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 22.2, Problem 3E
Program Plan Intro
To explain the BFS procedure would produce the same result if the line 18 were removed using a single bit to store each vertex color suffices.
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Improve Luby's Python-coded MIS method by randomly picking a vertex, locating its neighbours, and then finding the vertex with the lowest assigned random value to be included in the MIS.
Improve Luby’s MIS algorithm coded in Python by selecting a vertex at random,finding its neighbors and then finding the vertex with the minimum assignedrandom value to be included in the MIS.
Question 1. Find the shortest paths from a vertex with the remainder when the last digit of your
student number is divided by 9 to all other vertices using Dijsktra's Algorithm. Construct a
table as shown in the class. You can consider an undirected edge as two opposite directed
edges. (20P)
8
-7
4
0
-11
N
8
6
6
4
2
5
14
S
10
Chapter 22 Solutions
Introduction to Algorithms
Ch. 22.1 - Prob. 1ECh. 22.1 - Prob. 2ECh. 22.1 - Prob. 3ECh. 22.1 - Prob. 4ECh. 22.1 - Prob. 5ECh. 22.1 - Prob. 6ECh. 22.1 - Prob. 7ECh. 22.1 - Prob. 8ECh. 22.2 - Prob. 1ECh. 22.2 - Prob. 2E
Ch. 22.2 - Prob. 3ECh. 22.2 - Prob. 4ECh. 22.2 - Prob. 5ECh. 22.2 - Prob. 6ECh. 22.2 - Prob. 7ECh. 22.2 - Prob. 8ECh. 22.2 - Prob. 9ECh. 22.3 - Prob. 1ECh. 22.3 - Prob. 2ECh. 22.3 - Prob. 3ECh. 22.3 - Prob. 4ECh. 22.3 - Prob. 5ECh. 22.3 - Prob. 6ECh. 22.3 - Prob. 7ECh. 22.3 - Prob. 8ECh. 22.3 - Prob. 9ECh. 22.3 - Prob. 10ECh. 22.3 - Prob. 11ECh. 22.3 - Prob. 12ECh. 22.3 - Prob. 13ECh. 22.4 - Prob. 1ECh. 22.4 - Prob. 2ECh. 22.4 - Prob. 3ECh. 22.4 - Prob. 4ECh. 22.4 - Prob. 5ECh. 22.5 - Prob. 1ECh. 22.5 - Prob. 2ECh. 22.5 - Prob. 3ECh. 22.5 - Prob. 4ECh. 22.5 - Prob. 5ECh. 22.5 - Prob. 6ECh. 22.5 - Prob. 7ECh. 22 - Prob. 1PCh. 22 - Prob. 2PCh. 22 - Prob. 3PCh. 22 - Prob. 4P
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- Enhance the Python-coded Luby MIS algorithm by randomly choosing a vertex, determining its neighbours, and then identifying the vertex with the lowest assigned random value to be used in the MIS.arrow_forwardFor the graph below determine the minimum number of colors necessary to colorits vertices. Justify your answer, by (i) giving a coloring and (ii) explaining why it is not possibleto use fewer colors. You can represent colors by letters a, b, c, .... To show the coloring, mark eachvertex with its color.arrow_forwardDuring the execution of DFS, give the conditions under which there is an edge from a vertex u with color c1 has an edge to a vertex v with color c2. Consider the following color combinations, (c1, c2)= (w,w), (w,g), (g, b) and (b,g).arrow_forward
- By randomly selecting a vertex, identifying its neighbours, and then determining the vertex with the lowest assigned random value to be included in the MIS, Luby's Python-coded MIS algorithm can be improved.arrow_forwardLet V= {cities of Metro Manila} and E = {(x; y) | x and y are adjacent cities in Metro Manila.} (a) Draw the graph G defined by G = (V; E). You may use initials to name a vertex representing a city. (b) Apply the Four-Color Theorem to determine the chromatic number of the vertex coloring for G.arrow_forwardRepresent the following graph using an edge array, a list of edge objects, an adjacency matrix, an adjacency vertex list, and an adjacency edge list, respectively. 1 3 2arrow_forward
- Correct answer will be upvoted else downvoted. Computer science. There is another fascination in Singapore Zoo: The Infinite Zoo. The Infinite Zoo can be addressed by a chart with a limitless number of vertices marked 1,2,3,… . There is a guided edge from vertex u to vertex u+v if and provided that u&v=v, where and indicates the bitwise AND activity. There could be no different edges in the chart. Animal specialist has q inquiries. In the I-th question she will inquire as to whether she can venture out from vertex ui to vertex vi by going through coordinated edges. Input The main line contains an integer q (1≤q≤105) — the number of inquiries. The I-th of the following q lines will contain two integers ui, vi (1≤ui,vi<230) — an inquiry made by Zookeeper. Output For the I-th of the q inquiries, output "YES" in a solitary line if Zookeeper can head out from vertex ui to vertex vi. In any case, output "NO". You can print your reply regardless. For…arrow_forwardPlease help... Adding one more vertices... highlighted with with bold... Let A, B, C, D be the vertices of a square with side length 100. If we want to create a minimum-weight spanning tree to connect these four vertices, clearly this spanning tree would have total weight 300 (e.g. we can connect AB, BC, and CD). But what if we are able to add extra vertices inside the square, and use these additional vertices in constructing our spanning tree? Would the minimum-weight spanning tree have total weight less than 300? And if so, where should these additional vertices be placed to minimize the total weight? Let G be a graph with the vertices A, B, C, D, and possibly one or more additional vertices that can be placed anywhere you want on the (two-dimensional) plane containing the four vertices of the square. Determine the smallest total weight for the minimum-weightarrow_forwardYou are given a connected, undirected graph G. Devise an algorithm that produces a path that traverses each edge in G exactly once in each direction. A vertex may occur multiple times on the path. Provide a short justification about why your algorithm is correct, and analyze its efficiency.arrow_forward
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