APSP on Sparse Undirected Unweighted Graphs: Difference between revisions
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[[File:All-Pairs Shortest Paths (APSP) - APSP on Sparse Undirected Unweighted Graphs - Space.png|1000px]] | [[File:All-Pairs Shortest Paths (APSP) - APSP on Sparse Undirected Unweighted Graphs - Space.png|1000px]] | ||
== Space | == Time-Space Tradeoff == | ||
[[File:All-Pairs Shortest Paths (APSP) - APSP on Sparse Undirected Unweighted Graphs - Pareto Frontier.png|1000px]] | [[File:All-Pairs Shortest Paths (APSP) - APSP on Sparse Undirected Unweighted Graphs - Pareto Frontier.png|1000px]] | ||
Revision as of 14:42, 15 February 2023
Description
In this case, the graph $G=(V,E)$ that we consider is sparse ($m = O(n)$), is undirected, and is unweighted (or equivalently, has all unit weights).
Related Problems
Generalizations: APSP
Related: APSP on Dense Directed Graphs with Arbitrary Weights, APSP on Dense Undirected Graphs with Arbitrary Weights, APSP on Geometrically Weighted Graphs, 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, (5/3)-approximate ap-shortest paths
Parameters
n: number of vertices
m: number of edges
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Seidel's algorithm | 1995 | $O (V^{2.{37}3} \log V)$ | $O(V^{2})$ | Exact | Deterministic | Time |
Time Complexity Graph
_-_APSP_on_Sparse_Undirected_Unweighted_Graphs_-_Time.png)
Space Complexity Graph
_-_APSP_on_Sparse_Undirected_Unweighted_Graphs_-_Space.png)
Time-Space Tradeoff
_-_APSP_on_Sparse_Undirected_Unweighted_Graphs_-_Pareto_Frontier.png)