کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10333162 | 688607 | 2009 | 11 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The union of minimal hitting sets: Parameterized combinatorial bounds and counting
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نظریه محاسباتی و ریاضیات
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چکیده انگلیسی
A k-hitting set in a hypergraph is a set of at most k vertices that intersects all hyperedges. We study the union of all inclusion-minimal k-hitting sets in hypergraphs of rank r (where the rank is the maximum size of hyperedges). We show that this union is relevant for certain combinatorial inference problems and give worst-case bounds on its size, depending on r and k. For r=2 our result is tight, and for each r⩾3 we have an asymptotically optimal bound and make progress regarding the constant factor. The exact worst-case size for r⩾3 remains an open problem. We also propose an algorithm for counting all k-hitting sets in hypergraphs of rank r. Its asymptotic runtime matches the best one known for the much more special problem of finding one k-hitting set. The results are used for efficient counting of k-hitting sets that contain any particular vertex.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Discrete Algorithms - Volume 7, Issue 4, December 2009, Pages 391-401
Journal: Journal of Discrete Algorithms - Volume 7, Issue 4, December 2009, Pages 391-401
نویسندگان
Peter Damaschke, Leonid Molokov,