1)This problem will explore how different algorithms play out with the same weighted graph.a) Use the nearest neighbor algorithm to find an approximate solution to the traveling salesman problem for a circuit starting at vertex E, and find the weight of this circuit. The image depicts a complex geometric figure, specifically a pentagon with an inscribed star, formed by intersecting lines. Here is the detailed description:1. **Pentagon and Star Formation:** - The outer shape is a pentagon with vertices labeled A, B, C, D, and E. - Inside the pentagon, a star (specifically a five-pointed star) is drawn by connecting non-adjacent vertices.2. **Edges and Labels:** - The edges of the pentagon are labeled with numbers detailing distances or weights: - AB = 25 - BC = 21 - CD = 18 - DE = 11 - EA = 25 - The inner star has its own set of edges labeled with numbers: - AC = 22 - BD = 13 - CE = 24 - DB = 10 - EB = 19 - AD = 22 - BE = 93. **Intersection Points:** - The star is formed by intersecting lines within the pentagon, creating overlapping segments that contribute to the intricate geometric design.This diagram is an example of how polygons and star polygons can be used to explore geometric properties such as symmetry, congruence, and spatial visualization in educational settings.

We use nearest neighbour Algorithm to solve given problem. We find nearest neighbor from vertex E…

Answered: 3 19. | bartleby

Math

Advanced Math

3 19.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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4- Suppose we run Dijkstra's single source shortest-path algorithm on the following edge weighted directed graph with vertex P as the source. In what order do the nodes get included into the set of vertices for which the shortest path distances are finalized? P a) P,Q,R,U,T,S b) P.Q.T.R.U.S P,Q,R,U,S,T P,Q,R,S,T,U Leave blank JO 1 7 6 T 4 S 3 1 2 2 2 R 1 U
4. Does the graph whose adjacency matrix given by Find one if it does. 1 10 1 1 0 1 1 1 10 1 10 110 10 11 1 1 have a spanning tree?
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(5) The definition of weighted graph is such that every edge has positive weight. If the def- inition was changed to permit negative (or zero) weights, would Kruskal's and Dijkstra's algorithms continue to work? Give a proof or counterexample in each case.
We consider the Traveling Salesman Problem with the cost matrix 0 87 1 5 1086 3 7 10 15 9 2 70 5 8 2620 and apply Little's branch and bound algorithm. What is the initial lower bound on possible solutions at the very first step of the algorithm? Which edge (which entry of the cost matrix) is used for the first inclusion/exclusion branching? Enter the indices of vertices at both end points of this edge without any separators between them. (For example,if the edge (12) (or,in other words,the matrix entry c12) is chosen for inclusion/exclusion, enter 12 in the text box.) What is the lower bound on the solutions in the exclusion branch (after the fırst inclusion/exclusion branching)?
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