1. Recall that a flow network is a directed graph G = (V, E) with a source s, a sink t, and a capacity function c: V xV + Rj that is positive on E and 0 outside E.We only consider finite graphs here. Also, note that every flownetwork has a maximum flow. This sounds obvious but requires a proof (and we did not prove it in the videolecture).Which of the following statements are true for all flow networks (G, s,t,c)?O IfG = (V,E) has as cycle then it has at least two different maximum flows. (Recall: two flows f, f' aredifferent if they are different as functions V x V R. That is, if f(u, v) # f'(u, v) for some u, ve V.The number of maximum flows is at most the number of minimum cuts.The number of maximum flows is at least the number of minimum cuts.If the value of f is 0 then f(u, v) = 0 for all u, v.The number of maximum flows is 1 or infinity.The number of minimum cuts is finite.Need help, as you can see the checked boxesis not the right answer, something is missingaccording to Coursera system.

Recall that a flow network is a directed graph G = (V,E) with a source s, a sinkt. and a capacity function e: V V - Rộ that is positive on E and 0 outside E.We only consider finite graphs here. Also, note that every flow network has a maximum flow. This sounds obvious but requires a proof (and we did not prove it in the video lecture). Which of the following statements are true for all flow networks (G, s,t,e)?

Recall that a flow network is a directed graph G = (V,E) with a source s, a sinkt. and a capacity function e: V V - Rộ that is positive on E and 0 outside E.We only consider finite graphs here. Also, note that every flow network has a maximum flow. This sounds obvious but requires a proof (and we did not prove it in the video lecture). Which of the following statements are true for all flow networks (G, s,t,e)?

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

See similar textbooks

Similar questions

in a graph G = (N,E,C), where N are nodes, E edges between nodes, and the weight of an edge e ∈ E is given by C(e), where C(e) > 1, for all e ∈ E. the heuristic h that counts the least amount of edges from an initial state to a goal state. now removing edges from the graph, while keeping the heuristic values unchanged. Is the heuristic still consistent?
A system is said to be completely observable if there exists an unconstrained control u(t) that can transfer any initial state x(to) to any other desired location x(t) in a finite time to T. b. Investigate the observability of the system below. (X1 X2, -2 (X1 y = [1 2] Knowing that X = Ax + Bu and y= Cx.
Suppose you are given a directed graph G = (V, E) with a positive integer capacity ?? on each edge e, a designated source s ∈ V, and a designated sink t ∈ V. You are also given an integer maximum s-t flow value ?? on each edge e. Now suppose we pick a specific edge e belongs E and increase its capacity by one unit. Show how to find a maximum flow in the resulting capacitated graph in O(m + n), where m is the number of edges in G and n is the number on nodes.
Compute the maximum flow in the following flow network using Ford-Fulkerson's algorithm. 12 8 14 15 11 2 5 1 3 d 7 f 6 What is the maximum flow value? A minimum cut has exactly which vertices on one side? 4.
4. (1) Draw a transition graph for the dfa M={Q,E,8,q,,F ), where Q={q,,91»92 }; E = {a,b},F = {qo,92} and ở is definded as S(90,a) = q,,8(q,b) =q,,5(q,,a)=q0,8(q,,b) =q2,8(q2,a) =q2,8(q2,b) =q2 (2) Give the language accepted by the above dfa.
Prove that The number of augmenting paths needed in the shortest-augmenting-path implementation of the Ford-Fulkerson maxflow algorithm for a flow network with V vertices and E edges is at most EV /2.
Find the maximum flow of the following graph assuming node A is the source and node K is the sink. 12 11 10 17 15 自回

Let f be an s,t-flow in an s, t-network D = (V, A) with capacities c : A → R>o, and assume that there is no augmenting path. Let X be the set of vertices that can be reached from s by unsaturated paths. Let (a, b) E A(X,V\ X). Explain why f(a,b) = c(a, b).
Prove that there exists a maximum flow f in G, such that the set of edges carrying positive flowis acyclic. In other words, f has the property that for every directed cycle in G made up of edgese1, e2, . . . , ek, at least one of the values f (e1), f (e2), . . . , f (ek) is equal to zero.
Give me answer just 30 min
How can we merge parallel edges that are in the same direction in a flow network G?
Problem 3. Let G = (V, E) be a bipartite graph with verter partition V = LUR, and let G' be its corresponding flow network. Give a good upper bound on the length of any augmenting path found in G' during the execution of algorithm. FORD-FULKERSON