APSP on Geometrically Weighted Graphs: Difference between revisions
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== Parameters == | == Parameters == | ||
n: number of vertices | $n$: number of vertices | ||
m: number of edges | $m$: number of edges | ||
c: number of weights | $c$: number of unique weights | ||
== Table of Algorithms == | == Table of Algorithms == | ||
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| [[Chan (Geometrically Weighted) (APSP on Geometrically Weighted Graphs All-Pairs Shortest Paths (APSP))|Chan (Geometrically Weighted)]] || 2009 || $O( | | [[Chan (Geometrically Weighted) (APSP on Geometrically Weighted Graphs All-Pairs Shortest Paths (APSP))|Chan (Geometrically Weighted)]] || 2009 || $O(n^{2.{84}4})$ || $O(l n^{2})$ || Exact || Deterministic || [http://tmc.web.engr.illinois.edu/moreapsp.pdf Time] | ||
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Revision as of 07:52, 10 April 2023
Description
In this case, the graph $G=(V,E)$ that we consider may be dense or sparse, may be directed or undirected, and has weights from a fixed set of $c$ values.
Related Problems
Generalizations: APSP
Related: APSP on Dense Directed Graphs with Arbitrary Weights, APSP on Dense Undirected Graphs with Arbitrary Weights, APSP on Dense Undirected Graphs with Positive Integer Weights, APSP on Sparse Directed Graphs with Arbitrary Weights, APSP on Sparse Undirected Graphs with Positive Integer Weights, APSP on Sparse Undirected Graphs with Arbitrary Weights, APSP on Dense Directed Unweighted Graphs, APSP on Dense Undirected Unweighted Graphs, APSP on Sparse Directed Unweighted Graphs, APSP on Sparse Undirected Unweighted Graphs, (5/3)-approximate ap-shortest paths
Parameters
$n$: number of vertices
$m$: number of edges
$c$: number of unique weights
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Chan (Geometrically Weighted) | 2009 | $O(n^{2.{84}4})$ | $O(l n^{2})$ | Exact | Deterministic | Time |
Time Complexity Graph
_-_APSP_on_Geometrically_Weighted_Graphs_-_Time.png)
Space Complexity Graph
_-_APSP_on_Geometrically_Weighted_Graphs_-_Space.png)
Time-Space Tradeoff
_-_APSP_on_Geometrically_Weighted_Graphs_-_Pareto_Frontier.png)