2. Depth-first search can be used to detect cycles in undirected graphs (see lectures). As- suming an adjacency list representation of the graph, depth-first search has complexity (n+m). Explain why the complexity of the cycle detection algorithm by depth-first search is actually O(n) regardless of what m is.

2. Depth-first search can be used to detect cycles in undirected graphs (see lectures). As- suming an adjacency list representation of the graph, depth-first search has complexity (n+m). Explain why the complexity of the cycle detection algorithm by depth-first search is actually O(n) regardless of what m is.

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

See similar textbooks

Similar questions

Bellman-Ford algorithm Draw a graph G with weights of edges ranging from 3 to 9, is it possible to calculate the LONGEST PATH without altering the algorithm at all? Justify your answer by providing solid reasons.
Let n be an even positive integer. (a) Show that if the degree of every vertex in a simple graph G on n vertices is at least (i.e., greater than or equal to) n/2, then G must be connected. (b) Give an example of a disconnected simple graph on n vertices in which every vertex has degree (n/2) – 1.
5. Fleury's algorithm is an optimisation solution for finding a Euler Circuit of Euler Path in a graph, if they exist. Describe how this algorithm will always find a path or circuit if it exists. Describe how you calculate if the graph is connected at each edge removal. Fleury's Algorithm: The algorithm starts at a vertex of v odd degree, or, if the graph has none, it starts with an arbitrarily chosen vertex. At each step it chooses the next edge in the path to be one whose deletion would not disconnect the graph, unless there is no such edge, in which case it picks the remaining edge (a bridge) left at the current vertex. It then moves to the other endpoint of that edge and adds the edge to the path or circuit. At the end of the algorithm there are no edges left ( or all your bridges are burnt). (NOTE: Please elaborate on the answer and explain. Please do not copy-paste the answer from the internet or from Chegg.)
Suppose we represent a graph G = (V,E) as an adjacency matrix. Give a simple Implementation via pseudo code of Prim's algorithm for this case that runs in 0(V²) time. Explain why your code the running time has the upper bound as 0(v²).
We recollect that Kruskal's Algorithm is used to find the minimum spanning tree in a weighted graph. Given a weighted undirected graph G = (V , E, W), with n vertices/nodes, the algorithm will first sort the edges in E according to their weights. It will then select (n-1) edges with smallest weights that do not form a cycle. (A cycle in a graph is a path along the edges of a graph that starts at a node and ends at the same node after visiting at least one other node and not traversing any of the edges more than once.) Use Kruskal's Algorithm to nd the weight of the minimum spanning tree for the following graph.
Suppose are you given an undirected graph G = (V, E) along with three distinct designated vertices u, v, and w. Describe and analyze a polynomial time algorithm that determines whether or not there is a simple path from u to w that passes through v. [Hint: By definition, each vertex of G must appear in the path at most once.]
Draw a simple, connected, weighted graph with 8 vertices and 16 edges, each with unique edge weights. Identify one vertex as a “start” vertex and illustrate a running of Dijkstra’s algorithm on this graph. Problem R-14.23 in the photo
I want best algorithm for the problem. ALSO write its complexity and prove correctness of algorithm Given an undirected graph, with positive integer lengths c(e) on edges. Say that we replace c(s) by (c(2)^2) . Does this operation can make a shortest path between two vertees, into a path between vertices that is no longer a shortest path? Explain your answer precisely.
Deterministic PeArmutation (DP) AlgorithmInput: a positive integer n.Output: a permutation graph G[π] with ∆(G) = n 2 all of its vertices are at distance at most two apart to each other.
Deterministic PeArmutation (DP) AlgorithmInput: a positive integer n.Output: a permutation graph G[π] with ∆(G) = n 2 all of its vertices are at distance at most two apart to each other. write shortest algo....
please answer both of the questions. 7. The Bellman-Ford algorithm for single-source shortest paths on a graph G(V,E) as discussed in class has a running time of O|V |3, where |V | is the number of vertices in the given graph. However, when the graph is sparse (i.e., |E| << |V |2), then this running time can be improved to O(|V ||E|). Describe how how this can be done.. 8. Let G(V,E) be an undirected graph such that each vertex has an even degree. Design an O(|V |+ |E|) time algorithm to direct the edges of G such that, for each vertex, the outdegree is equal to the indegree. Please give proper explanation and typed answer only.
Let G be a directed acyclic graph. You would like to know if graph G contains directed path that goes through every vertex exactly once. Give an algorithm that tests this property. Provide justification of the correctness and analyze running time complexity of your algorithm. Your algorithm must have a running time in O(|V | + |E|). Detailed pseudocode is required.