Related papers: Certification of minimal approximant bases
Barrier certificates, a form of state invariants, provide an automated approach to the verification of the safety of dynamical systems. Similarly to barrier certificates, recent works explore the notion of closure certificates, a form of…
Inspired by branch-and-bound and cutting plane proofs in mixed-integer optimization and proof complexity, we develop a general approach via Hoffman's Helly systems. This helps to distill the main ideas behind optimality and infeasibility…
We consider the problem of multi-fidelity zeroth-order optimization, where one can evaluate a function $f$ at various approximation levels (of varying costs), and the goal is to optimize $f$ with the cheapest evaluations possible. In this…
Local certification is a mechanism for certifying to the nodes of a network that a certain property holds. In this framework, nodes are assigned labels, called certificates, which are supposed to prove that the property holds. The nodes…
Using polynomial equations to model combinatorial problems has been a popular tool both in computational combinatorics as well as an approach to proving new theorems. In this paper, we look at several combinatorics problems modeled by…
An algorithm which either finds an nonzero integer vector ${\mathbf m}$ for given $t$ real $n$-dimensional vectors ${\mathbf x}_1,...,{\mathbf x}_t$ such that ${\mathbf x}_i^T{\mathbf m}=0$ or proves that no such integer vector with norm…
The Subset Sum problem is a classical NP-complete problem with a long-standing $O^*(2^{n/2})$ deterministic bound due to Horowitz and Sahni. We present results at two distinct levels of generality. First (instance-sensitive bound), we…
We consider decision-making problems that are formulated as non-convex optimization programs where uncertainty enters the constraints through an additive term, independent of the decision variables, and robustness is imposed using a finite…
In this note, we present a simple algorithm for computing a \emph{$k$-connectivity certificate} in dynamic graph streams. Our algorithm uses $O(n \log^2 n \cdot \max\{k, \log n \log k\})$ bits of space which improves upon the $O(kn \log^3…
In this paper we design a new primal-dual algorithm for the classic discrete optimization problem of maximizing a monotone submodular function subject to a cardinality constraint achieving the optimal approximation of $(1-1/e)$. This…
A robustness certificate is the minimum distance of a given input to the decision boundary of the classifier (or its lower bound). For {\it any} input perturbations with a magnitude smaller than the certificate value, the classification…
The product of a matrix chain consisting of $n$ matrices can be computed in $C_{n-1}$ (Catalan's number) different ways, each identified by a distinct parenthesisation of the chain. The best algorithm to select a parenthesisation that…
Local certification consists in assigning labels to the nodes of a network to certify that some given property is satisfied, in such a way that the labels can be checked locally. In the last few years, certification of graph classes…
We develop an automated framework for proving lower bounds on the bilinear complexity of matrix multiplication over finite fields. Our approach systematically combines orbit classification of the restricted first matrix and dynamic…
Minimising the longest travel distance for a group of mobile robots with interchangeable goals requires knowledge of the shortest length paths between all robots and goal destinations. Determining the exact length of the shortest paths in…
In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…
We investigate replicable learning algorithms. Ideally, we would like to design algorithms that output the same canonical model over multiple runs, even when different runs observe a different set of samples from the unknown data…
In their paper on the "chasm at depth four", Agrawal and Vinay have shown that polynomials in m variables of degree O(m) which admit arithmetic circuits of size 2^o(m) also admit arithmetic circuits of depth four and size 2^o(m). This…
The $2 \rightarrow q$ norm of a matrix $X \in \mathbb{R}^{n \times d}$ is defined as $\lVert X \rVert_{2 \rightarrow q} = \sup_{\lVert v \rVert_2 = 1} \lVert Xv \rVert_q$. We give polynomial-time multiplicative approximation algorithms for…
Given an n-vertex graph G=(V,E) and a set R \subseteq {{x,y} | x,y \in V} of requests, we consider to assign a set of edges to each vertex in G so that for every request {u, v} in R the union of the edge sets assigned to u and v contains a…