APSP on Dense Undirected Unweighted Graphs: Difference between revisions
No edit summary |
No edit summary |
||
| (2 intermediate revisions by the same user not shown) | |||
| Line 12: | Line 12: | ||
== Parameters == | == Parameters == | ||
n: number of vertices | $n$: number of vertices | ||
m: number of edges | $m$: number of edges | ||
== Table of Algorithms == | == Table of Algorithms == | ||
| Line 24: | Line 24: | ||
|- | |- | ||
| [[Seidel's algorithm (APSP on Dense Undirected Unweighted Graphs; APSP on Sparse Undirected Unweighted Graphs All-Pairs Shortest Paths (APSP))|Seidel's algorithm]] || 1995 || $O ( | | [[Seidel's algorithm (APSP on Dense Undirected Unweighted Graphs; APSP on Sparse Undirected Unweighted Graphs All-Pairs Shortest Paths (APSP))|Seidel's algorithm]] || 1995 || $O (n^{2.{37}3} \log n)$ || $O(n^{2})$ || Exact || Deterministic || [https://www.sciencedirect.com/science/article/pii/S0022000085710781 Time] | ||
|- | |- | ||
|} | |} | ||
| Line 31: | Line 31: | ||
[[File:All-Pairs Shortest Paths (APSP) - APSP on Dense Undirected Unweighted Graphs - Time.png|1000px]] | [[File:All-Pairs Shortest Paths (APSP) - APSP on Dense Undirected Unweighted Graphs - Time.png|1000px]] | ||
Latest revision as of 09:07, 28 April 2023
Description
In this case, the graph $G=(V,E)$ that we consider is dense ($m = O(n^2)$), 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 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
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Seidel's algorithm | 1995 | $O (n^{2.{37}3} \log n)$ | $O(n^{2})$ | Exact | Deterministic | Time |