dynamic algorithm for the all-pairs shortest-paths problem in directed unweighted graphs with an amortized update time of (we use to hide small poly-logarithmic factors) and a worst case query time is O ( n 3/4 ). A deterministic O ( n 2 log n ) time algorithm for constructing an O (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.
AbstractList	We obtain the following results related to dynamic versions of the shortest-paths problem: Reductions that show that the incremental and decremental single-source 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. A randomized fully-dynamic algorithm for the all-pairs shortest-paths problem in directed unweighted graphs with an amortized update time of (we use to hide small poly-logarithmic factors) and a worst case query time is O ( n 3/4 ). A deterministic O ( n 2 log n ) time algorithm for constructing an O (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	Roditty, Liam Zwick, Uri
Author_xml	– sequence: 1 givenname: Liam surname: Roditty fullname: Roditty, Liam email: liamr@macs.biu.ac.il organization: Dept. of Computer Science, Bar-Ilan University – sequence: 2 givenname: Uri surname: Zwick fullname: Zwick, Uri organization: School of Computer Science, Tel-Aviv University
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Keywords	Spanners Dynamic algorithms Graph Shortest paths Tree(graph) Logarithmic function Worst case method Shortest path Updating Routing Randomized algorithm Weighted graph Direct problem Spanning tree Digraph Deterministic approach Non directed graph
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SubjectTerms	Algorithm Analysis and Problem Complexity Algorithms Applied sciences Computer Science Computer science; control theory; systems Computer Systems Organization and Communication Networks Data Structures and Information Theory Exact sciences and technology Information retrieval. Graph Mathematics of Computing Theoretical computing Theory of Computation
Title	On Dynamic Shortest Paths Problems
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