Related papers: How inefficient can a sort algorithm be?
Differentiable sorting algorithms allow training with sorting and ranking supervision, where only the ordering or ranking of samples is known. Various methods have been proposed to address this challenge, ranging from optimal…
Online learning to rank is a core problem in machine learning. In Lattimore et al. (2018), a novel online learning algorithm was proposed based on topological sorting. In the paper they provided a set of self-normalized inequalities (a) in…
This paper tightens the best known analysis of Hein's 1989 algorithm to infer the topology of a weighted tree based on the lengths of paths between its leaves. It shows that the number of length queries required for a degree-$k$ tree of $n$…
In this article, we describe an algorithm to determine whether a permutation class C given by a finite basis B of excluded patterns contains a finite number of simple permutations. This is a continuation of the work initiated in [Brignall,…
For linear recurrence systems, the problem of finding rational solutions is reduced to the problem of computing polynomial solutions by computing a content bound or a denominator bound. There are several bounds in the literature. The…
Imagine we want to split a group of agents into teams in the most \emph{efficient} way, considering that each agent has their own preferences about their teammates. This scenario is modeled by the extensively studied \textsc{Coalition…
This manuscript explores novel complexity results for the feasibility problem over $p$-order cones, extending the foundational work of Porkolab and Khachiyan. By leveraging the intrinsic structure of $p$-order cones, we derive refined…
We obtain a new lower bound on the information-based complexity of first-order minimization of smooth and convex functions. We show that the bound matches the worst-case performance of the recently introduced Optimized Gradient Method,…
The prototypical high-dimensional statistics problem entails finding a structured signal in noise. Many of these problems exhibit an intriguing phenomenon: the amount of data needed by all known computationally efficient algorithms far…
We consider a practically motivated variant of the canonical online fair allocation problem: a decision-maker has a budget of perishable resources to allocate over a fixed number of rounds. Each round sees a random number of arrivals, and…
We consider the problem of counting the number of answers to a first-order formula on a finite structure. We present and study an extension of first-order logic in which algorithms for this counting problem can be naturally and conveniently…
We present a type inference algorithm for lambda-terms in Elementary Affine Logic using linear constraints. We prove that the algorithm is correct and complete.
We show through case studies that it is easier to estimate the fundamental limits of data processing than to construct explicit algorithms to achieve those limits. Focusing on binary classification, data compression, and prediction under…
Classical problems of sorting and searching assume an underlying linear ordering of the objects being compared. In this paper, we study a more general setting, in which some pairs of objects are incomparable. This generalization is relevant…
Algorithms to compute the quantum Fourier transform over a cyclic group are fundamental to many quantum algorithms. This paper describes such an algorithm and gives a proof of its correctness, tightening some claimed performance bounds…
The quantum adversary method is a versatile method for proving lower bounds on quantum algorithms. It yields tight bounds for many computational problems, is robust in having many equivalent formulations, and has natural connections to…
Artificial intelligence (AI) is supposed to help us make better choices. Some of these choices are small, like what route to take to work, or what music to listen to. Others are big, like what treatment to administer for a disease or how…
We use stack words to find a new, simple proof for the best known upper bound for the number of 3-stack sortable permutations of a given length. This is the first time that stack words are used to obtain such a result.
We prove lower bounds on the complexity of finding $\epsilon$-stationary points (points $x$ such that $\|\nabla f(x)\| \le \epsilon$) of smooth, high-dimensional, and potentially non-convex functions $f$. We consider oracle-based complexity…
The lower and upper bound of any given algorithm is one of the most crucial pieces of information needed when evaluating the computational effectiveness for said algorithm. Here a novel method of Boolean Algebraic Programming for symbolic…