Related papers: Asymptotic Results for the Queen Packing Problem

We consider the problem of testing and learning quantum $k$-juntas: $n$-qubit unitary matrices which act non-trivially on just $k$ of the $n$ qubits and as the identity on the rest. As our main algorithmic results, we give (a) a…

Quantum tunneling across multiple barriers as yet is an unsolved problem for barrier numbers greater than five. The complexity of the mathematical analysis even for small number of barriers pushed it into the realms of Numerical Analysis.…

Define a(k,q) to be the smallest positive multiple of k such that the sum of its digits in base q is equal to k. The asymptotic behavior, lower and upper bound estimates of a(k,q) are investigated. A characterization of the minimality…

In this work we study weighted total least squares problems on infinite dimensional spaces. We show that in most cases this problem does not admit a solution (except in the trivial case) and then, we consider a regularization on the…

In this paper we study the following problem: Discrete partitioning problem (DPP): Let $\mathbb{F}_q P^n$ denote the $n$-dimensional finite projective space over $\mathbb{F}_q$. For positive integer $k \leq n$, let $\{ A^i\}_{i=1}^N$ be a…

Rule k is a localized approximation algorithm that finds a small connected dominating set in a graph. We estimate the expected size of the Rule k dominating set for the model of random unit disk graphs constructed from n random points in an…

In a large-scale network, we want to choose some influential nodes to make a profit by paying some cost within a limited budget so that we do not have to spend more budget on some nodes adjacent to the chosen nodes; our problem is the…

We analyze constrained quantum systems where the dynamics do not preserve the constraints. This is done in particular for the restriction of a quantum particle in Euclidean n-space to a curved submanifold, and we propose a method of…

This paper presents theoretical and practical results for the bin packing problem with scenarios, a generalization of the classical bin packing problem which considers the presence of uncertain scenarios, of which only one is realized. For…

Many of the envisioned use-cases for quantum computers involve optimisation processes. While there are many algorithmic primitives to perform the required calculations, all eventually lead to quantum gates operating on quantum bits, with an…

We consider the $k$-center problem in which the centers are constrained to lie on two lines. Given a set of $n$ weighted points in the plane, we want to locate up to $k$ centers on two parallel lines. We present an $O(n\log^2 n)$ time…

We consider the problem of cutting a set of edges on a polyhedral manifold surface, possibly with boundary, to obtain a single topological disk, minimizing either the total number of cut edges or their total length. We show that this…

The Planar Contraction problem is to test whether a given graph can be made planar by using at most k edge contractions. This problem is known to be NP-complete. We show that it is fixed-parameter tractable when parameterized by k.

We present a fixed-parameter tractable (FPT) algorithm to find a shortest curve that encloses a set of k required objects in the plane while paying a penalty for enclosing unwanted objects. The input is a set of interior-disjoint simple…

In 1967, Moon and Moser proved a tight bound on the critical density of squares in squares: any set of squares with a total area of at most 1/2 can be packed into a unit square, which is tight. The proof requires full knowledge of the set,…

Sharp bounds on the least eigenvalue of an arbitrary graph are presented. Necessary and sufficient (just sufficient) conditions for the lower (upper) bound to be attained are deduced using edge clique partitions. As an application, we prove…

We consider the Minimum Convex Partition problem: Given a set P of n points in the plane, draw a plane graph G on P, with positive minimum degree, such that G partitions the convex hull of P into a minimum number of convex faces. We show…

We introduce a new set of problems based on the Chain Editing problem. In our version of Chain Editing, we are given a set of anonymous participants and a set of undisclosed tasks that every participant attempts. For each participant-task…

We consider the problem of covering the boundary of a simple polygon on n vertices using the minimum number of geodesic unit disks. We present an O(n \log^2 n+k) time 2-approximation algorithm for finding the centers of the disks, with k…

Benchmarking Quantum Process Units (QPU) at an application level usually requires considering the whole programming stack of the quantum computer. One critical task is the minor-embedding (resp. transpilation) step, which involves…