A quadratic lower bound for Topswops

被引：2

作者：

Morales, Linda ^{[1
]}

Sudborough, Hal ^{[1
]}

机构：

[1] Univ Texas Dallas, Dept Comp Sci, Erik Jonsson Sch Engn & Comp Sci, Richardson, TX 75083 USA

来源：

THEORETICAL COMPUTER SCIENCE | 2010年 / 411卷 / 44-46期

关键词：

Topswops; Reverse card shuffle; Pancake problem; Prefix reversals; Lower bounds; Permutations; Conway card games;

D O I：

10.1016/j.tcs.2010.08.011

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

A quadratic lower bound for the topswops function is exhibited. This provides a non-trivial lower bound for a problem posed by J.H. Conway, D.E. Knuth, M. Gardner and others. We describe an infinite family of permutations, each taking a linear number of steps for the topswops process to terminate, and a chaining process that creates from them an infinite family of permutations taking a quadratic number of steps to reach a fixed point with the identity permutation. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：3965 / 3970

页数：6

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