Q1:We define the capacity of a path in a weighted graph G(V, E) to be the minimum weight ofan edge along that path. For example, the capacity of the path [V0, V1, V2] in the graphbelow is 5 and the capacity of the path V1, V0, V3, V2 is 3. A maximum-capacity pathbetween u and v is a simple path between u and v whose capacity is larger than or equal tothose of all paths from u to v. In the graph below, the maximum capacity path from V0 toV3 is [V0, V1, V2, V3].(a) Show that if [a, b, ... , u, v] is a maximum-capacity path from a to v, then a maximum-capacity path from a to u followed by the edge (u, v) is a maximum-capacity path froma to v.(b) Is it true that if [a, b, c, u, v] is a maximum-capacity path from a to v, then [a, b, c, u]is a maximum-capacity path from a to u? Why?(c) Can you think of an algorithm you have seen before that can be modified to find themaximum-capacity paths from a particular vertex s to all other vertices in the graph?How? 10Vo3V225V3V4

Path Capacities Maximum Capacities Vo V3 V4 3, 8 3 Vo V1 V2 V3 10, 5, 25 25 Vo V1 V2 V3…

Q1: We define the capacity of a path in a weighted graph G(V, E) to be the minimum weight of an edge along that path. For example, the capacity of the path [V0, V1, V2] in the graph below is 5 and the capacity of the path V1, V0, V3, V2 is 3. A maximum-capacity path between u and v is a simple path between u and v whose capacity is larger than or equal to those of all paths from u to v. In the graph below, the maximum capacity path from V0 to V3 is [V0, V1, V2, V3].

Q1: We define the capacity of a path in a weighted graph G(V, E) to be the minimum weight of an edge along that path. For example, the capacity of the path [V0, V1, V2] in the graph below is 5 and the capacity of the path V1, V0, V3, V2 is 3. A maximum-capacity path between u and v is a simple path between u and v whose capacity is larger than or equal to those of all paths from u to v. In the graph below, the maximum capacity path from V0 to V3 is [V0, V1, V2, V3].

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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. Let G be a weighted, connected, undirected graph, and let V1 and V2 be a partition of the vertices of G into two disjoint nonempty sets. Furthermore, let e be an edge in the minimum spanning tree for G such that e has one endpoint in V1 and the other in V2. Give an example that shows that e is not necessarily the smallest- weight edge that has one endpoint in V1 and the other in V2.
In this task you will work with an undirected Graph G = {V, E}, where V = {f,p,s,b,l,j,t,c,d} and E = {(1,2), (1,3), (3,8), (4,8), (8,9), (1,7), (2,6), (2,3), (5,6), (6,7), (7,9), (8,1)}. Assume that the nodes are stored in an indexed linear structure (e.g., an array or a vector) numbered consecutively from 1 (node f) to 9 (node d). Run, by hand, a depth-first search (DFS) traversal of the graph G, starting at node p. When choosing which node to visit next amongst the possibilities, choose the one that is next in alphabetical order. Give your answer by listing the edges in the order that DFS will select.
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In the game of Nim, an arbitrary number of chips are divided into an arbitrary number of piles. Each player can remove as many chips as desired from any single pile. The last player to remove a chip wins. Consider a limited version of this game, in which three piles contain 3, 5, and 8 chips, respectively. You can represent this game as a directed graph. Each vertex in this graph is a possible configuration of the piles (chips in each pile). The initial configuration, for example, is (3, 5, 8). Each edge in the graph represents a legal move in the game. Write Java statements that will construct this directed graph. Discuss how a computer program might use this graph to play Nim. java program