scholarly journals Inverse Generalized Maximum Flow Problems

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 899 ◽  
Author(s):  
Javad Tayyebi ◽  
Adrian Deaconu
Keyword(s):  
Flow Problem ◽  
Natural Extension ◽  
Maximum Flow ◽  
Fast Method ◽  
Np Hard ◽  
Flow Problems ◽  
Maximum Flow Problem ◽  
Hard Problems ◽  
Optimum Solution ◽  
Np Hard Problems

A natural extension of maximum flow problems is called the generalized maximum flow problem taking into account the gain and loss factors for arcs. This paper investigates an inverse problem corresponding to this problem. It is to increase arc capacities as less cost as possible in a way that a prescribed flow becomes a maximum flow with respect to the modified capacities. The problem is referred to as the generalized maximum flow problem (IGMF). At first, we present a fast method that determines whether the problem is feasible or not. Then, we develop an algorithm to solve the problem under the max-type distances in O ( m n · log n ) time. Furthermore, we prove that the problem is strongly NP-hard under sum-type distances and propose a heuristic algorithm to find a near-optimum solution to these NP-hard problems. The computational experiments show the accuracy and the efficiency of the algorithm.

scholarly journals Lexicographically Maximum Flows under an Arc Interdiction

2021 ◽  
Vol 4 (2) ◽  
pp. 8-14
Author(s):  
Phanindra Prasad Bhandari ◽  
Shree Ram Khadka
Keyword(s):  
Network Flow ◽  
Flow Problem ◽  
Maximum Flow ◽  
Directed Network ◽  
Network System ◽  
Residual Flow ◽  
Network Flow Problems ◽  
Flow Problems ◽  
Maximum Flow Problem ◽  
Maximum Flows

Network interdiction problem arises when an unwanted agent attacks the network system to deteriorate its transshipment efficiency. Literature is flourished with models and solution approaches for the problem. This paper considers a single commodity lexicographic maximum flow problem on a directed network with capacitated vertices to study two network flow problems under an arc interdiction. In the first, the objective is to find an arc on input network to be destroyed so that the residual lexicographically maximum flow is lexicographically minimum. The second problem aims to find a flow pattern resulting lexicographically maximum flow on the input network so that the total residual flow, if an arc is destroyed, is maximum. The paper proposes strongly polynomial time solution procedures for these problems.

scholarly journals Single-based and Population-Based Metaheuristics Algorithms Performances in Solving NP-hard Problems

2021 ◽  
Author(s):  
Saman Almufti
Keyword(s):  
Real Life ◽  
Optimal Solution ◽  
Population Based ◽  
Performance Evaluations ◽  
Np Hard ◽  
Life Problems ◽  
Hard Problems ◽  
Optimum Solution ◽  
Over Time ◽  
Np Hard Problems

Metaheuristics is one of the most well-known field of researches uses to find optimum solution for Non-deterministic polynomial hard problems (NP-Hard), that are difficult to find an optimal solution in a polynomial time. Over time many algorithms have been developed based on the heuristics to solve difficult real-life problems, this paper will introduce Metaheuristic-based algorithms and its classifications, Non-deterministic polynomial hard problems. It also will compare the performance two metaheuristic-based algorithms (Elephant Herding optimization algorithm and Tabu Search) to solve Traveling Salesman Problem (TSP), which is one of the most known problem belongs to Non-deterministic polynomial hard problem and widely used in the performance evaluations for different metaheuristics-based optimization algorithms. the experimental results of the paper compare the results of EHO and TS for solving 10 different problems from the TSPLIB95.

scholarly journals Two Flow Problems in Dynamic Networks

2016 ◽  
Vol 12 (1) ◽  
pp. 103 ◽  
Author(s):  
Camelia Schiopu ◽  
Eleonor Ciurea
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Flow Problem ◽  
Dynamic Networks ◽  
Maximum Flow ◽  
Flow Problems ◽  
Maximum Flow Problem

In this paper we study two flow problems: the feasible flow problem in dynamic networks and the maximum flow problem in bipartite dynamic networks with lower bounds. We mention that the maximum flow problem in bipartite dynamic networks with lower bound was presented in paper [8]a. For these problems we give examples.

NP vs QMA_\log(2)

2010 ◽  
Vol 10 (1&2) ◽  
pp. 141-151
Author(s):  
S. Beigi
Keyword(s):  
Quantum Algorithms ◽  
Np Hard ◽  
Complete Problems ◽  
Hard Problems ◽  
Np Complete ◽  
Np Hard Problems

Although it is believed unlikely that $\NP$-hard problems admit efficient quantum algorithms, it has been shown that a quantum verifier can solve NP-complete problems given a "short" quantum proof; more precisely, NP\subseteq QMA_{\log}(2) where QMA_{\log}(2) denotes the class of quantum Merlin-Arthur games in which there are two unentangled provers who send two logarithmic size quantum witnesses to the verifier. The inclusion NP\subseteq QMA_{\log}(2) has been proved by Blier and Tapp by stating a quantum Merlin-Arthur protocol for 3-coloring with perfect completeness and gap 1/24n^6. Moreover, Aaronson et al. have shown the above inclusion with a constant gap by considering $\widetilde{O}(\sqrt{n})$ witnesses of logarithmic size. However, we still do not know if QMA_{\log}(2) with a constant gap contains NP. In this paper, we show that 3-SAT admits a QMA_{\log}(2) protocol with the gap 1/n^{3+\epsilon}} for every constant \epsilon>0.

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.

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