Marc Gengler

An efficient algorithm for solving the token distribution problem on k-ary d-cube networks

In parallel programs where the problem data is dynamically generated, it is very useful to be able to rely on an efficient load balancing algorithm. The token distribution problem (TDP) is a generalization of the static load balancing problem. The paper describes a novel algorithm for solving the TDP for k-ary d-cube topology networks. Compared to other algorithms, our method is more general and does not rely on every processor knowing the exact number of tokens associated to each processor. The correctness of the algorithm is proved and its complexity is informally studied.<<ETX>>

A Parallel Best-First B&B with Synchronization Phases

We present a new parallel best-first Branch and Bound algorithm conceived for machines with distributed memory. Based on the notion of problems having the same lower bound, the algorithm evaluates these problems in parallel, during each phase of its execution. These computationally intensive phases alternate with control phases where synchronization and information exchange between processors takes place. We propose a probabilistic model for predicting the performances of this algorithm and discuss the results obtained on a MIMD multiprocessor for the Asymmetric Non-Euclidean TSP.

A PARALLEL BEST-FIRST B&B ALGORITHM AND ITS AXIOMATIZATION

We present a new parallel best-first Branch and Bound algorithm designed for distributed memory machines. Starting from an axiomatization of the Branch and Bound pardigm, we develop the notion of fringes in the Branch and Bound tree which correspond to sets of equivalent problems. The algorithm proposed in this paper evaluates these sets of problems in parallel, during each phase of its execution. These computationally intensive phases alternate with control phases where synchronization and information exchange between processors lakes place. We use a probabilistic model for predicting the performances of this algorithm. Finally, we discuss the performances obtained on MIMD-DM multiprocessors for the asymmetric non-Euclidean Traveling Salesman Problem.

A Survey on Minimax Trees And Associated Algorithms

This paper surveys theoretical results about minimax game trees and the algorithms used to explore them. The notion of game tree is formally introduced and its relation with game playing described. The first part of the survey outlines major theoretical results about minimax game trees, their size and the structure of their subtrees. In the second part of this paper, we survey the various sequential algorithms that have been developed to explore minimax trees. The last part of this paper tries to give a succinct view on the state of the art in parallel minimax game tree searching.

Software-Development Strategies for Parallel Computer Architectures

Abstract As pragmatic users of high performance supercomputers, we believe that nowadays parallel computer architectures with disturbed memories are not yet mature to be used by a wide range of application engineers. A big effort should be made to bring these very promising computers closer to the users. One major flaw of massively parallel machines is that the programmer has to take care himself of the data flow which is often different on different parallel computers. To overcome this problem, we propose that data structures be standardized. The data base then can become an integrated part of the system and the data flow for a given algorithm can be easily prescribed. Fixing data structures forces the computer manufacturer to rather adapt his machine to users demands and not, as it happens now, the user has to adapt to the innovative computer science approach of the computer manufacturer. In this paper, we present data standards chosen for our ASTRID programming platform for research scientist and engineers, as well as a plasma physics application which won the Cray Gigaflop Performance Awards 1989 and 1990 and which was succesfully ported on an INTEL iPSC/2 hypercube.

Comparing two Probabilistic Models of the Computational Complexity of the Branch and Bound Algorithm

We study two probabilistic models developed in order to predict the computational complexity of the branch and bound algorithm as well as its suitability for a parallelization based on the simultaneous exploration of all subproblems having a same common lower bound We show that both models, starting from different assumptions, yield asymptotically the same results but differ for small problems. Both models agree to predict a quick increase of the number of subproblems as a function of their lower bounds offering a convenient approach for parallelization of the branch and bound algorithm.

A parallel best-first B&B algorithm and its axiomatization

A new parallel best-first branch and bound algorithm designed for distributed memory machines is presented. Starting from an axiomatization of the branch and bound paradigm, the authors develop the notion of fringes in the branch and bound tree which correspond to sets of equivalent problems. The algorithm proposed evaluates these sets of problems in parallel, during each phase of its execution. These computationally intensive phases alternate with control phases where synchronization and information exchange between processors take place. The authors use a probabilistic model for predicting the performance of this algorithm. The performance obtained on multiple instruction/multiple data (MIMD)-DM multiprocessors for the asymmetric non-Euclidean traveling salesman problem is discussed.<<ETX>>

AN EXTENDED DIMENSION ORDER TOKEN DISTRIBUTION ALGORITHM ON k-Ary d-CUBES AND ITS COMPLEXITY

Parallel programs that dynamically generate data generally need good load balancing algorithms. The token distribution problem is a generalization of the static load balancing problem. We solve this problem by an algorithm, called dimension order token distribution algorithm, designed for k-ary d-cube topologies. The algorithm is formally stated and proved correct. We analyze its message-passing and computational complexities and show that it is optimal. We also discuss generalizations of this algorithm, showing how the algorithm can be adapted so as to handle tokens of different kinds or so as to let the sender of a token know the destination of the migrating token.

The alignment problem in a linear algebra framework

Two important aspects have to be addressed when automatically parallelizing loop nests for massively parallel distributed memory computers, namely maximizing parallelism and minimizing communication overhead due to nonlocal data accesses. This paper studies the problem of finding a computation mapping and data distributions that minimize the number of remote data accesses for a given degree of parallelism. This problem is called the constant-degree parallelism alignment problem and is shown to be NP-hard. The algorithm presented uses a linear algebra framework and assumes affine data access functions. It proceeds by enumerating all interesting bases of the set of vectors representing the alignments between computation and data accesses that should be satisfied. It is shown in a comparison with related work how the approach presented allows one to express previous results as special cases. The algorithm is applied to benchmark programs and is shown to be superior to more basic mappings.

Experiments with a Parallel Synchronized Branch and Bound Algorithm

In this paper we present an efficient parallel synchronized branch and bound (PSBB) algorithm. This parallelization of a sequential branch and bound best-first algorithm is based on the concept of alternating computation and synchronization or macro-communication steps. The computational steps simplify the problem to solve whereas the synchronization phases solve the problem of load balancing and data distribution. We will describe the implementation of heuristics for solving mixed integer linear programs. Experimental results will show the efficiency of the proposed PSBB algorithm when executed on a massively parallel Cray T3D machine.