Divide and conquer algorithm

J.D. Becker, I. Eisele, F.W.M. Demann, Implementation of Divide-and-Conquer Algorithms on Multiprocessors, Artif. Intell., 1991, 565, 121-136. 

The divide-and-conquer algorithm is a natural parallel algorithm [43]. Full scale first-principle calculations for large molecules will become feasible as parallel computing technology improves. It is expected that the present method will play a vital role in our quest of relationship among electronic structure, stability, and functions of macromolecules. 

A divide-and-conquer algorithm for a binary predicate r over parameters X and Y works as follows. Let X be the induction parameter. IfX is minimal, then Y is (usually) easily found by directly solving the problem. Otherwise, that is if X is non-minimal, decompose X into a vector HX of heads of X and a vector TX of tails of X, the tails being of the same type as X, as well as smaller than X according to some well-founded relation. The tails TX recursively yield tails TY of Y. The heads HX are processed into a vector HY of heads of Y. Finally, Y is composed from its heads HY and tails TY. 

A divide-and-conquer algorithm for a binary jffedicate r over parameters X and Y works as follows. LetX be the induction parameter. IfX is minimal, then Y is (usually)... 

D. R. Smith. Top-down synthesis of divide-and-conquer algorithms. Artificial Intelligence 27(l) 43-96,1985. Also in [Rich and Waters 86a], pp. 35-61. [Smith 88]... 

In Part III, we develop an actual logic algorithm synthesis mechanism from specifications by examples and properties, as seen in Chapter 6. It fits the particular non-incremental synthesis strategy presented in Chapter 7, is guided by the divide-and-conquer algorithm schema seen in Chapter 8, and uses the tool-box of methods developed in Chapters 9 and 10. 

Divide and Conquer Algorithm for DMA Combinatorial Library Synthesis... 

Embedded Divide-and-Conquer Algorithm on Hierarchical Real-Space Grids Parallel Molecular Dynamics Simulation Based on Linear-Scaling Density Functional Theory. 

The divide-and-conquer method [34,35] was the first Kohn Sham algorithm which delivered linear scaling computational costs that grow linearly with the size of the system. In this technique, one first projects the density matrix onto a basis set, typically... 

Yang s divide-and-conquer method is reviewed and shown to be as accurate as the conventional Kohn-Sham method and to be a practical algorithm for large molecule calculations. The working mechanism of the method is thoroughly examined. 

A recursive work distribution scheme involves recursive subdivisions of the computational problem to create smaller tasks that can be solved concurrently by individual processes. Recursive work distribution schemes are typically used for computational problems that lend themselves to a divide-and-conquer parallelization approach. For instance, finding the maximum value in an imsorted array and sorting the elements in an array are problems that can be solved using recursive algorithms. 

This paper presents a new mechanism for alleviating the two previous drawbacks by 1) Decomposing the global problem in sub-problems by a divide-and-conquer approach that reduces memory requirements and 2) Using a parallel implementation of the algorithms, as parallel architectures represent a natural environment to overcome these limitations. 

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