Computing equality-free and repetitive string factorisations
Computing equality-free and repetitive string factorisations
复制标题
计算不等式和重复的字符串分解
DOI：
10.1016/j.tcs.2016.01.006
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Markus L. Schmid
中科院分区：
文献类型：
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作者：
Markus L. Schmid
对于字符串w，因子分解是满足w= u 1 <$u 2 <$uk的任何字符串元组（u 1，u 2，...，u k）。如果每两个因子是不同的，则因子分解被称为不相等的，它的大小是因子的数量（计算每次出现的重复因子），它的宽度是任何因子的最大长度。对于一个字符串w和一个数m，判断w是否有一个大小至少为（或宽度至多为）m的无等式因子分解是NP完全问题。我们进一步调查这些问题的复杂性，我们还研究了计算的因式分解，在很大程度上不平等的自由，即，因式分解的大小至少（或宽度最多）m这样的总数不同的因素不超过一个给定的界限k的逆问题。
For a string w, a factorisation is any tuple (u 1, u 2,…, u k) of strings that satisfies w= u 1⋅ u 2⋯ u k. A factorisation is called equality-free if each two factors are different, its size is the number of factors (counting each occurrence of repeating factors) and its width is the maximum length of any factor. To decide, for a string w and a number m, whether w has an equality-free factorisation with a size of at least (or a width of at most) m are NP-complete problems. We further investigate the complexity of these problems and we also study the converse problems of computing a factorisation that is to a large extent not equality-free, ie, a factorisation of size at least (or width at most) m such that the total number of different factors does not exceed a given bound k.