Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 34.1, Problem 2E
Program Plan Intro
To define the problem of finding the longest simple cycle in an undirected graph. To give a related problem and to define the language corresponding to decision problem.
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Design a dynamic programming algorithm for the bigger-is-smarterelephant problem by comparing it, as done previously, with the problem of finding thelongest weighted path within a directed level graph problem.
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LONG-Route is the issue of finding whether or not there is a simple path in G from u to v with a length of at least k given the inputs (G, u, v, k), where G is a graph, u and v are vertices, and k is an integer.Demonstrate that LONG-PATH is an NP-complete problem.
Chapter 34 Solutions
Introduction to Algorithms
Ch. 34.1 - Prob. 1ECh. 34.1 - Prob. 2ECh. 34.1 - Prob. 3ECh. 34.1 - Prob. 4ECh. 34.1 - Prob. 5ECh. 34.1 - Prob. 6ECh. 34.2 - Prob. 1ECh. 34.2 - Prob. 2ECh. 34.2 - Prob. 3ECh. 34.2 - Prob. 4E
Ch. 34.2 - Prob. 5ECh. 34.2 - Prob. 6ECh. 34.2 - Prob. 7ECh. 34.2 - Prob. 8ECh. 34.2 - Prob. 9ECh. 34.2 - Prob. 10ECh. 34.2 - Prob. 11ECh. 34.3 - Prob. 1ECh. 34.3 - Prob. 2ECh. 34.3 - Prob. 3ECh. 34.3 - Prob. 4ECh. 34.3 - Prob. 5ECh. 34.3 - Prob. 6ECh. 34.3 - Prob. 7ECh. 34.3 - Prob. 8ECh. 34.4 - Prob. 1ECh. 34.4 - Prob. 2ECh. 34.4 - Prob. 3ECh. 34.4 - Prob. 4ECh. 34.4 - Prob. 5ECh. 34.4 - Prob. 6ECh. 34.4 - Prob. 7ECh. 34.5 - Prob. 1ECh. 34.5 - Prob. 2ECh. 34.5 - Prob. 3ECh. 34.5 - Prob. 4ECh. 34.5 - Prob. 5ECh. 34.5 - Prob. 6ECh. 34.5 - Prob. 7ECh. 34.5 - Prob. 8ECh. 34 - Prob. 1PCh. 34 - Prob. 2PCh. 34 - Prob. 3PCh. 34 - Prob. 4P
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- I really want to learn. Please explain too. For each graph representation, what is the appropriate worst-case time complexity for checking if two distinct vertices are connected. The choices are: O(1), O(V), O(E), or O(V+E) Adjancy Matrix = ____ Edge List = ____ Adjacency List = ____arrow_forwardGive a simple graph with an edge with a negative weight, and showthat Dijkstra’s algorithm gives the wrong answerarrow_forwardPlease solve with the computer Question 2: Draw a simple undirected graph G that has 11 vertices, 7 edges.arrow_forward
- Write Algorithm Bar VisibilityInput: a biconnected plane graph G = (V,E)Output: a bar visibility representation of Garrow_forwardSay that a graph G has a path of length three if there exist distinct vertices u, v, w, t with edges (u, v), (v, w), (w, t). Show that a graph G with 99 vertices and no path of length three has at most 99 edges.arrow_forwardconstruct an algorithm pseudocode to find all connected components in an undirected graph Garrow_forward
- Let G be a graph such that |V(G)| = |E(G)|. Show that δ(G) < 3.arrow_forwardGive an algorithm that determines whether or not a given undirected graph G D .V; E/ contains a cycle. Your algorithm should run in O.V / time, independent of |E|.arrow_forwardRun a Program to experiments to determine empirically the probability that DepthFirstPaths finds a path between two randomly chosen vertices and to calculate the average length of the paths found, for various graph models.arrow_forward
- To find the shortest path between nodes in a graph, compare Dijkstra's algorithm and Ford's algorithm with proper explanationarrow_forwardLet G = (V, E) be an undirected graph. Design algorithms for the following and discuss the complexity of your algorithm: (a) Let S be a subset of edges s.t. every cycle of G has at least one edge in S. Find a minimum size subset S.arrow_forwardThe third-clique problem is about deciding whether a given graph G = (V, E) has a clique of cardinality at least |V |/3.Show that this problem is NP-complete.arrow_forward
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