Claude G. Diderich

Solving the Constant-Degree Parallelism Alginment Problem

We describe an exact algorithm for finding a computation mapping and data distributions that minimize, for a given degree of parallelism, the number of remote data accesses in a distributed memory parallel computer (DMPC). This problem is shown to be NP-hard.

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 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.

Solving Traveling Salesman Problems Using a Parallel Synchronized Branch and Bound Algorithm

In this paper we describe an efficient parallel synchronized branch and bound (PSBB) algorithm for distributed memory parallel computers. The parallelization of the sequential best-first branch and bound algorithm is based on the concept of alternating computation and synchronization steps. The computational steps simplify the problem to solve whereas the synchronization phases solve the problem of load balancing and data distribution. Experimental results show the efficiency of the proposed PSBB algorithm when solving traveling salesman problems on a massively parallel Cray T3D machine.

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.

Synchronization as a Strategy for Designing Efficient Parallel Algorithms

This paper presents a simple to use and general approach for designing efficient parallel algorithms for distributed memory machines. This approach is well suited for solving both regular and irregular problems using dynamic data. It is based on the notion of synchronized iterative algorithms. The idea is to alternate between computation and macro-communication steps, where a macro-communication step is composed of synchronization and load balancing or data redistribution operations. The simplicity and generality of this approach is shown on a theoretical example by proving non trivial lower and upper bounds for the efficiency. Experimental results certify the validity of the approach by parallelizing the best-first branch and bound algorithm for solving traveling salesman problems on a Cray T3D machine.

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.

A heuristic approach for finding a solution to the constant-degree parallelism alignment problem

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 non-local 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. The heuristic presented uses a linear algebra framework and assumes affine data access functions. It proceeds by incrementally building a basis of the set of vectors representing the alignments between computation and data accesses that should be satisfied. The heuristic algorithm is applied to benchmark programs and shown superior to more basic mappings.

Some Strategies for Load Balancing

In this paper we discuss the needs for load balancing, also called scheduling. We exhibit different reasons that render static (compile-time) scheduling impossible and that determine the dynamic (run-time) load balancing schemes needed in order to get efficient parallel algorithms One distinguishes between local load balancing policies where processors base their decisions on information about the load in some neighborhood and global load balancing policies where processors base their decisions on the load of the entire machine. Depending on the static information available and on the dependencies between the different tasks, some parallel algorithms accommodate with simple load balancing or load sharing mechanisms while others need more sophisticated solutions. The former are typically local while the later are global load balancing schemes. In particular, we analyze the branch and bound algorithm and show that it needs smart load balancing mechanisms ideally founded on global knowledge. We argue that for this algorithm a global load balancing policy may be interesting. Indeed, the best-first branch and bound algorithm can be defined as a sequence of independent computations allowing the design of a parallel algorithm that alternates between coarse grained parallel computation phases and so-called synchronization phases which provide perfect global load balancing.