13 20 Show the execution of Dijkstra's shortest path algorithm, starting from vertex A. Draw the graph. After each relaxation, you will cross the previous best length and assign a new best length. Which list below shows the list of "best lengths" of the node C? O a. co0,6,5 O b. co,5 O .6,5 O d. 00,6

13 20 Show the execution of Dijkstra's shortest path algorithm, starting from vertex A. Draw the graph. After each relaxation, you will cross the previous best length and assign a new best length. Which list below shows the list of "best lengths" of the node C? O a. co0,6,5 O b. co,5 O .6,5 O d. 00,6

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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Use Prim's Algorithm starting at vertex SS to construct a minimum spanning tree of the graph below. If we tie-break alphabetically, what is the order of edges we construct our spanning tree? a. {S,T}, {S,V}, {V,Z}, {W,Z}, {Y,Z}, {W,X}, {U,Y} b. {S,T}, {S,W}, {W,Z}, {V,Z}, {Y,Z}, {W,X}, {U,Y} c. {S,T}, {V,Z}, {W,Z}, {Y,Z}, {S,V}, {W,X}, {U,Y} d. {S,T}, {S,V}, {S,W}, {V,Z}, {W,X}, {Y,Z}, {U,Y}
A mathematician applies Prim’s Algorithm to find a minimum spanning tree for the weighted graph starting at vertex D. The order of the edges picked so far is AD, AB, BE, and EF. The next edge selected when applying Prim’s Algorithm should be BF FG CG CE What is the total weight of the tree that uses the edges DE, CE, CG, FG and BF? 93 92 91 90 The tree described in problem #8 is a spanning True False
Draw a tree with 14 vertices Draw a directed acyclic graph with 6 vertices and 14 edges Suppose that your computer only has enough memory to store 40000 entries. Which best graph data structure(s) – you can choose more than 1 -- should you use to store a simple undirected graph with 200 vertices, 19900 edges, and the existence of edge(u,v) is frequently asked? - Adjacency Matrix - Adjacency List - Edge List
Run BFS algorithm on the following graph starting with vertex s. Whenever there is a choice of vertices, choose the one that is alphabetically first. What is the order that the vertices are visited? What is the shortest path from vertex s to vertex b?
What vertex will be picked up to execute the 1st iteration of the Shortest Path Algorithm in order to calculate the distance between vertex A and the other vertices in the following graph?
Algorithm 7.3 Dijkstra’s Algorithm1: Input : G = (V, E, w) connected, weighted graph G and a source vertex s2: Output : d[n] and p[n] distances and parents of vertices in shortest path tree3: for all v ∈ V \ {s} do initialize all vertices except source s4: d[v]←∞5: p[v]←−16: end for7: d[s] = 0; p[s] = s initialize source8: S ← V9: while S = Ø do10: find u ∈ S with minimum distance value11: for all (u, v) ∈ E do update neighbor distances to v12: if d[v] > d[u] + w(u, v) then13: d[v] ← d[v] > d[u] + w(u, v)14: p[v] ← u update parent15: end if16: end for17: S ← S \ {u} remove u from searched18: end while Write code for algorithm
lines (93 sloc) 3.18 KB Raw Blame Given an undirected, connected and weighted graph G(V, E) with V number of vertices (which are numbered from 0 to V-1) and E number of edges. Find and print the Minimum Spanning Tree (MST) using Kruskal's algorithm. For printing MST follow the steps - 1. In one line, print an edge which is part of MST in the format - v1 v2 w where, v1 and v2 are the vertices of the edge which is included in MST and whose weight is w. And v1 <= v2 i.e. print the smaller vertex first while printing an edge. 2. Print V-1 edges in above format in different lines. Note : Order of different edges doesn't matter. Input Format : Line 1: Two Integers V and E (separated by space) Next E lines : Three integers ei, ej and wi, denoting that there exists an edge between vertex ei and vertex ej with weight wi (separated by space) Output Format : Print the MST, as described in the task. Constraints : 2 <=…
A B C D E F A -- 32 44 33 31 34 B 32 -- 6 23 25 10 C 44 6 -- 2 58 13 D 33 23 2 -- 15 50 E 31 25 58 15 -- 5 F 34 10 13 50 5 -- The weights of edges in a graph are shown in the table above. Apply the nearest neighbor algorithm to the graph starting at vertex A. Give your answer as a list of vertices, starting and ending at vertex A. Example: ABCDEFA
Use breadth-first search starting at vertex S to construct a spanning tree of the graph below. If we tie-break alphabetically, what is the order of edges we construct our spanning tree? a. {S,T}, {S,V}, {S,W}, {T,X}, {V,Z}, {X,Y}, {U,Y} b. {S,V}, {S,T}, {S,W}, {V,Z}, {T,X}, {Y,Z}, {U,Y} c. {S,V}, {S,W}, {S,T}, {V,Z}, {T,X}, {Y,Z}, {U,Y} d. {S,T}, {S,W}, {S,V}, {T,X}, {V,Z}, {X,Y}, {U,Y}
Use depth-first search starting at vertex SS to construct a spanning tree of the graph below. If we tie-break alphabetically, what is the order of edges we construct our spanning tree? a. {S,T}, {T,X}, {W,X}, {W,Z}, {V,Z}, {X,Y}, {U,Y} b. {S,T}, {S,V}, {V,Z}, {W,Z}, {W,X}, {T,X}, {X,Y}, {U,Y} c. {S,T}, {T,X}, {W,X}, {S,V}, {V,Z}, {Y,Z}, {U,Y} d. {S,T}, {T,X}, {W,X}, {W,Z}, {V,Z}, {Z,Y}, {U,Y}
2. Consider the graph G2(V2, E2) below. 2a. Find the MST of this graph with Kruskal’s algorithm. Draw the MST, and show the table [edge] [w(u, v)] [mark]. 2b. Find the MST of this graph with Prim’s algorithm starting at vertex 'a'. Draw the MST and list the vertices in order you added them to the MST. 2c. Would you get a different MST if you repeat 2b starting at vertex 'e'? Why or why not?
a. How many links would such a circuit have? b. How many different paths would this algorithm examine? c. If this algorithm is run on a computer where it takes 0.0001 seconds to examine a single path, what is the total time required to examine all paths? d. On the same computer, what is the approximate total time required to examine all paths in a graph withe 12 nodes, each of which has four choices for the next node?