Weakened Random Oracle Models (WROMs) are variants of the Random Oracle Model (ROM) under some weakened collision resistance assumptions. Cryptographic schemes proven secure in WROMs can ensure security even when the underlying random oracles are susceptible to certain extent of collision attacks, second pre-image attacks, or first pre-image attacks. In this paper, we show that a WROM variant c...

A set S of vertices of a graph is a defensive alliance if, for each element of S, the majority of its neighbors is in S. The problem of finding a defensive alliance of minimum size in a given graph is NP-hard and there are polynomial-time algorithms if certain parameters are bounded by a fixed constant. In particular, fixed-parameter tractability results have been obtained for some structural p...

UNLABELLED Temporal ordering and auditory attention are important skills in information processing, being evaluated by a behavioral test, as the frequency pattern test (FPT) in temporal ordering (TO) and electrophysiological testing, as the P300 in auditory attention. OBJECTIVE To analyze the applicability of FPT and P300 as testing for auditory processing. METHOD We performed an integrativ...

OBJECTIVE We aimed to compare Theory of Mind (ToM) functions and investigate the relationship between ToM functions and verbal working memory (VWM) in first degree relatives of bipolar disorder and schizophrenia patients. METHOD The sample consisted of first degree relatives of patients with bipolar disorder (n=22), schizophrenia (n=28), and age, gender, education and total IQ matched healthy...

For a minimization (resp, maximization) problem P , and a parameter k, an algorithm is called a (r(k), t(k))-FPT-approximation algorithm, if for an instance I of size n with optimum opt, the algorithm either computes a feasible solution for I, with value at most k · r(k) (resp, at least k/r(k)) or it computes a certificate that k < opt (resp, k > opt), in time t(k) · poly(n). For maximization p...

Poljak and Turzík (Discrete Math. 1986) introduced the notion of λ-extendible properties of graphs as a generalization of the property of being bipartite. They showed that for any 0 < λ < 1 and λ-extendible property Π, any connected graph G on n vertices and m edges contains a spanning subgraph H ∈ Π with at least λm+ 1−λ 2 (n−1) edges. The property of being bipartite is λ-extendible for λ = 1/...

We study the parameterized complexity of approximating the k-Dominating Set (DomSet) problem where an integer k and a graph G on n vertices are given as input, and the goal is to find a dominating set of size at most F(k) · k whenever the graph G has a dominating set of size k. When such an algorithm runs in time T(k) · poly(n) (i.e., FPT-time) for some computable function T, it is said to be a...

For a minimization (resp, maximization) problem P , and a parameter k, an algorithm is called an (r(k), t(k))-FPT-approximation algorithm, if for an instance I of size n with optimum opt, the algorithm either computes a feasible solution for I, with value at most k · r(k) (resp, at least k/r(k)) or it computes a certi cate that k < opt (resp, k > opt), in time t(k) · poly(n). For maximization p...

In Fixed Parameter Tractability (FPT) theory, we are given a problem with a special parameter k. In this paper we are only interested in k equal the size of the optimum. A FPT algorithm for a problem is an exact algorithm that runs in time h(k) · nO(1) for a function h that may be arbitrarily large. In FPT approximation we seek a g(k) ratio that runs in time h(k) · nO(1), so that h,g are two in...

Poljak and Turzík (Discrete Math. 1986) introduced the notion of λ-extendible properties of graphs as a generalization of the property of being bipartite. They showed that for any 0 < λ < 1 and λ-extendible property Π, any connected graph G on n vertices and m edges contains a spanning subgraph H ∈ Π with at least λm+ 1−λ 2 (n−1) edges. The property of being bipartite is λ-extendible for λ = 1/...