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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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-010-9401-5