This paper deals with fuzzy quantities and relations in multi-objective minimum cost flow problem. When t-norms and t-conorms are available, the goal programming is applied tominimize the deviation among themultiple costs of fuzzy flows and the given targets when the fuzzy supplies and demands are satisfied. To obtain the most optimistic and the most pessimistic satisficing solutions of this pr...

We consider the CONGEST model on a network with n nodes, m edges, diameter D, and integer costs capacities bounded by $${{\,\textrm{poly}\,}}n$$ . In this paper, we show how to find an exact solution minimum cost flow problem in $$n^{1/2+o(1)}(\sqrt{n}+D)$$ rounds, improving state of art algorithm running time $$m^{3/7+o(1)}(\sqrt{n}D^{1/4}+D)$$ [16], which only holds for special case unit capa...

Many emerging sensor network applications require sensor node deployment in challenging environments that are remote and inaccessible. In such applications, it is not always possible to deploy base stations in or near the sensor field to collect sensory data. Therefore, the overflow data generated by some nodes is first offloaded to other nodes inside the network to be preserved, then gets coll...

We present an algorithm to compute a complete set of efficient solutions for the biobjective integer minimum cost flow problem. We use the two phase method with a parametric network simplex algorithm in phase 1 to compute all supported non-dominated extreme points. In phase 2, the remaining nondominated points (non-extreme supported and non-supported) are computed using a k best flow algorithm ...

The dynamic version of the minimum cost multicommodity flow problem that generalizes the static minimum cost multicommodity flow problem is formulated and studied. This dynamic problem is considered on directed networks with a set of commodities, time-varying capacities, fixed transit times on arcs, and a given time horizon. We assume that cost functions, defined on edges, are nonlinear and dep...

The constrained maximum flow problem is to send the maximum possible flow from a source node s to a sink node t in a directed network subject to a budget constraint that the cost of flow is no more than D. In this paper, we consider two versions of this problem: (i) when the cost of flow on each arc is a linear function of the amount of flow; and (ii) when the cost of flow is a convex function ...

The constrained maximum flow problem is to send the maximum possible flow from a source node s to a sink node t in a directed network subject to a budget constraint that the cost of flow is no more than D. In this paper, we consider two versions of this problem: (i) when the cost of flow on each arc is a linear function of the amount of flow; and (ii) when the cost of flow is a convex function ...

The cost scaling push-relabel method has been shown to be efficient for solving minimum-cost flow problems. In this paper we apply the method to the assignment problem and investigate implementations of the method that take advantage of assignment's special structure. The results show that the method is very promising for practical use.

Similarity of edge labeled graphs is considered in the sense of minimum squared distance between corresponding values. Vertex correspondences are established by isomorphisms if both graphs are of equal size and by subisomorphisms if one graph has fewer vertices than the other. Best fit isomorphisms and subisomorphisms amount to solutions of quadratic assignment problems and are computed exactly...

We present strongly polynomial time algorithms for the minimum cost flow problem and for the weighted bipartite matching problem, also known as the assignment problem. 1 The minimum cost flow problem A flow network with costs, demands and capacities N = (G, a, b, c) is composed of a directed graph G = (V,E), a cost function a : E → R, a demand function b : V → R, and a capacity function c : E →...