let $g$ be a finite group with the identity $e$‎. ‎the subgroup intersection graph $gamma_{si}(g)$ of $g$ is the graph with vertex set $v(gamma_{si}(g)) = g-e$ and two distinct vertices $x$ and $y$ are adjacent in $gamma_{si}(g)$ if and only if $|leftlangle xrightrangle capleftlangle yrightrangle|>1$‎, ‎where $leftlangle xrightrangle $ is the cyclic subgroup of $g$ generated by $xin g$‎. ‎in th...

Threshold private set intersection (TPSI) allows a receiver to obtain the when cardinality of is greater or equal threshold, which has wide range applications such as fingerprint matching, online dating and ridesharing. Existing TPSI protocols are inefficient because almost all them rely on lots expensive public-key techniques require an exponential number possible combinations among shares. In...

A private set intersection (PSI) protocol allows players to obtain the intersection of their inputs. While in its unilateral version only the client can obtain the intersection, the mutual PSI protocol enables all players to get the desired result. In this work, we construct a mutual PSI protocol that is significantly more efficient than the stateof-the-art in the computation overhead. To the b...

This paper deals with weighted set systems (V, E , q), where V is a set of indices, E ⊂ 2 and the weight q is a nonnegative integer function on E . The basic idea of the paper is to apply weighted set systems to formulate restrictions on intersections. It is of interest to know whether a weighted set system can be represented by set intersections. An intersection representation of (V, E , q) is...

A new approach is presented for computing the interior medial axes of generic regions in R bounded by C-smooth parametric B-spline surfaces. The generic structure of the 3D medial axis is a set of smooth surfaces along with a singular set consisting of edge curves, branch curves, fin points and six junction points. In this work, the medial axis singular set is first computed directly from the B...

This article indicates another set-theoretic formula, solely in terms of union and intersection, for the set limits any given sequence (net, general) an arbitrary T 1 space; this representation particular gives a new characterization space.

Consider the problem of maintaining a family F of dynamic sets subject to insertions, deletions, and set-intersection reporting queries: given S, S′ ∈ F , report every member of S ∩S′ in any order. We show that in the word RAM model, where w is the word size, given a cap d on the maximum size of any set, we can support set intersection queries in O( d w/ log2 w ) expected time, and updates in O...

Set constraints are inclusions between expressions denoting sets of trees. The eficiency of their satisfiabili ty test is a central issue in set-based program analysis, their main application domain. W e introduce the class of set constraints with intersection (the only operators forming the expressions are constructors and intersection) and show that i ts satisfiability problem as DEXPTIME-com...