Various Monte Carlo techniques for random point generation over sets of interest are widely used in many areas computational mathematics, optimization, data processing, etc. Whereas regularly shaped such sampling is immediate to arrange, nontrivial, implicitly specified domains these not easy implement. We consider the so-called Hit-and-Run algorithm, a representative class Markov chain methods...

A novel approach to supervised learning, called Lattice Machine , was proposed in 5]. In the Lattice Machine, it was assumed that data are structured as relations. In this paper we investigate the application of the Lattice Machine in the area of text classiication, where textual data are unstructured. We represent a set of textual documents as a collection of Boolean feature vectors, where eac...

Abstract We introduce constrained polynomial zonotopes, a novel non-convex set representation that is closed under linear map, Minkowski sum, Cartesian product, convex hull, intersection, union, and quadratic as well higher-order maps. show the computational complexity of above-mentioned operations for zonotopes at most in size. The fact are generalizations polytopes, Taylor models, ellipsoids ...

Topological relations have found applications in many fields such as similarity analysis, spatial query, object matching, inconsistency detection, spatial association rule mining, spatial reasoning, and so on. This paper is concentrated on the hierarchical representation of the topological relations between a line and a region in IR. In this study, line-region relations are classified into basi...

We introduce a general implicit algorithm for finding a common element of‎ ‎the set of solutions of systems of equilibrium problems and the set of common fixed points‎ ‎of a sequence of nonexpansive mappings and a continuous representation of nonexpansive mappings‎. ‎Then we prove the strong convergence of the proposed implicit scheme to the unique solution of the minimization problem on the so...

Private set intersection (PSI) refers to a special case of secure two-party computation in which the parties each have a set of items and compute the intersection of these sets without revealing any additional information. In this paper we present improvements to practical PSI providing security in the presence of malicious adversaries. Our starting point is the protocol of Dong, Chen & Wen (CC...

Let F be a k-uniform set system defined on a ground set of size n with no singleton intersection; i.e., no pair A,B ∈ F has |A ∩ B| = 1. Frankl showed that |F| ≤ (n−2 k−2 ) for k ≥ 4 and n sufficiently large, confirming a conjecture of Erdős and Sós. We determine the maximum size of F for k = 4 and all n, and also establish a stability result for general k, showing that any F with size asymptot...

Private Set Intersection (PSI) and other private set operations have many current and emerging applications. Numerous PSI techniques have been proposed that vary widely in terms of underlying cryptographic primitives, security assumptions as well as complexity. One recent strand of PSI-related research focused on an additional privacy property of hiding participants’ input sizes. Despite some i...

In this paper we present a new problem, the fast set intersection problem, which is to preprocess a collection of sets in order to efficiently report the intersection of any two sets in the collection. In addition we suggest new solutions for the two-dimensional substring indexing problem and the document listing problem for two patterns by reduction to the fast set intersection problem.

In this paper, we focus on sorted-set intersection which is an important part in many algorithms, e.g., RID-list intersection, inverted indexes, and others. In contrast to traditional scalar sorted-set intersection algorithms that try to reduce the number of comparisons, we propose a parallel algorithm that relies on speculative execution of comparisons. In general, our algorithm requires more ...