Complexity classes of equivalence problems revisited
نویسندگان
چکیده
منابع مشابه
Complexity Classes of Equivalence Problems Revisited
To determine if two given lists of numbers are the same set, we would sort both lists and see if we get the same result. The sorted list is a canonical form for the equivalence relation of set equality. Other canonical forms for equivalences arise in graph isomorphism and its variants, and the equality of permutation groups given by generators. To determine if two given graphs are cospectral (h...
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We prove that at least 3k−4 k(2k−3) ( n 2 ) − O(k) equivalence tests and no more than 2 k ( n 2 ) + O(n) equivalence tests are needed in the worst case to identify the equivalence classes with at least k members in set of n elements. The upper bound is an improvement by a factor 2 compared to known results. For k = 3 we give tighter bounds. Finally, for k > n 2 we prove that it is necessary and...
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Let $G$ be a non-abelian group and let $Gamma(G)$ be the non-commuting graph of $G$. In this paper we define an equivalence relation $sim$ on the set of $V(Gamma(G))=Gsetminus Z(G)$ by taking $xsim y$ if and only if $N(x)=N(y)$, where $ N(x)={uin G | x textrm{ and } u textrm{ are adjacent in }Gamma(G)}$ is the open neighborhood of $x$ in $Gamma(G)$. We introduce a new graph determined ...
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ژورنال
عنوان ژورنال: Information and Computation
سال: 2011
ISSN: 0890-5401
DOI: 10.1016/j.ic.2011.01.006