A comparative analysis of parallel disk-based Methods for enumerating implicit graphs

It is only in the last five years that researchers have begun to use disk-based search techniques on a large scale. The primary examples of its use come from symbolic algebra and from artificial intelligence. In the field of parallel search, disk-based search has been forced on researchers because the historical growth in the amount of RAM per CPU core has now stopped. Indeed, the current trend toward multi-core CPUs now threatens to take us backwards. This article makes an original contribution to the design of disk-based parallel search algorithms. It presents a survey of disk-based techniques side-by-side, for the first time. This allows researchers to choose from a menu of techniques, and also to create new hybrid algorithms from the building blocks presented here.

[1]  Gene Cooperman,et al.  New Methods for Using Cayley Graphs in Interconnection Networks , 1992, Discret. Appl. Math..

[2]  Gene Cooperman,et al.  Twenty-six moves suffice for Rubik's cube , 2007, ISSAC '07.

[3]  Jürgen Müller,et al.  A disk-based parallel implementation for direct condensation of large permutation modules , 2007, ISSAC '07.

[4]  Eric A. Hansen,et al.  Domain-Independent Structured Duplicate Detection , 2006, AAAI.

[5]  Gene Cooperman,et al.  Memory-based and disk-based algorithms for very high degree permutation groups , 2003, ISSAC '03.

[6]  Richard E. Korf,et al.  Best-First Frontier Search with Delayed Duplicate Detection , 2004, AAAI.

[7]  Gene Cooperman,et al.  New sequential and parallel algorithms for generating high dimension Hecke algebras using the condensation technique , 1996, ISSAC '96.

[8]  Alexander Hamilton Frey,et al.  Handbook of Cubik Math , 1982 .

[9]  Gene Cooperman,et al.  A parallel architecture for disk-based computing over the Baby Monster and other large finite simple groups , 2006, ISSAC '06.

[10]  Eric A. Hansen,et al.  Structured Duplicate Detection in External-Memory Graph Search , 2004, AAAI.

[11]  Gene Cooperman,et al.  A new Existence Proof of Janko’s Simple Group J4 , 1999 .

[12]  Richard E. Korf,et al.  Large-Scale Parallel Breadth-First Search , 2005, AAAI.

[13]  Michael Weller.  Construction of Large Permutation Representations for Matrix Groups II , 2001, Applicable Algebra in Engineering, Communication and Computing.

[14]  Andrew William Roscoe,et al.  Model-checking CSP , 1994 .

[15]  Bryant W. York,et al.  Constructing Permutation Representations for Matrix Groups , 1997, J. Symb. Comput..

[16]  Michael Weller.  Construction of Large Permutation Representations for Matrix Groups , 1999 .

[17]  Richard E. Korf,et al.  Frontier search , 2005, JACM.

[18]  Frank Lübeck,et al.  Enumerating Large Orbits and Direct Condensation , 2001, Exp. Math..

[19]  David J. DeWitt,et al.  Duplicate record elimination in large data files , 1983, TODS.

[20]  J. Conway,et al.  ATLAS of Finite Groups , 1985 .