The algorithm presented in this paper solves the minimum flow problem in a parametric network with linear lower bound functions by computing a parametric maximum flow from the sink node to the source node. The algorithm does not work directly in the original parametric network but in the parametric residual network defined as for the parametric maximum flow problem. The complexity of the parame...

The Max-Min Diversity Problem (MMDP) consists in selecting a subset of elements from a given set in such a way that the diversity among the selected elements is maximized. The problem is NP-hard and can be formulated as an integer linear program. Since the 1980s, several solution methods for this problem have been developed and applied to a variety of fields, particularly in the social and biol...

The Multi-Depot Vehicle Routing Problem (MDVRP) is a generalization of the Single-Depot Vehicle Routing Problem (SDVRP) in which vehicle(s) start from multiple depots and return to their depots of origin at the end of their assigned tours. The traditional objective in MDVRP is to minimize the sum of all tour lengths, and existing literature handles this problem with a variety of assumptions and...

We consider a new combinatorial optimization problem related to linear systems (MIN PFS) that consists, given an infeasible system, in finding a partition into a minimum number of feasible subsystems. MIN PFS allows formalization of the fundamental problem of piecewise linear model estimation, which is an attractive alternative when modeling a wide range of nonlinear phenomena. Since MIN PFS tu...

Abstract. The worst-case residual norms of the GMRES method for linear algebraic systems [3] can, in case of a normal matrix, be characterized by a min-max approximation problem on the matrix eigenvalues. In [2] we derive a lower bound on this min-max value (worst-case residual norm) for each step of the GMRES iteration. We conjecture that the lower bound and the min-max value agree up to a fac...

We use a branch-and-cut search to solve the Whizzkids’96 vehicle routing problem, demonstrating that the winning solution in the 1996 competition is in fact optimal. Our algorithmic framework combines the LP-based traveling salesman code of Applegate, Bixby, Chvátal, and Cook, with specialized cutting planes and a distributed search algorithm, permitting the use of a computing network located a...

A survivable connection usually requires computing link-disjoint primary and backup paths. Finding a min-sum pair of link-disjoint paths whose total cost is minimized can be solved in polynomial time. However, adding extra requirements may render the problem NP-complete. In this paper, we study different variants of the min-sum link-disjoint paths problem. We examine the complexity of these pro...

Min Storage is an NP–hard optimization problem that arises in a natural way when one considers computations in which the amount of energy provided with the input values is preserved during the computation. In this paper we propose a polynomial time membrane algorithm that computes approximate solutions to the instances of Min Storage, and we study its behavior on (almost) uniformly randomly cho...