Question: Let G = (V, E) be a flow network with source s, sink t, and integer capacities. Suppose that we are given a maximum flow

Let G = (V, E) be a flow network with source s, sink t, and integer capacities. Suppose that we are given a maximum flow in G.
a. Suppose that the capacity of a single edge (u, v) ⁪¬ E is increased by 1. Give an O (V + E)-time algorithm to update the maximum flow.
b. Suppose that the capacity of a single edge (u, v) ¬⁪ E is decreased by 1. Give an O (V + E)-time algorithm to update the maximum flow.

Step by Step Solution

★★★★★

3.32 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Just execute one iteration of the FordFulkerson algorithm The edge u v in E with increased capacity ensures that the edge u v is in the residual gra... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

C-S-A (163).docx

120 KBs Word File

Students Have Also Explored These Related Algorithms Questions!

Suppose that we are testing H0: 1 = 2 versus H1: 1  2 and we plan to use equal sample sizes from the two populations. Both populations are assumed to be normal with unknown but equal...

Suppose that we are given a directed acyclic graph G = (V, E) with real-valued edge weights and two distinguished vertices s and t. Describe a dynamic-programming approach for finding a longest...

Suppose that we are given a key k to search for in a hash table with positions 0, 1, ..., m - 1, and suppose that we have a hash function h mapping the key space into the set {0, 1, ..., m -1. The...

Problem 14: Problem 26-5, Page 694; (CLRS) Let G = (V, E) be a ow network with source .9, sink t, and an integer capacity C(u, v) on each edge (um) E E. Let C = maxmnaeE c(u,v). a. b. Argue that a...

( b ) Let G = ( V , E ) be a flow network with source s and sink t in which each edgee has positive integer capacity ce M . Suppose that we run Ford - Fulkerson ( with no extraoptimization ) to find...

Let G = (V, E) be a flow network with source s and sink t. We say that an edge e is a bottleneck in G if it belongs to every minimum capacity cut separating s from t. Give a polynomial-time algorithm...

The Edmonds - Karp algorithm implements the Ford - Fulkerson algorithm by always choosing a shortest augmenting path in the residual network. Suppose instead that the Ford - Fulkerson algorithm...

In a standard s t maximum flow problem, we assume edges have capacities, and there is no limit on how much flow is allowed to flow through a node. In this problem, we consider the variant of the...

( 2 0 points ) Let G = ( V , E ) be a flow network with source s , sink t , and integer capacities. Suppose that we are given a maximum flow in G . Let n and m be the numbers of vertices and edges in...

Let G = ( V , E ) be a flow network with integer capacities. Let e be an edge in E , and let G be a flow network that is the same as G except that the capacity of edge e is one lower in G than in G ....

Contracts may have many types of clauses or terms and conditions. Write a brief synopsis of Dispute Resolution Clause

Following are Newman projections for the three tartaric acids (R,R), (S,S), and meso. Which is which? CO,H CO,H OH HO HO CO,H CO H CO H

30. LO.4 Peck, Inc., a U.S. corporation, purchases weight-lifting equipment for resale from HiDisu, a Japanese corporation, for 75 million yen. On the date of purchase, 75 yen is equal to $1 U.S....

For a person with normal hearing, the faintest sound that can be heard at a frequency of 400 Hz has a pressure amplitude of about 6.0 X 10-5 Pa. Calculate the (a) Intensity; (b) Sound intensity...

A box is separated by a partition into two parts of equal volume. The left side of the box contains 500 molecules of nitrogen gas; the right side contains 100 molecules of oxygen gas. The two gases...

Figure shows an initially stationary block of mass m on a floor. A force of magnitude 0.500mg is then applied at upward angle = 20 o . What is the magnitude of the acceleration of the block across...

An 80.0-m-long brass rod is struck at one end. A person at b the other end hears two sounds as a result of two longitudinal waves, one traveling in the metal rod and the other traveling in the air....

Consider a sound wave in air that has displacement amplitude 0.0200 mm. Calculate the pressure amplitude for frequencies of (a) 150 Hz; (b) 1500 Hz; (c) 15,000 Hz. In each case compare the result to...

Donna Jamison, a graduate of the University of Tennessee with four years of banking experience, was recently brought in as assistant to the chairman of the board of Computron Industries, a...

2. (6 pts) A major piece of your company's manufacturing equipment has failed and you need to buy a replacement. There are three alternatives. Which one should be selected based on rate of return...

Chapter 5 Assignment Seved 9 Your landscaping company can lease a truck for $7,300 a year (paid at year-end) for 5 years. It can instead buy the truck for $32,000. The truck will be valueless after 5...

Suppose that you are flipping 5 biased coins independently from one another. Theprobability of a coin landing HEAD is 0.6, and the probability of a coin landing TAILis 0.4. (a) What is the...