An improved estimate concerning 3n+1 predecessor sets

Improved data structures for predecessor queries in integer sets

We consider the problem of maintaining a dynamic ordered set of n integers in the range 0 : :2 w ?1, under the operations of insertion, deletion and predecessor queries, on a unit-cost RAM with a word length of w bits. We show that all the operations above can be performed in O(minflogw; 1 + logn= logwg) expected time, assuming the updates are oblivious, i.e., independent of the random choices ...

An improved estimate on sums of product sets

In a recent paper [2] A. Glibichuk proved that if A, B are subsets of an arbitrary finite filed Fq, such that |A||B| > q, then 16AB = Fq. We improve this to 10AB = Fq. Let Fq be a finite field of q elements. As usual, for A,B ⊆ Fq, ξ ∈ F∗q , where F ∗ q stands for the multiplicative group of Fq, we denote A+B = {a+ b : a ∈ A, b ∈ B}, AB = {ab : a ∈ A, b ∈ B}, ξB = {ξ}B, −A = {−1}A, dA = A+ . . ...

Predecessor Queries in Dynamic Integer Sets

We consider the problem of maintaining a set of n integers in the range 0::2 w ? 1 under the operations of insertion, deletion, predecessor queries, minimum queries and maximum queries on a unit cost RAM with word size w bits. Let f (n) be an arbitrary nondecreasing smooth function satisfying log log n f (n) p log n. A data structure is presented supporting insertions and deletions in worst cas...

Concerning Maximal Sets

Predecessor Sets of Dynamic Pushdown Networks with Tree-Regular Constraints

Dynamic Pushdown Networks (DPNs) are a model for parallel programs with (recursive) procedures and process creation. The goal of this paper is to develop generic techniques for more expressive reachability analysis of DPNs. In the first part of the paper we introduce a new tree-based view on executions. Traditional interleaving semantics model executions by totally ordered sequences. Instead, w...