丁克诠.随机置换的分量与单调重新构组问题的计算等价性(英文)[J].数学研究及应用,1991,11(1):1~8
随机置换的分量与单调重新构组问题的计算等价性(英文)
Computational Equivalence Between the Problems of Sorting and Monotone Reconstruction for Random Permutations
  
DOI:10.3770/j.issn:1000-341X.1991.01.001
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丁克诠 Department of Mathematics
University of Wisconsin-Madison Madison
WI 53706
USA 
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      In this note, it is shown that the monotone reconstruction problem is equi-valent to that of sorting, in the sense of computational complexity. In particular from any given sorting algorithm A, an algorithm B for the monotone reconstruc-tion problem can be developed with at most O(m) time and O( m) space cost more than that used in A, and vice versa. As a consequence of this result, it is obtai-ned that the time complexity of the monotone reconstruction problem of n-ele-ment random permutations is O(nlogn).
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