We consider a restricted version of the general Set Covering problem in which each set in the given set system intersects with any other set in at most 1 element. We show that the Set Covering problem with intersection 1 cannot be approximated within a o(log n) factor in random polynomial time unless N P ZT IM E(n O(log log n)). We also observe that the main challenge in derandomizing this redu...

The intersection dimension of a bipartite graph with respect to a type L is the smallest number t for which it is possible to assign sets Ax ⊆ {1, . . . , t} of labels to vertices x so that any two vertices x and y from different parts are adjacent if and only if |Ax ∩Ay| ∈ L. The weight of such a representation is the sum ∑x |Ax| over all vertices x. We exhibit explicit bipartite n×n graphs wh...

Two variations of set intersection representation are investigated and upper and lower bounds on the minimum number of labels with which a graph may be represented are found which hold for almost all graphs. Speciically, if k (G) is deened to be the minimum number of labels with which G may be represented using the rule that two vertices are adjacent if and only if they share at least k labels,...

In this work we study the problem of private set-intersection in the multi-party setting and design two protocols with the following improvements compared to prior work. First, our protocols are designed in the so-called star network topology, where a designated party communicates with everyone else, and take a new approach of leveraging the 2PC protocol of [FNP04]. This approach minimizes the ...

Private Set Intersection (PSI) is usually implemented as a sequence of encryption rounds between pairs of users, whereas the present work implements PSI in a simpler fashion: each set only needs to be encrypted once, after which each pair of users need only one ordinary set comparison. This is typically orders of magnitude faster than ordinary PSI at the cost of some “fuzziness” in the matching...

We introduce a method for surface reconstruction from point sets that is able to cope with noise and outliers. First, a splat-based representation is computed from the point set. A robust local 3D RANSAC-based procedure is used to filter the point set for outliers, then a local jet surface – a lowdegree surface approximation – is fitted to the inliers. Second, we extract the reconstructed surfa...

In this paper we solve the satisfiability problem for a quantifier-free fragment of set theory involving the powerset and the singleton operators and a finiteness predicate, besides the basic Boolean set operators of union, intersection, and difference. The more restricted fragment obtained by dropping the finiteness predicate has been shown to have a solvable satisfiability problem in a previo...

Type-2 fuzzy sets let us model and minimize the effects of uncertainties in rule-base fuzzy logic systems. However, they are difficult to understand for a variety of reasons which we enunciate. In this paper, we strive to overcome the difficulties by: 1) establishing a small set of terms that let us easily communicate about type-2 fuzzy sets and also let us define such sets very precisely, 2) p...

In this paper, we re-visit the problem of unconditionally secure multiparty set intersection in information theoretic model. Li et.al [24] have proposed a protocol for n-party set intersection problem, which provides unconditional security when t < n 3 players are corrupted by an active adversary having unbounded computing power. Moreover, they have claimed that their protocol takes six rounds ...

We consider the problem of computing the intersection of private datasets of two parties, where the datasets contain lists of elements taken from a large domain. This problem has many applications for online collaboration. We present protocols, based on the use of homomorphic encryption and balanced hashing, for both semi-honest and malicious environments. For lists of length k, we obtain O(k) ...