# Randomized Graph Data-Structures for Approximate Shortest Paths

Authored by: Surender Baswana , Sandeep Sen

# Handbook of Data Structures and Applications

Print publication date:  March  2018
Online publication date:  February  2018

Print ISBN: 9781498701853
eBook ISBN: 9781315119335

10.1201/9781315119335-39

#### Abstract

Let G = (V, E) be an undirected weighted graph on n = |V| vertices and m = |E| edges. Length of a path between two vertices is the sum of the weights of all the edges of the path. The shortest path between a pair of vertices is the path of least length among all possible paths between the two vertices in the graph. The length of the shortest path between two vertices is also called the distance between the two vertices. An α-approximate shortest path between two vertices is a path of length at-most α times the length of the shortest path.

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