WebThe proof relies on the new notion of a robust hitting set which is a set of inputs such that any nonzero polynomial that can be computed by a polynomial size algebraic circuit, evaluates to a not too small value on at least one element of the set. Proving the existence of such a robust hitting set is the main technical difficulty in the proof. Weba hitting set of Fif all edges in Fare hit by at least one vertex in H. Formally, H V is a hitting set of Fif and only if 8F 2F: H \F 6= ;. We call a hitting set minimum if no smaller hitting …
Refined algorithms for hitting many intervals - ScienceDirect
WebDec 6, 2024 · The classical lemma of Ore-DeMillo-Lipton-Schwartz-Zippel states that any nonzero polynomial f(x1,...,xn) of degree at most s will evaluate to a nonzero value at some point on a grid S^n of in F^n with S > s . Thus, there is an explicit hitting set for all n-variate degree s, size s algebraic circuits of size (s+1)^n. We prove the following results: … WebA subset H ⊆ A has the hitting set property, or is a hitting set, iff H∩ F i 6= ∅ for all 1 ≤i m (i.e., “hits” each setP F i). If we are given a cost function c : A → N, the cost of H is a∈H c(a). A hitting set is of minimum cost if its cost is minimal among all hitting sets. The problem of finding a minimum-cost hitting set ... discounted annuity
On Hitting All Maximum Cliques with an Independent Set
WebOct 6, 2024 · An instance of the Hitting Set is a collection C of subset, S in X, and k. Since an NP-complete problem, by definition, is a problem … WebJun 30, 2024 · The H-hitting set problem is NP-complete for every connected graph H with at least two vertices. Theorem 6 follows immediately from Lemma 1 and Lemma 2 … Weba hitting set of Fif all edges in Fare hit by at least one vertex in H. Formally, H V is a hitting set of Fif and only if 8F 2F: H \F 6= ;. We call a hitting set minimum if no smaller hitting set for the same hypergraph exists. We refer to a hitting set as minimal if it contains no other hitting set as proper subset. four seasons health care head office number