APSP on Geometrically Weighted Graphs (All-Pairs Shortest Paths (APSP))
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)