The minimum cut problem (or mincut problem) is to find a cut of minimum cost. If all costs are 1 then the problem becomes the problem of finding a cut with as few edges as possible. Cuts are often defined in a different, not completely equivalent, way. Define a cutset to be a set of edges whose removal disconnects the graph into at least two connected components. Minimal cutsets (a minimal cuts...

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...

The minimum concave cost network flow problem (MCCNFP) has many applications in areas such as telecommunication network design, facility location, production and inventory planning, and traffic scheduling and control. However, it is a well known NP-hard problem, and all existing search based exact algorithms are not practical for networks with even moderate numbers of vertices. Therefore, the r...

We consider a minimum-cost dynamic network-flow problem on a very special network. This network flow problem models an infinite-horizon, lot-sizing problem with deterministic demand and periodic data. We permit two different objectives: minimize long-run average-cost per period and minimize the discounted cost. In both cases we give polynomial algorithms when certain arc costs are fixed charge ...

In this paper we study two basic problems related to dynamic flows: maximum multicommodity flow and the minimum cost multicommodity flow problems. We consider these problems on dynamic networks with time-varying capacities of edges. For minimum cost multicommodity flow problem we assume that cost functions, defined on edges, are nonlinear and depending on time and flow, and the demand function ...

In the present paper we extend the out-of-kilter method for the ordinary minimum-cost flow problem to the submodular flow problem considered by Edmonds and Giles. From the algorithmic point of view, there is no essential difference between a submodular flow problem described by a submodular function on a crossing family and one described by a submodular function on a distributive lattice, if we...

We study the TAPF (combined target-assignment and pathfinding) problem for teams of agents in known terrain, which generalizes both the anonymous and non-anonymous multiagent path-finding problems. Each of the teams is given the same number of targets as there are agents in the team. Each agent has to move to exactly one target given to its team such that all targets are visited. The TAPF probl...