A cactus is a connected graph that does not contain K4 − e as minor. Given G = (V,E) and an integer k ≥ 0, Cactus Vertex Deletion (also known Diamond Hitting Set) the problem of deciding whether has vertex set size at most whose removal leaves forest cacti. The previously best deterministic parameterized algorithm for this was due to Bonnet et al. [WG 2016], which runs in time 26knO(1), where n...

Abstract Quantum search algorithms have important applications in quantum information, which been experimentally demonstrated several systems with database sizes up to 16. We first propose an efficient scheme based on optimized Grover’s algorithm and a novel encoding method. With this scheme, target element can be deterministically searched large using only single qubit. Then we implement linea...

The purpose of this paper is to study the convergence and the almost sure T-stability of the modied SP-type random iterative algorithm in a separable Banach spaces. The Bochner in-tegrability of andom xed points of this kind of random operators, the convergence and the almost sure T-stability for this kind of generalized asymptotically quasi-nonexpansive random mappings are obtained. Our result...

We show that in any finite field Fq a primitive root can be found in time O(q’ ‘+’ ) Let Fq denote a finite field of q elements. An element 0 E IFq is called a primitive root if it generates the multiplicative group F;,“. We show that a combination of known results on distribution primitive roots and the factorization algorithm of [6] leads to a deterministic algorithm to find a primitive root ...

Hittmeir recently presented a deterministic algorithm that provably computes the prime factorisation of positive integer $N$ in $N^{2/9+o(1)}$ bit operations. Prior to this breakthrough, best known complexity bound for problem was $N^{1/4+o(1)}$, result going back 1970s. In paper we push Hittmeir's techniques further, obtaining rigorous, factoring with $N^{1/5+o(1)}$.