scholarly journals The inverse maximum flow problem with lower and upper bounds for the flow

2008 ◽  
Vol 18 (1) ◽  
pp. 13-22 ◽  
Author(s):  
Adrian Deaconu
Keyword(s):  
Upper Bound ◽  
Flow Problem ◽  
Maximum Flow ◽  
Upper Bounds ◽  
Initial Vector ◽  
Polynomial Algorithms ◽  
Lower And Upper Bounds ◽  
L1 Norm ◽  
Maximum Flow Problem

The general inverse maximum flow problem (denoted GIMF) is considered, where lower and upper bounds for the flow are changed so that a given feasible flow becomes a maximum flow and the distance (considering l1 norm) between the initial vector of bounds and the modified vector is minimum. Strongly and weakly polynomial algorithms for solving this problem are proposed. In the paper it is also proved that the inverse maximum flow problem where only the upper bound for the flow is changed (IMF) is a particular case of the GIMF problem.

scholarly journals The inverse maximum flow problem under Lk norms

2012 ◽  
Vol 28 (1) ◽  
pp. 59-66
Author(s):  
ADRIAN DEACONU ◽  
◽  
ELEONOR CIUREA ◽  
Keyword(s):  
Polynomial Time ◽  
Flow Problem ◽  
Maximum Flow ◽  
Upper Bounds ◽  
Initial Vector ◽  
Lower And Upper Bounds ◽  
Maximum Flow Problem ◽  
The Given

The problem consists in modifying the lower and upper bounds of a given feasible flow f in a network G so that the given flow becomes a maximum flow in G and the distance between the initial vector of bounds and the modified one measured using Lk norm (k ∈ N∗) is minimum. A fast apriori fesibility test is presented. An algorithm for solving this problem is deduced. Strongly and weakly polynomial time implementations of this algorithm are presented. Some particular cases of the problem are discussed.

scholarly journals Inverse Minimum Cut Problem with Lower and Upper Bounds

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1494
Author(s):  
Adrian Deaconu ◽  
Laura Ciupala
Keyword(s):  
Polynomial Algorithm ◽  
Upper Bounds ◽  
Inverse Optimization ◽  
Initial Vector ◽  
Minimum Cut ◽  
Lower And Upper Bounds ◽  
L1 Norm ◽  
Strongly Polynomial Algorithm ◽  
Minimum Cut Problem ◽  
Strongly Polynomial

The inverse minimum cut problem is one of the classical inverse optimization researches. In this paper, the inverse minimum cut with a lower and upper bounds problem is considered. The problem is to change both, the lower and upper bounds on arcs so that a given feasible cut becomes a minimum cut in the modified network and the distance between the initial vector of bounds and the modified one is minimized. A strongly polynomial algorithm to solve the problem under l1 norm is developed.

Efficiency of the Network Simplex Algorithm for the Maximum Flow Problem

1988 ◽  
Author(s):  
Andrew V. Goldberg ◽  
Michael D. Grigoriadis ◽  
Robert E. Tarjan
Keyword(s):  
Flow Problem ◽  
Maximum Flow ◽  
Simplex Algorithm ◽  
Maximum Flow Problem ◽  
Network Simplex Algorithm ◽  
Network Simplex

Reverse maximum flow problem under the weighted Chebyshev distance

2018 ◽  
Vol 52 (4-5) ◽  
pp. 1107-1121 ◽  
Author(s):  
Javad Tayyebi ◽  
Abumoslem Mohammadi ◽  
Seyyed Mohammad Reza Kazemi
Keyword(s):  
Flow Problem ◽  
Maximum Flow ◽  
Binary Search ◽  
Second Phase ◽  
Sink Node ◽  
Search Technique ◽  
Bound Constraints ◽  
Maximum Flow Problem ◽  
Optimal Value ◽  
Two Phases

Given a network G(V, A, u) with two specific nodes, a source node s and a sink node t, the reverse maximum flow problem is to increase the capacity of some arcs (i, j) as little as possible under bound constraints on the modifications so that the maximum flow value from s to t in the modified network is lower bounded by a prescribed value v0. In this paper, we study the reverse maximum flow problem when the capacity modifications are measured by the weighted Chebyshev distance. We present an efficient algorithm to solve the problem in two phases. The first phase applies the binary search technique to find an interval containing the optimal value. The second phase uses the discrete type Newton method to obtain exactly the optimal value. Finally, some computational experiments are conducted to observe the performance of the proposed algorithm.

scholarly journals Engineering Bi-Connected Component Overlay for Maximum-Flow Parallel Acceleration in Large Sparse Graph

2018 ◽  
Vol 36 (5) ◽  
pp. 955-962
Author(s):  
Yang Liu ◽  
Wei Wei ◽  
Heyang Xu
Keyword(s):  
Large Scale ◽  
Flow Problem ◽  
Maximum Flow ◽  
Low Complexity ◽  
Connected Components ◽  
Sparse Graphs ◽  
Fully Integrated ◽  
Flow Acceleration ◽  
Maximum Flow Problem ◽  
Graph Contraction

Network maximum flow problem is important and basic in graph theory, and one of its research directions is maximum-flow acceleration in large-scale graph. Existing acceleration strategy includes graph contraction and parallel computation, where there is still room for improvement:(1) The existing two acceleration strategies are not fully integrated, leading to their limited acceleration effect; (2) There is no sufficient support for computing multiple maximum-flow in one graph, leading to a lot of redundant computation. (3)The existing preprocessing methods need to consider node degrees and capacity constraints, resulting in high computational complexity. To address above problems, we identify the bi-connected components in a given graph and build an overlay, which can help split the maximum-flow problem into several subproblems and then solve them in parallel. The algorithm only uses the connectivity in the graph and has low complexity. The analyses and experiments on benchmark graphs indicate that the method can significantly shorten the calculation time in large sparse graphs.

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