Gerard A. P. Kindervater

Asynchronous Parallel Branch and Bound and Anomalies

The parallel execution of branch and bound algorithms can result in seemingly unreasonable speedups or slowdowns. Almost never the speedup is equal to the increase in computing power. For synchronous parallel branch and bound, these effects have been studied extensively. For asynchronous parallelizations, only little is known.

The parallel complexity of TSP heuristics

Abstract We consider eight heuristics for constructing approximate solutions to the traveling salesman problem and analyze their complexity in a model of parallel computation. The problems of finding a tour by the nearest neighbor, nearest merger, nearest insertion, cheapest insertion, and farthest insertion heuristics are shown to be P -complete. Hence, it is unlikely that such tours can be obtained in polylogarithmic work space on a sequential computer or in polylogarithmic time on a computer with unbounded parallelism. The double minimum spanning tree and nearest addition heuristics can be implemented to run in polylogarithmic time on a polynomial number of processors. For the Christofides heuristic, we give a randomized polylogarithmic approximation scheme requiring a polynomial number of processors.

OR Forum—Perspectives on Parallel Computing

Operations research is one problem domain that is likely to benefit from advances in parallel computing. We briefly review what has been achieved in recent years and try to sketch what may be expected in the near future. We argue that the lack of uniformity in available architectures is the main obstacle for the breakthrough of parallel computing. Also, formal techniques will have to be developed for the design and implementation of efficient parallel algorithms, and more realism will be required in theoretical models of parallel computation.

A queueing network model for analyzing a class of branch-and-bound algorithms on a master-slave architecture

Partitioning methods lend themselves very well to implementation on parallel computers. In recent years, branch-and-bound algorithms have been tested on various types of architectures. In this paper, we develop a queueing network model for the analysis of a class of branch-and-bound algorithms on a master–slave architecture. The analysis is based on a fluid flow approximation. Numerical examples illustrate the concepts developed. Finally, related branch-and-bound algorithms are studied using a machine repair queueing model.

Finding a Feasible Solution for a Class of Distributed Problems with a Single Sum Constraint Using Agents

In this paper, we describe a Multi-Agent System which is capable of finding a feasible solution of a class of distributed problems, in which the subproblems share a single a sum constraint. Emphasis is given to correctness issues and termination detection.

Sequential and parallel local search for the time-constrained traveling salesman problem

Local search has proven to be an effective solution approach for the traveling salesman problem. We consider variants of the TSP in which each city is to be visited within one or more given time windows. The travel times are symmetric and satisfy the triangle inequality; the objective is to minimize the tour duration. We develop efficient sequential and parallel algorithms for the verification of local optimality of a tour with respect to k-exchanges.

Towards an abstract parallel branch and bound machine

textabstractMany (parallel) branch and bound algorithms look very different from each other at first glance. They exploit, however, the same underlying computational model. This phenomenon can be used to define branch and bound algorithms in terms of a set of basic rules that are applied in a specific (predefined) order. In the sequential case, the specification of Mittens rules turns out to be sufficient for the development of branch and bound algorithms. In the parallel case, the situation is a bit more complicated. We have to consider extra parameters such as work distribution and knowledge sharing. Here, the implementation of parallel branch and bound algorithms can be seen as a tuning of the parameters combined with the specification of Mittens rules. These observations lead to generic systems, where the user provides the specifications of the problem to be solved, and the system generates a branch and bound algorithm running on a specific architecture. We will discuss some proposals that appeared in the literature. Next, we raise the question whether the proposed models are flexible enough. We analyze the design decisions to be taken when implementing a parallel branch and bound algorithm. It results in a classification model, which is validated by checking whether it captures existing branch and bound implementations. Finally, we return to the issue of flexibility of existing systems, and propose to add an abstract machine model to the generic framework. The model defines a virtual parallel branch and bound machine, within which the design decisions can be expressed in terms of the abstract machine. We will outline some ideas on which the machine may be based, and present directions of future work.