3-Hitting set on bounded degree hypergraphs: Upper and lower bounds on the kernel size
نویسندگان
چکیده
منابع مشابه
3-hitting set on Bounded Degree Hypergraphs: Upper and Lower Bounds on the Kernel Size
We study upper and lower bounds on the kernel size for the 3-hitting set problem on hypergraphs of degree at most 3, denoted 33-hs. We first show that, unless P=NP, 3-3-hs on 3-uniform hypergraphs does not have a kernel of size at most 35k/19 > 1.8421k. We then give a 4k − k kernel for 3-3-hs that is computable in time O(k). This result improves the upper bound of 4k on the kernel size for 33-h...
متن کاملParametric Duality and Kernelization: Lower Bounds and Upper Bounds on Kernel Size
Determining whether a parameterized problem is kernelizable and has a small kernel size has recently become one of the most interesting topics of research in the area of parameterized complexity and algorithms. Theoretically, it has been proved that a parameterized problem is kernelizable if and only if it is fixed-parameter tractable. Practically, applying a data reduction algorithm to reduce ...
متن کاملUpper Bounds on the Minimum Size of Hamilton Saturated Hypergraphs
For 1 6 ` < k, an `-overlapping k-cycle is a k-uniform hypergraph in which, for some cyclic vertex ordering, every edge consists of k consecutive vertices and every two consecutive edges share exactly ` vertices. A k-uniform hypergraph H is `-Hamiltonian saturated if H does not contain an `-overlapping Hamiltonian k-cycle but every hypergraph obtained from H by adding one edge does contain such...
متن کاملKernel: Lower and Upper Bounds
Through this lecture note we try to provide a portal into the emerging filed of kernelization. We exhibit through examples various tools to prove both lower and upper bounds on the kernel sizes.
متن کاملOn Ryser's Conjecture for $t$-Intersecting and Degree-Bounded Hypergraphs
A famous conjecture (usually called Ryser’s conjecture) that appeared in the PhD thesis of his student, J. R. Henderson, states that for an r-uniform r-partite hypergraph H, the inequality τ(H) 6 (r − 1)·ν(H) always holds. This conjecture is widely open, except in the case of r = 2, when it is equivalent to Kőnig’s theorem, and in the case of r = 3, which was proved by Aharoni in 2001. Here we ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics, Algorithms and Applications
سال: 2015
ISSN: 1793-8309,1793-8317
DOI: 10.1142/s1793830915500111