Related papers: Complexity of strong approximation on the sphere
The three domatic number problem asks whether a given undirected graph can be partitioned into at least three dominating sets, i.e., sets whose closed neighborhood equals the vertex set of the graph. Since this problem is NP-complete, no…
Triangular map is a recent construct in probability theory that allows one to transform any source probability density function to any target density function. Based on triangular maps, we propose a general framework for high-dimensional…
We consider a recently introduced fair repetitive scheduling problem involving a set of clients, each asking for their associated job to be daily scheduled on a single machine across a finite planning horizon. The goal is to determine a job…
Some properties of generalized convexity for sets and for functions are identified in case of the reliability polynomials of two dual minimal networks. A method of approximating the reliability polynomials of two dual minimal network is…
In this paper we consider polynomial representability of functions defined over $Z_{p^n}$, where $p$ is a prime and $n$ is a positive integer. Our aim is to provide an algorithmic characterization that (i) answers the decision problem: to…
We construct a structure preserving non-conforming finite element approximation scheme for the bi-harmonic wave maps into spheres equation. It satisfies a discrete energy law and preserves the non-convex sphere constraint of the continuous…
We revisit the classical problem of determining the largest copy of a simple polygon $P$ that can be placed into a simple polygon $Q$. Despite significant effort, known algorithms require high polynomial running times. (Barequet and…
The subset sum problem is known to be an NP-hard problem in the field of computer science with the fastest known approach having a run-time complexity of $O(2^{0.3113n})$. A modified version of this problem is known as the perfect sum…
In Polyamorous Scheduling, we are given an edge-weighted graph and must find a periodic schedule of matchings in this graph which minimizes the maximal weighted waiting time between consecutive occurrences of the same edge. This NP-hard…
We investigate the representation of symmetric polynomials as a sum of squares. Since this task is solved using semidefinite programming tools we explore the geometric, algebraic, and computational implications of the presence of discrete…
This paper describes an algorithm which computes the characteristic polynomial of a matrix over a field within the same asymptotic complexity, up to constant factors, as the multiplication of two square matrices. Previously, this was only…
Most of the existing works on provable guarantees for low-rank matrix completion algorithms rely on some unrealistic assumptions such that matrix entries are sampled randomly or the sampling pattern has a specific structure. In this work,…
Determining the number of realisations of a graph for a specific choice of edge lengths is a fundamental problem in discrete geometry. In this article we prove that the $d$-dimensional realisation number of an Erd\H{o}s-Renyi random graph…
In this paper, we study robust transshipment under consistent flow constraints. We consider demand uncertainty represented by a finite set of scenarios and characterize a subset of arcs as so-called fixed arcs. In each scenario, we require…
The existence of string functions, which are not polynomial time computable, but whose graph is checkable in polynomial time, is a basic assumption in cryptography. We prove that in the framework of algebraic complexity, there are no such…
We provide a perfect sampling algorithm for the hard-sphere model on subsets of $\mathbb{R}^d$ with expected running time linear in the volume under the assumption of strong spatial mixing. A large number of perfect and approximate sampling…
This paper makes three contributions to estimating the number of perfect matching in bipartite graphs. First, we prove that the popular sequential importance sampling algorithm works in polynomial time for dense bipartite graphs. More…
We provide a polynomial time 4/3 approximation algorithm for TSP on metrics arising from the metric completion of cubic 3-edge connected graphs.
We design a Quasi-Polynomial time deterministic approximation algorithm for computing the integral of a multi-dimensional separable function, supported by some underlying hyper-graph structure, appropriately defined. Equivalently, our…
The problem of maximizing the $p$-th power of a $p$-norm over a halfspace-presented polytope in $\R^d$ is a convex maximization problem which plays a fundamental role in computational convexity. It has been shown in 1986 that this problem…