Hitting Set of Bundles generalizes the ordinary Hitting Set problem in the way that prescribed bundles of elements rather than single elements have to be put in a hitting set. The goal is to minimize the total number of distinct elements in the solution. First we prove that Hitting Set of Bundles, with the number of hyperedges and the solution size as parameter, is W [1]-complete. This contrast...

In the hitting set problem one is given m subsets of a nite set N and one has to nd an X N of minimum cardinality that hits intersects all of them The problem is NP hard It is not known whether there exists a polynomial time approximation algorithm for the hitting set problem with a nite performance ratio Special cases of the hitting set problem are described for which nite performance ratios a...

In this paper, we study a special case of the Metropolis algorithm, the Independence Metropolis Sampler (IMS), in the finite state space case. The IMS is often used in designing components of more complex Markov Chain Monte Carlo algorithms. We present new results related to the first hitting time of individual states for the IMS. These results are expressed mostly in terms of the eigenvalues o...

Large unweighted directed graphs are commonly used to capture relations between entities. A fundamental problem in the analysis of such networks is to properly define the similarity or dissimilarity between any two vertices. Despite the significance of this problem, statistical characterization of the proposed metrics has been limited. We introduce and develop a class of techniques for analyzin...

In the hitting set problem one is given m subsets of a nite set N and one has to nd an X N of minimum cardinality that \hits" (intersects) all of them. The problem is NP-hard. It is not known whether there exists a polynomial-time approximation algorithm for the hitting set problem with a nite performance ratio. Special cases of the hitting set problem are described for which nite performance r...

In machine learning, a popular tool to analyze the structure of graphs is the hitting time and the commute distance (resistance distance). For two vertices u and v, the hitting time Huv is the expected time it takes a random walk to travel from u to v. The commute distance is its symmetrized version Cuv = Huv +Hvu. In our paper we study the behavior of hitting times and commute distances when t...

The 3-Hitting Set problem involves a family of subsets F of size at most three over an universe U . The goal is to find a subset of U of the smallest possible size that intersects every set in F . The version of the problem with parity constraints asks for a subset S of size at most k that, in addition to being a hitting set, also satisfies certain parity constraints on the sizes of the interse...

In this paper we complete and improve the study of the simulation of the hitting times of some given boundaries for Bessel processes. These problems are of great interest in many application fields as finance and neurosciences. In a previous work [9], the authors introduced a new method for the simulation of hitting times for Bessel processes with integer dimension. The method, called walk on m...

Next to the shortest path distance, the second most popular distance function between vertices in a graph is the commute distance (resistance distance). For two vertices u and v, the hitting time Huv is the expected time it takes a random walk to travel from u to v. The commute time is its symmetrized version Cuv = Huv + Hvu. In our paper we study the behavior of hitting times and commute dista...

We consider various hitting and piercing problems for the family of axis-parallel rectangles induced by a point set. Selection Lemmas on induced objects are classical results in discrete geometry that have been well studied and have applications in many geometric problems like weak epsilon nets and slimming Delaunay triangulations. Selection Lemma type results typically bound the maximum number...