Say that a directed graph G is semiconnected if for each two vertices u, v there is either a directed path from u to v or a directed path from v to uu. This is a stronger property than weak connectivity, but weaker than strong connectivity. How to decide whether G is semiconnected in time O(n + m)?

Say that a directed graph G is semiconnected if for each two vertices u, v there is either a directed path from u to v or a directed path from v to uu. This is a stronger property than weak connectivity, but weaker than strong connectivity. How to decide whether G is semiconnected in time O(n + m)?

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Concept explainers

Depth First Search

Depth-first search (DFS) also known as Depth First traversal is an algorithm used to traverse or search the nodes in a tree or graph data structure. Traversal usually means visiting all the nodes of a graph. DFS performs in a depth-ward manner. It uses a stack to remember the vertices it has visited. The search starts from the root node, where any arbitrary node is selected as a root node in a graph, and then each node is explored along each branch before performing backtracking. The DFS algorithm uses a recursive technique by following the idea of backtracking. DFS algorithm does this by performing an in-depth search of all the nodes by traversing in a forward direction. If the required node is not found, it starts backtracking to previously visited nodes.

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Say that a directed graph G is semiconnected if for each two vertices u, v there is either a directed path from u to v or a
directed path from v to uu. This is a stronger property than weak connectivity, but weaker than strong connectivity. How
to decide whether G is semiconnected in time O(n + m)?

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