I've recently started practising some graph theory problems, and I wanted to know if there is a method which would allow us to approach the Max Flow problem through dynamic programming. I cannot seem to find any resources where they outline a similar approach, and in most places, they seem to utilise either Linear Programming or algorithms, such as the Ford–Fulkerson algorithm. I would be extremely grateful for any suggestions about books/videos where they consider it, or for any ideas that would help me to derive the method by myself. Thanks in advance!
2026-03-26 00:58:47.1774486727
Is there a way to represent a Max Flow problem as a dynamic programming task?
1k Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in GRAPH-THEORY
- characterisation of $2$-connected graphs with no even cycles
- Explanation for the static degree sort algorithm of Deo et al.
- A certain partition of 28
- decomposing a graph in connected components
- Is it true that if a graph is bipartite iff it is class 1 (edge-coloring)?
- Fake induction, can't find flaw, every graph with zero edges is connected
- Triangle-free graph where every pair of nonadjacent vertices has exactly two common neighbors
- Inequality on degrees implies perfect matching
- Proving that no two teams in a tournament win same number of games
- Proving that we can divide a graph to two graphs which induced subgraph is connected on vertices of each one
Related Questions in LINEAR-PROGRAMMING
- Proving dual convex cone property
- Linear algebra: what is the purpose of passive transformation matrix?
- Building the model for a Linear Programming Problem
- Show that $ \ x_ 0 \ $ cannot be an optimal solution
- Is there any way to model this situation in integer programming?
- How to Solve a Linear Programming Problem in $n$ Dimension Space?
- How to solve a linear program without any given data?
- Constraints for continuous path within graph with at least one obligatory node in path
- Select the smallest strict positive value from a list of variables in a linear program.
- How to add nonnegative constraint to an LP problem
Related Questions in OPERATIONS-RESEARCH
- correctness for minimizing average completition time for scheduling problem with release times
- the effect of an operation
- Reasonable/unreasonable exponentially distributed interarrival (service) times
- Optimally allocating inventory, does this problem have a name?
- Linear Programming: What is the rationale behind the Gauss Jordan Row operations we do after determining the leaving and entering variables?
- Linear programming: Converting nested absolute value
- How to find infinite optimal solutions for linear program?
- Ways to speed up solving an LP with Google's ortools
- A Mixed Integer Model with Mixed Integer sub-Problems
- Does zero considered as a leaving variable in simplex method?
Related Questions in DYNAMIC-PROGRAMMING
- Dynamic programming for Knapsack problem
- DP algorithm for covering the distance between two points with a set of intervals
- Solution of an HJB equation in continuous time
- correctness for minimizing average completition time for scheduling problem with release times
- Zero-sum differential game
- An enclosing polygon with minimum area
- Divide set into two subsets of equal sum and maximum this sum
- Stochastic Dynamic Programming: Deriving the Steady-State for a Lottery
- How would you prove that a dynamic programming problem is solvable by a greedy algorithm?
- How to find minimal distances route for a trip of $t$ days, given distances for each stop?
Related Questions in NETWORK-FLOW
- Flow graph force flow to "move" together
- min cost flow in offline bipartite graph problem
- Looking for some information on applications of integer linear programming
- Linear Programming Primal-Dual tough question
- question about the min cut max flow theorm
- Flows: Graph Theory/Groups, Empty Set
- Max number of vertex disjoint S-T paths in time O(VE)
- Minimum cut on a directed graph with negative term
- Minimum capacity cut reduction from digraph with two edge weight sets
- Dual Of Integer Network Formulation
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Hi: This is not an answer but I'm putting it here because it's easier to type and there's more room. The link below says that a greedy algorithm can be used to get an approximation but it does not result in optimality. To me, that's a hint that dynamic programming will not lead to an optimal solution because dynamic programming is really only applicable when greedy-ness works. So, I'm waving my hands here for sure but my guess is that you'll be going into a dark cave if you try to solve maximum flow using dynamic programming.
https://www.geeksforgeeks.org/max-flow-problem-introduction/
Also, just from a practical standoint, really smart people have been working on this problem for a long time. So, if a dynamic programming approach has not been used, chances are that it's not the way to proceed. Although, at the same time, if you did come up with such a result, it would most likely be viewed as an amazing achievement.