The Product Replacement Prospector
نویسندگان
چکیده
منابع مشابه
The Product Replacement
The \product replacement algorithm" is a commonly used heuristic to generate random group elements in a nite group G, by running a random walk on generating k-tuples of G. While experiments showed outstanding performance, the theoretical explanation remained mysterious. In this paper we propose a new approach to study of the algorithm, by using Kazhdan's property (T) from representation theory ...
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;its minimal faithful permutation and matrix representation degrees are respectively 97 239 461 142 009 186 000 and 196 882. This makes it far harder to work with than the 25 smaller sporadics. In Section 3, we describe techniques which allow limited computation in the Monster. In Section 4, we describe our experiments to assess the effectiveness of combining these techniques with a suitable ve...
متن کاملVariants of Product Replacement
We present new variations on the product replacement method for generating random elements in a black box group, together with some basic analysis and conjectures.
متن کاملThe product replacement algorithm is polynomial
The product replacement algorithm is a heuristic designed to generate random group elements. The idea is to run a random walk on generating k-tuples of the group, and then output a random component. The algorithm was designed by Leedham-Green and Soicher ([31]), and further investigated in [12]. It was found to have an outstanding performance, much better than the the previously known algorithm...
متن کاملGrowth in Product Replacement Graphs
We prove the exponential growth of product replacement graphs for a large class of groups. Much of our effort is dedicated to the study of product replacement graphs of Grigorchuk groups, where the problem is most difficult.
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2012
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2011.08.017