Flow Network Capacity Augmentation

AI Thread Summary
To maximize the flow in a flow network with integer edge capacities and a budget of n dollars, strategic allocation of funds is essential. Increasing the capacity of bottleneck edges, which limit flow, can significantly enhance overall network capacity. The max-flow min-cut theorem serves as a foundational principle for developing an effective spending strategy. Analyzing the current flow and identifying critical edges for capacity augmentation is crucial for optimal results. Ultimately, a well-planned investment in edge capacities can lead to substantial improvements in network flow.
mXSCNT
Messages
310
Reaction score
1
Suppose that you have a http://en.wikipedia.org/wiki/Flow_network" with integer edge capacities, and n dollars. You may spend one dollar to increase the capacity of an existing edge by one. The question is, how can you spend your dollars so that the maximum flow through the resulting network is maximized?
 
Last edited by a moderator:
Mathematics news on Phys.org
mXSCNT said:
Suppose that you have a http://en.wikipedia.org/wiki/Flow_network" with integer edge capacities, and n dollars. You may spend one dollar to increase the capacity of an existing edge by one. The question is, how can you spend your dollars so that the maximum flow through the resulting network is maximized?

The max-flow min-cut theorem might be a good place to start in constructing a spending strategy.
 
Last edited by a moderator:
Thread 'Video on imaginary numbers and some queries'

Thread 'Video on imaginary numbers and some queries'

Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »
Thread 'Unit Circle Double Angle Derivations'

Thread 'Unit Circle Double Angle Derivations'

Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
View full post »

Similar threads

Dynamics and convergence of a general flow network
Replies
11
Views
1K
I How to understand experiment to measure heat capacity of solid?
Replies
1
Views
2K
How Does the Ford-Fulkerson Algorithm Determine Maximum Flow in a Network?
Replies
1
Views
2K
What is the purpose of the OSI model and how does it partition the flow of data?
Replies
1
Views
2K
Entropy and Heat Capacity have the same units. Connection? Redundancy?
Replies
30
Views
7K
I Galaxy redshift and thermodynamics
Replies
10
Views
3K
Network Flow - Bipartite Matching
Replies
1
Views
3K
I Can chatgpt accurately calculate expected lengths in Pascal's triangle?
2
Replies
66
Views
7K
Comp Sci Help with coin game C++ assignment?
Replies
6
Views
3K
Air flow velocity - big to small and vice versa
Replies
3
Views
7K

Hot Threads

Recent Insights

Back
Top