We give an upper bound for the number of different basic feasible solutions generated by Dantzig’s simplex method (the simplex method with the most negative pivoting rule) for LP with bounded variables by extending the result of Kitahara and Mizuno (2010). We refine the analysis by them and improve an upper bound for a standard form of LP. Then we utilize the improved bound for an LP with bound...

Motivated by a famous open question on the single-source unsplittable minimum cost flow problem, we present a new approximation result for the relaxation of the problem where, for a given number k, each commodity must be routed along at most k paths. © 2009 Elsevier B.V. All rights reserved.

This paper presents an algorithm that achieves hyper-arc consistency for the soft alldifferent constraint. To this end, we prove and exploit the equivalence with a minimum-cost flow problem. Consistency of the constraint can be checked in O(nm) time, and hyper-arc consistency is achieved in O(m) time, where n is the number of variables involved and m is the sum of the cardinalities of the domai...

In this paper we study the min-cost flow problem in planar networks. We start with the min-cost flow problem and apply two transformations, one is based on geometric duality of planar graphs and the other on linear programming duality. The result is a min-cost flow problem in a related planar network whose balance constraints are defined by the costs of the original problem and whose costs are ...

Let G = (N, A) be a network with a designated source node s, a designated sink node t, and a finite integral capacity uij < U on each arc (ij) E A. An elementary K-flow is a flow of K units from s to t such that the flow on each arc is 0 or 1. A K-route flow is a flow from s to t that may be expressed as a non-negative linear sum of elementary Kflows. In this paper, we show how to determine a m...

A diversity of tracking problems exists in which cohorts of densely packed particles move in an organized fashion, however the stability of individual particles within the cohort is low. Moreover, the flows of cohorts can regionally overlap. Together, these conditions yield a complex tracking scenario that can not be addressed by optical flow techniques that assume piecewise coherent flows, or ...

In this paper we study minimum flow algorithms in bipartite networks with unit capacities combining the algorithms for minimum flow in bipartite networks with the algorithms for minimum flow in unit capacity networks. Key–Words: Network flows, minimum flow problem, unit capacity networks, bipartite networks, maximum cut.