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 ...

We investigate the effect of query rewriting on joins involving set-valued attributes in object-relational database management systems. We show that by unnesting set-valued attributes (that are stored in an internal nested representation) prior to the actual set containment or intersection join we can improve the performance of query evaluation by an order of magnitude. By giving example query ...

A (n, l, γ)-sharing set family of sizem is a family of sets S1, . . . , Sm ⊆ [n] s.t. each set has size l and each pair of sets shares at most γ elements. We let m (n, l, γ) denote the maximum size of any such set family and we consider the following question: How large can m (n, l, γ) be? (n, l, γ)-sharing set families have a rich set of applications including the construction of pseudorandom ...

For a family F of sets, let ex(F) := {A : A is an extremal intersecting sub-family of F}. The Erd®s-Ko-Rado (EKR) Theorem states that {A ∈ ( [n] r ) : 1 ∈ A} ∈ ex( ( [n] r ) ) if r ≤ n/2. The Hilton-Milner (HM) Theorem states that if r ≤ n/2 and A is a nontrivial intersecting sub-family of ( [n] r ) then |A| ≤ |{A ∈ ( [n] r ) : 1 ∈ A,A ∩ [2, r + 1] 6= ∅} ∪ {[2, r + 1]}|; hence {{A ∈ ( [n] r ) :...

Let 2 ≤ d ≤ k be fixed and n be sufficiently large. Suppose that G is a collection of k-element subsets of an n-element set, and |G| > ( n−1 k−1 ) . Then G contains d sets with union of size at most 2k and empty intersection. This verifies a conjecture of the first author for large n.

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,...

This paper presents a principal-agent model of IMF conditional lending, in the aftermath of a “capital-account” liquidity crisis. We show that traditional ex-post conditionality can be e¤ective in safeguarding the Fund’s resources, allowing for the provision of e¢cient emergency lending and reducing ine¢cient ex-ante credit rationing if the capital out‡ow which triggers the crisis is not excess...

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 ...