کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10331863 | 686963 | 2015 | 5 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Detecting monomials with k distinct variables
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We study the complexity of detecting monomials with special properties in the sum-product expansion of a polynomial represented by an arithmetic circuit of size polynomial in the number of input variables and using only multiplication and addition. We focus on monomial properties expressed in terms of the number of distinct variables occurring in a monomial. Our first result is a randomized FPT algorithm for detection of a monomial having at least k distinct variables, parametrized with respect to k. For a more restricted class of circuits, we can also provide a deterministic FPT algorithm for detection of a monomial having at most k distinct variables parametrized by the degree of the polynomial represented by the input circuit. Furthermore, we derive several hardness results on detection of monomials with such properties within exact, parametrized and approximation complexity. In particular, we observe that the detection of a monomial having at most k distinct variables is W[2]-hard for the parameter k.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Information Processing Letters - Volume 115, Issue 2, February 2015, Pages 82-86
Journal: Information Processing Letters - Volume 115, Issue 2, February 2015, Pages 82-86
نویسندگان
Peter Floderus, Andrzej Lingas, Mia Persson, Dzmitry Sledneu,