Related papers: Improved Bounds for $(b,k)$-hashing
Asymptotically tight lower bounds are derived for the Input/Output (I/O) complexity of a class of dynamic programming algorithms including matrix chain multiplication, optimal polygon triangulation, and the construction of optimal binary…
We consider the asymptotic shape of clusters in the Eden model on a d-dimensional hypercubical lattice. We discuss two improvements for the well-known upper bound to the growth velocity in different directions by that of the independent…
The asymptotic dimension of metric spaces is an important notion in geometric group theory introduced by Gromov. The metric spaces considered in this paper are the ones whose underlying spaces are the vertex-sets of graphs and whose metrics…
We derive lower and upper bounds on possible growth rates of certain sets of positive integers $A_k=\{1= a_1 < a_2 < ... < a_{k}\}$ such that all integers $n\in \{0, 1, 2, ..., ka_{k}\}$ can be represented as a sum of no more than $k$…
Separating hash families are useful combinatorial structures which are generalizations of many well-studied objects in combinatorics, cryptography and coding theory. In this paper, using tools from graph theory and additive number theory,…
The problem of non-monotone $k$-submodular maximization under a knapsack constraint ($\kSMK$) over the ground set size $n$ has been raised in many applications in machine learning, such as data summarization, information propagation, etc.…
We present an informal review of recent work on the asymptotics of Approximate Bayesian Computation (ABC). In particular we focus on how does the ABC posterior, or point estimates obtained by ABC, behave in the limit as we have more data?…
We discuss avoidance of sure loss and coherence results for semicopulas and standardized functions, i.e., for grounded, 1-increasing functions with value $1$ at $(1,1,\ldots, 1)$. We characterize the existence of a $k$-increasing…
We give a number of results about families of Ulam sets. Generalizing behavior of Ulam sets U(1,n), we prove using an novel model theoretic approach that there is a rigidity phenomenon for Ulam sets U(a,b) as b increases. Based on this, we…
Given feasible strongly regular graph parameters $(v,k,\lambda,\mu)$ and a non-negative integer $d$, we determine upper and lower bounds on the order of a $d$-regular induced subgraph of any strongly regular graph with parameters…
An important problem in combinatorial noncommutative algebra is to characterize the growth functions of finitely generated algebras (equivalently, semigroups, or hereditary languages). The growth function of every finitely generated,…
Building on previous results of Xing, we give new lower bounds on the rate of intersecting codes over large alphabets. The proof is constructive, and uses algebraic geometry, although nothing beyond the basic theory of linear systems on…
This paper presents a new extension of the classical Heron problem, termed the generalized $(k,m)$-Heron problem, which seeks an optimal configuration among $k$ feasible and $m$ target non-empty closed convex sets in $\mathbb{R}^n$. The…
We give an efficient deterministic algorithm that outputs an expanding generating set for any finite abelian group. The size of the generating set is close to the randomized construction of Alon and Roichman (1994), improving upon various…
In this paper, we derive non-asymptotic achievability and converse bounds on the random number generation with/without side-information. Our bounds are efficiently computable in the sense that the computational complexity does not depend on…
We study bootstrap inference for the $k$th largest coordinate of a normalized sum of independent high-dimensional random vectors. Existing second-order theory for maxima does not directly extend to order statistics, because the event…
In the online checkpointing problem, the task is to continuously maintain a set of k checkpoints that allow to rewind an ongoing computation faster than by a full restart. The only operation allowed is to replace an old checkpoint by the…
Over the last several decades, improvements in the fields of analytic combinatorics and computer algebra have made determining the asymptotic behaviour of sequences satisfying linear recurrence relations with polynomial coefficients largely…
It has long been known that random regular graphs are with high probability good expanders. This was first established in the 1980s by Bollob\'as by directly calculating the probability that a set of vertices has small expansion and then…
Addressing a question of Cameron and Erd\Ho s, we show that, for infinitely many values of $n$, the number of subsets of $\{1,2,\ldots, n\}$ that do not contain a $k$-term arithmetic progression is at most $2^{O(r_k(n))}$, where $r_k(n)$ is…