Efficient dual simplex algorithms for the assignment problem

Efficient algorithms based upon Balinski's signature method are described for solving then × n assignment problem. These algorithms are special variants of the dual simplex method and are shown to have computational bounds of O(n ³). Variants for solving sparse assignment problems withm arcs that require O(m) space and O(mn + n ² logn) time in the worst case are also presented.This research was supported in part by the National Science Foundation under Grant No. MCS-8006064 and by the Army Research Office under Contracts No. DAAG 29-82-K0163 and DAAG 29-83-K0106     

Routing optimization in packet switching communication networks

For routing assignments a special model and an optimization algorithm are proposed. The efficiency of the routing assignments is evaluated by the average value of the total cost of delays for all packets in the network. It is the objective function. The main idea is that traffic, which is transmitted from the source node to the destination node, can be split between two or more logical paths. The minimum of the objective function can be found by varying the traffic on every path and simultaneously from all the source nodes to the destination nodes. If this approach is applied, then the objective function is nonseparable and nonlinear. Because its shape is unknown in advance, an adaptive nonlinear optimization algorithm is proposed. For evaluating its efficiency a special set of test functions has been used.     

A unification of two classes ofQ-matrices

This note presents a class ofQ-matrices which includes Saigal's classN ofQ-matrices with negative principal minors and the classE of strictly semi-monotoneQ-matrices.Research supported by the Office of Naval Research under Contract N00014-75-C-0621 NR 047-048.     

Stability of the linear complementarity problem at a solution point

In this paper we study the behavior of a solution of the linear complementarity problem when data are perturbed. We give characterizations of strong stability of the linear complementarity problem at a solution. In the case of stability we give sufficient and necessary conditions.     

On the Fermat—Weber problem with convex cost functions

We treat an extension of the generalized Fermat—Weber problem with convex cost functions. It is shown that the entire sequence of iterates (as opposed to selected subsequences) generated by each of the two proposed algorithms converges to a minimum although the economic function is not strictly convex. The general idea is to associate, with the economic function calledh, a family of more regular strictly convex functions, the lower envelope of which is the functionh.     

Heat output as a bio-marker of the dimethyl sulfoxide-induced decrease in rat hepatoma cell metabolism in vitro

Dimethyl sulfoxide (DMSO) is widely and routinely used as a vehicle in various investigations, especially within the pharmaceutical industry. It has been used for the evaluation of the effects of hydrophobic xenobiotics on cells, as well as for the cryopreservation of biological material. Isothermal microcalorimetry is a powerful tool for monitoring heat production, which is a function of general cellular metabolic activity. Employing this microcalorimetric technique, a low concentration of DMSO routinely used for the addition of hydrophobic substances to, e.g., cell cultures, was shown to decrease heat production (per unit DNA) by the rat hepatoma cell lines FAO, Morris 7800C1 and H4IIE by 32–38%. However, such low concentrations of DMSO did not influence the cell cycle or the degree of apoptosis in these cell populations. Caution is thus advisable when utilizing DMSO as a vehicle in cell culture experiments.     

A new branching strategy for time constrained routing problems with application to backhauling

In this paper, we explore a new branching strategy for branch-and-bound approaches based on column generation for the vehicle routing problems with time windows. This strategy involves branching on resource variables (time or capacity) rather than on network flow variables. We also examine criteria for selecting network nodes for branching. To test the effectiveness of the branching strategy, we conduct computational experiments on time window constrained vehicle routing problems where backhauling is permitted only after all the shipments to clients have been made. The branching method proved very effective. In cases where time was the more binding constraint, time-based branching succeeded in decreasing the number of nodes explored by two thirds and the total computation time by more than half when compared to flow-based branching. The computational results also show that the overall algorithm was successful in optimally solving problems with up to 100 customers. It produced an average cost decrease of almost 7% when backhauling was permitted as compared to the cost involved when the client and the distributor routes were distinct.     

The adjacency relation on the traveling salesman polytope is NP-Complete

We consider the problem of determining whether two traveling salesman tours correspond to non-adjacent vertices of the convex polytope associated with the traveling salesman problem. This problem is shown to be NP-Complete for both the symmetric and nonsymmetric traveling salesman problem. Several implications are discussed.This Research was supported by NSF Grant GK-420488, the U.S. Army Research Office-Durham under Grant DAHC04-75-G0192, and an IBM Fellowship.     

WDM网络中的一个改进的最优半光通道路由算法

本文在一个限定的条件下，提出了一个WDM网络中的寻找最优半光通道算法，使时间复杂度从O（k^2n km knlog(kn))提高到O（k^2n km nlogn)。     

A note on solution of large sparse maximum entropy problems with linear equality constraints

This paper describes a method to solve large sparse maximum entropy problems with linear equality constraints using Newtons and the conjugate gradient method. A numerical example is given to introduce the reader to possible applications of entropy models and this method. Some experience from large scale problems is also reported.