Jeffery L. Kennington

An empirical evaluation of the KORBX algorithms for military airlift applications

KORBX® a registered trademark of ATT and some pure network problems were solved using NETFLO, MPSX, and XMP.

A polynomially bounded algorithm for a singly constrained quadratic program

This paper presents a characterization of the solutions of a singly constrained quadratic program. This characterization is then used in the development of a polynomially bounded algorithm for this class of problems.

Primal simplex network codes: State-of-the-art implementation technology

In recent years there have been several extremely successful specialization of the primal simplex method for solving network flow problems. Much of this success is due to the development of highly efficient computational techniques for implementing the primal simplex algorithm. We view these efficient techniques as a new body of knowledge which we call implementation technology. This exposition presents the state-of-the-art of implementation technology.

Hierarchical cellular network design with channel allocation

Abstract The design of a cellular network is a complex process that encompasses the selection and configuration of cell sites and the supporting network infrastructure. This investigation presents a net revenue maximizing model that can assist network designers in the design and configuration of a cellular system. The integer programming model takes as given a set of candidate cell locations with corresponding costs, the amount of available bandwidth, the maximum demand for service in each geographical area, and the revenue potential in each customer area. Based on these data, the model determines the size and location of cells, and the specific channels to be allocated to each cell. To solve problem instances, a maximal clique cut procedure is developed in order to efficiently generate tight upper bounds. A lower bound is constructed by solving the discrete optimization model with some of the discrete variables fixed. Computational experiments on 72 problem instances demonstrate the computational viability of our new procedure.

A generalization of Polyak's convergence result for subgradient optimization

This paper generalizes a practical convergence result first presented by Polyak. This new result presents a theoretical justification for the step size which has been successfully used in several specialized algorithms which incorporate the subgradient optimization approach.

A Shortest Augmenting Path Algorithm for the Semi-Assignment Problem

The objective of this study is to develop a shortest augmenting path algorithm for solving the semi-assignment problem and conduct an extensive computational comparison with the best alternative approaches. The algorithm maintains dual feasibility and complementary slackness and works toward satisfying primal feasibility. Effective heuristics arc used to achieve an excellent advanced start, and convergence is assured via the use of the shortest augmenting path procedure using reduced costs for arc lengths. Unlike other algorithms, such as the primal simplex or the auction algorithm, each iteration during the final phase of the procedure also known as the end-game achieves one additional assignment. The software implementations of our algorithm are fastest for the semi-assignment problems that we tested. Our dense code is also faster than the best software for assignment problems. In addition, the algorithm has the best polynomial worst-case running time bound that we have seen; and the memory requirements are relatively small.

Wavelength Routing and Assignment in a Survivable WDM Mesh Network

All-optical networks with wavelength division multiplexing (WDM) capabilities are prime candidates for future wide-area backbone networks. The simplified processing and management of these very high bandwidth networks make them very attractive. A procedure for designing low cost WDM networks is the subject of this investigation.In the literature, this design problem has been referred to as the routing and wavelength assignment problem. Our proposed solution involves a three-step process that results in a low-cost design to satisfy a set of static point-to-point demands. Our strategy simultaneously addresses the problem of routing working traffic, determining backup paths for single node or single link failures, and assigning wavelengths to both working and restoration paths.An integer linear program is presented that formally defines the routing and wavelength assignment problem (RWA) being solved along with a simple heuristic procedure. In an empirical analysis, the heuristic procedure successfully solved realistically sized test cases in under 30 seconds on a Compaq AlphaStation. CPLEX 6.6.0 using default settings required over 1,000 times longer to obtain only slightly better solutions than those obtained by our new heuristic procedure.

The one-to-one shortest-path problem: an empirical analysis with the two-tree Dijkstra algorithm

Four new shortest-path algorithms, two sequential and two parallel, for the source-to-sink shortest-path problem are presented and empirically compared with five algorithms previously discussed in the literature. The new algorithm, S22, combines the highly effective data structure of the S2 algorithm of Dial et al., with the idea of simultaneously building shortest-path trees from both source and sink nodes, and was found to be the fastest sequential shortest-path algorithm. The new parallel algorithm, PS22, is based on S22 and is the best of the parallel algorithms. We also present results for three new S22-type shortest-path heuristics. These heuristics find very good (often optimal) paths much faster than the best shortest-path algorithm.

An Empirical Analysis of the Dense Assignment Problem: Sequential and Parallel Implementations

The best algorithms for the dense assignment problem are acknowledged to be the auction algorithm and the shortest augmenting path algorithm. In this investigation we present an empirical analysis of two of the current best software implementations of these two methods on three different serial machines. These software implementations were developed by D. P. Bertsekas of the Massachusetts Institute of Technology and by R. Jonker and T. Volgenant of the University of Amsterdam. This report is an independent evaluation of the software implementation of these two algorithms. For the sample of problems examined and the sample of hardware used (IBM 3081D, Sequent Symmetry S81, and VAX 750), we found that the shortest augmenting path algorithm was the fastest. We also report our empirical results with a parallel version of the shortest augmenting path algorithm. On 1200×1200 dense assignment problems, speedups of approximately four were achieved using ten processors. Million arc problems were solved in less than twelve seconds on a Sequent Symmetry S81 with the parallel shortest augmenting path algorithm. INFORMS Journal on Computing , ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

Base Station Location and Service Assignments in W--CDMA Networks

Designing a wideband code division multiple access (W--CDMA) network is a complicated task requiring the selection of sites for radio towers, analysis of customer demand, and assurance of service quality in terms of signal-to-interference ratio requirements. This investigation presents a net-revenue maximization model that can help a network planner with the selection of tower sites and the calculation of service capacity. The integer programming model takes as input a set of candidate tower locations with corresponding costs, a number of customer locations with corresponding demand for traffic, and the revenue potential for each unit of capacity allocated to each demand point. Based on these data, the model can be used to determine the selection of radio towers and the service capacity of the resulting radio network. The basic model is a large integer program and requires a special algorithm for practical solution. Our algorithm uses a priority branching scheme, an optimization-gap tolerance between 1% and 10%, and two sets of global valid inequalities that tighten the upper bounds obtained from the linear programming relaxation. The algorithm has been implemented in software for the AMPL/CPLEX system and an empirical investigation has been conducted. Using over 300 problem instances with up to 40 towers and 250 service locations, various combinations of algorithm settings have been evaluated. Using the recommended setting results in a design tool that generally runs in under 20 minutes on a 667 MHz AlphaStation.