کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10328283 | 683918 | 2011 | 14 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On the approximability of the minimum strictly fundamental cycle basis problem
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نظریه محاسباتی و ریاضیات
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چکیده انگلیسی
We consider the problem of finding a strictly fundamental cycle basis of minimum weight in the cycle space associated with an undirected connected graph G, where a nonnegative weight is assigned to each edge of G and the total weight of a basis is defined as the sum of the weights of all the cycles in the basis. Several heuristics have been proposed to tackle this NP-hard problem, which has some interesting applications. In this paper we show that this problem is APX-hard, even when restricted to unweighted graphs, and hence does not admit a polynomial-time approximation scheme, unless P=NP. Using a recent result on the approximability of lower-stretch spanning trees (Elkin et al. (2005) [7]), we obtain that the problem is approximable within O(log2nloglogn) for arbitrary graphs. We obtain tighter approximability bounds for dense graphs. In particular, the problem restricted to complete graphs admits a polynomial-time approximation scheme.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Applied Mathematics - Volume 159, Issue 4, 28 February 2011, Pages 187-200
Journal: Discrete Applied Mathematics - Volume 159, Issue 4, 28 February 2011, Pages 187-200
نویسندگان
Giulia Galbiati, Romeo Rizzi, Edoardo Amaldi,