# APSP on Sparse Undirected Graphs with Positive Integer Weights (All-Pairs Shortest Paths (APSP))

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## Description

In this case, the graph $G=(V,E)$ that we consider is sparse ($m = O(n)$), is undirected, and has positive integer 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 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

## Table of Algorithms

Name | Year | Time | Space | Approximation Factor | Model | Reference |
---|---|---|---|---|---|---|

Thorup | 1999 | $O(mn)$ | $O(mn)$ | Exact | Deterministic | Time & Space |