Ishwar Murthy

A parametric approach to solving bicriterion shortest path problems

Abstract In this paper a new algorithm is developed to solve bicriterion shortest path problems (BSP). This algorithm first relaxes the integrality conditions and solves a simple bicriterion network problem. The bicriterion network problem is solved parametrically, exploiting properties associated with adjacent basis trees. Those Pareto-optimal paths not obtained by solving the LP relaxation are obtained using a label correcting procedure. Computational results comparing the parametric approach to the label setting approach and the K -th shortest path approach are also presented. They indicate that the parametric approach is orders of magnitude faster than the K -th shortest path approach for most problems tested. For problems with a positive correlation between the two cost coefficients, the parametric approach is seen to be significantly faster than the label setting approach.

A Relaxation-Based Pruning Technique for a Class of Stochastic Shortest Path Problems

In this paper a form of the stochastic shortest path problem is considered where the optimal path is one that maximizes the expected utility which is concave and quadratic. The principal contribution of this paper is the development of a relaxation based pruning technique which is incorporated into a label setting procedure. The basic label setting procedure solves the problem by generating all Pareto-optimal paths. However, the number of such paths can grow exponentially with the size of the problem. The relaxation based pruning technique developed here is able to recognize and discard most of the Pareto-optimal paths that do not contribute to the optimal path. Our computational results show that the label setting procedure that incorporates the pruning technique consistently outperforms the basic label setting procedure, and is able to solve large problems very quickly.

Solving min‐max shortest‐path problems on a network

In this article we consider the problem of determining a path between two nodes in a network that minimizes the maximum of r path length values associated with it. This problem has a direct application in scheduling. It also has indirect applications in a class of routing problems and when considering multiobjective shortest-path problems. We present a label-correcting procedure for this problem. We also develop two pruning techniques, which, when incorporated in the label-correcting algorithm, recognize and discard many paths that are not part of the optimal path. Our computational results indicate that these techniques are able to speed up the label-correcting procedure by many orders of magnitude for hard problem instances, thereby enabling them to be solved in a reasonable time.

Exact algorithms for the stochastic shortest path problem with a decreasing deadline utility function

In this paper, the stochastic shortest path problem of determining a path that maximizes the expected utility is considered. The nature of the utility function used to evaluate paths is of a decreasing deadline type. The principal contribution of this paper is the development of exact algorithms that use two types of pruning techniques that are incorporated in labeling procedures. One type of pruning makes use of the concept of local preference relations while the other type makes use of relaxations. Specifically two algorithms are developed, each containing the same preference relation, but two different relaxations. Our extensive computational testing indicate that both these algorithms are able to solve even large size problems quickly. More importantly, even for large problems, both the algorithms solved them by enumerating a very small percentage of all paths.

An interactive procedure using domination cones for bicriterion shortest path problems

Abstract In this paper an interactive procedure is developed for the bicriterion shortest path problem. It is assumed that the decision makers inherant utility function is quasi-concave and non-increasing, and that the network consists of non-negative, integer valued arc lengths. The proposed procedure uses the concept of domination cones, which it develops from pairwise comparisons of alternatives. These domination cones are used to fathom a large number of Pareto-optimal solutions. Extensive computational testing was performed on large grid networks, simulating the decision makers response using polynomial utility functions. The results indicate that our proposed procedure is able to converge to the optimal solution in a reasonably small number of pairwise comparisons, even for those problems with a large number of Pareto-optimal solutions.

File allocation problem: comparison of models with worst case and average communication delays

A major design issue facing the designer of a distributed computing system involves the determination of the number of file copies and their locations in the distributed environment. This problem is commonly referred to as the file allocation problem (FAP). This paper considers two FAP models that seek to minimize operating costs (i.e., the total cost of file storage and query/update communication). The first model ensures the attainment of acceptable levels of communication delay during peak network traffic periods (worst-case scenario). The second model considers average communication delay. Unlike previous FAP research, the proposed models treat communication delay on a query-by-query basis, and not as a single, system-wide average delay constraint. For both models, a Lagrangian relaxation-based solution procedure is proposed for the resulting 0/1 integer programming problem. In the case of average delays, we utilize a hybrid model combining analytic and simulation procedures. The results of computatio...

Constructing efficient belief network structures with expert provided information

Presents a technique to construct efficient belief network structures for application areas where large amounts of data are available and information on the ordering of the variables can be obtained from domain experts. We identify classes of networks that are efficient for propagating beliefs. We formulate the problem as one of determining the belief network representation from a given class that best represents the data. We use the I-Divergence measure which is known to have certain desirable properties for evaluating different approximations. We present some theoretical findings that characterize the nature of solutions that are obtained. These theoretical results lead to an efficient solution procedure for finding the best network representation. We also discuss other information that may be reasonably obtained from experts, and show how such information leads to improving the efficiency of the technique to find the best network structure.

File allocation involving worst case response times and link capacities: Model and solution procedure

Abstract A major design issue facing the designer of a distributed computing system involves the determination of the number of file copies and their locations in the distributed environment. This problem is commonly referred to as the file allocation problem (FAP). In this paper, a FAP model is formulated that seeks to obtain the lowest cost file allocation strategy, that ensures the attainment of acceptable levels of response times during peak demand periods, for all on-line queries. Unlike previous FAP research, the proposed model treats response time on a query-by-query basis, and not as a single, system wide average delay constraint . A Laggrangian relaxation based solution procedure is proposed for the resulting 0/1 integer programming problem. Results of computational experiments with the proposed solution procedure are reported.

A solution procedure for the file allocation problem with file availability and response time

A major design issue facing the designer of a distributed computing system involves the dertermination of the number of file copies and their locations in the distributed environment. This problem is commonly referred to as the file allocation problem (FAP). In this paper, a FAP model is formulated that seeks to obtain the lowest cost file allocation strategy. The model ensures, for all on-line queries, the attainment of acceptable levels of (i) response times during peak demand periods, and (ii) file availability. Unlike previous FAP research, the proposed model treats response time on a query-by-query basis, and not as a single, system-wide average delay constraint. Similarly, file availability is treated on a file-by-file basis. A branch-and-bound solution procedure is proposed for solving the resulting 01 integer programming problem to optimality. Results of computational experiment with the proposed solution procedure are reported.

An information theoretic technique to design belief network based expert systems

Abstract This paper addresses the problem of constructing belief network based expert systems. We discuss a design tool that assists in the development of such expert systems by comparing alternative representations. The design tool uses information theoretic measures to compare alternative structures. Three important capabilities of the design tool are discussed: (i) evaluating alternative structures based on sample data; (ii) finding optimal networks with specified connectivity conditions; and (iii) eliminating weak dependencies from derived network structures. We have examined the performance of the design tool on many sets of simulated data, and show that the design tool can accurately recover the important dependencies across variables in a problem domain. We illustrate how this program can be used to design a belief network for evaluating the financial distress situation for banks.