
Algorithms and Complexity for the Almost Equal Maximum Flow Problem
In the Equal Maximum Flow Problem (EMFP), we aim for a maximum flow wher...
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A CostScaling Algorithm for MinimumCost NodeCapacitated Multiflow Problem
In this paper, we address the minimumcost nodecapacitated multiflow pr...
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On the Bicriterion Maximum Flow Network Interdiction Problem
This article focuses on a biobjective extension of the maximum flow netw...
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A Combinatorial Algorithm for the Multicommodity Flow Problem
This paper researches combinatorial algorithms for the multicommodity f...
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Minmax Centered kPartitioning of Trees and Applications to Sink Evacuation with Dynamic Confluent Flows
Let T=(V,E) be a tree with associated costs on its subtrees. A minmax k...
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Network Interdiction Using Adversarial Traffic Flows
Traditional network interdiction refers to the problem of an interdictor...
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Distributed Data Compression in Sensor Clusters: A Maximum Independent Flow Approach
Let a cluster (network) of sensors be connected by the communication lin...
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Robust Minimum Cost Flow Problem Under Consistent Flow Constraints
The robust minimum cost flow problem under consistent flow constraints (RobMCF≡) is a new extension of the minimum cost flow (MCF) problem. In the RobMCF≡ problem, we consider demand and supply that are subject to uncertainty. For all demand realizations, however, we require that the flow value on an arc needs to be equal if it is included in the predetermined arc set given. The objective is to find feasible flows that satisfy the equal flow requirements while minimizing the maximum occurring cost among all demand realizations. In the case of a discrete set of scenarios, we derive structural results which point out the differences with the polynomial time solvable MCF problem on networks with integral capacities. In particular, the Integral Flow Theorem of Dantzig and Fulkerson does not hold. For this reason, we require integral flows in the entire paper. We show that the RobMCF≡ problem is strongly 𝒩𝒫hard on acyclic digraphs by a reduction from the (3,B2)Sat problem. Further, we demonstrate that the RobMCF≡ problem is weakly 𝒩𝒫hard on seriesparallel digraphs by providing a reduction from Partition and a pseudopolynomial algorithm based on dynamic programming. Finally, we propose a special case on seriesparallel digraphs for which we can solve the RobMCF≡ problem in polynomial time.
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