Related papers: The normalized algorithmic information distance ca…

A classic result by Cook, Gerards, Schrijver, and Tardos provides an upper bound of $n \Delta$ on the proximity of optimal solutions of an Integer Linear Programming problem and its standard linear relaxation. In this bound, $n$ is the…

Datalogo is an extension of Datalog that allows for aggregation and recursion over an arbitrary commutative semiring. Like Datalog, Datalogo programs can be evaluated via the natural iterative algorithm until a fixed point is reached.…

The problem of minimizing the maximum of $N$ convex, Lipschitz functions plays significant roles in optimization and machine learning. It has a series of results, with the most recent one requiring $O(N\epsilon^{-2/3} + \epsilon^{-8/3})$…

We present a technique of proving lower bounds for noisy computations. This is achieved by a theorem connecting computations on a kind of randomized decision trees and sampling based algorithms. This approach is surprisingly powerful, and…

We devise an analytically simple as well as invertible approximate expression, which describes the relation between the minimum distance of a binary code and the corresponding maximum attainable code-rate. For example, for a rate-(1/4),…

We put forward a Quantum Amplitude Estimation algorithm delivering superior performance (lower quantum computational complexity and faster classical computation parts) compared to the approaches available to-date. The algorithm does not…

We consider an approximation scheme for multivariate information assuming that synergistic information only appearing in higher order joint distributions is suppressed, which may hold in large classes of systems. Our approximation scheme…

Biological and physical systems often exhibit distinct structures at different spatial/temporal scales. Persistent homology is an algebraic tool that provides a mathematical framework for analyzing the multi-scale structures frequently…

Approximate Bayesian computation (ABC) is a widely used inference method in Bayesian statistics to bypass the point-wise computation of the likelihood. In this paper we develop theoretical bounds for the distance between the statistics used…

Let $T$ be an arbitrary phylogenetic tree with $n$ leaves. It is well-known that the average quartet distance between two assignments of taxa to the leaves of $T$ is $\frac 23 \binom{n}{4}$. However, a longstanding conjecture of Bandelt and…

We use the venerable "fooling set" method to prove new lower bounds on the quantum communication complexity of various functions. Let f:X x Y-->{0,1} be a Boolean function, fool^1(f) its maximal fooling set size among 1-inputs, Q_1^*(f) its…

We revisit the standard ``telescoping sum'' argument ubiquitous in the final steps of analyzing evaluation complexity of algorithms for smooth nonconvex optimization, and obtain a refined formulation of the resulting bound as a function of…

We study the arithmetic (real) function f=g*1, with g "essentially bounded" and supported over the integers of [1,Q]. In particular, we obtain non-trivial bounds, through f "correlations", for the "Selberg integral" and the "symmetry…

A suitable measure for the similarity of shapes represented by parameterized curves or surfaces is the Fr\'echet distance. Whereas efficient algorithms are known for computing the Fr\'echet distance of polygonal curves, the same problem for…

Holomorphic functions are amazing because their values in an ever so small disk in the complex plane completely determine the function values at arbitrary points in their maximum possible domain. The process of extending such a function…

The capacity of finite state channels (FSCs) has been established as the limit of a sequence of multi-letter expressions only and, despite tremendous effort, a corresponding finite-letter characterization remains unknown to date. This paper…

We develop a framework for approximation limits of polynomial-size linear programs from lower bounds on the nonnegative ranks of suitably defined matrices. This framework yields unconditional impossibility results that are applicable to any…

Let $\Omega$ be a countable infinite product $\Omega^\N$ of copies of the same probability space $\Omega_1$, and let ${\Xi_n}$ be the sequence of the coordinate projection functions from $\Omega$ to $\Omega_1$. Let $\Psi$ be a possibly…

Maximum parsimony distance is a measure used to quantify the dissimilarity of two unrooted phylogenetic trees. It is NP-hard to compute, and very few positive algorithmic results are known due to its complex combinatorial structure. Here we…

We prove an optimal $\Omega(n)$ lower bound on the randomized communication complexity of the much-studied Gap-Hamming-Distance problem. As a consequence, we obtain essentially optimal multi-pass space lower bounds in the data stream model…