Related papers: A note on multipivot Quicksort
A simple method to produce a random order type is to take the order type of a random point set. We conjecture that many probability distributions on order types defined in this way are heavily concentrated and therefore sample inefficiently…
Data-driven algorithm selection is a powerful approach for choosing effective heuristics for computational problems. It operates by evaluating a set of candidate algorithms on a collection of representative training instances and selecting…
This paper deals with the clustering of univariate observations: given a set of observations coming from $K$ possible clusters, one has to estimate the cluster means. We propose an algorithm based on the minimization of the "KP" criterion…
Post-processing is a significant step in quantum key distribution(QKD), which is used for correcting the quantum-channel noise errors and distilling identical corrected keys between two distant legitimate parties. Efficient error…
Algorithmic efficiency is essential to reducing energy and time usage for computational problems. Optimizing efficiency is important for tasks involving multiple resources, for example in stochastic calculations where the size of the random…
A Dirichlet $k$-partition of a domain is a collection of $k$ pairwise disjoint open subsets such that the sum of their first Laplace--Dirichlet eigenvalues is minimal. In this paper, we propose a new relaxation of the problem by introducing…
We develop an efficient algorithm for sampling the eigenvalues of random matrices distributed according to the Haar measure over the orthogonal or unitary group. Our technique samples directly a factorization of the Hessenberg form of such…
This paper addresses the challenge of scaling quantum computing by employing distributed quantum algorithms across multiple processors. We propose a novel circuit partitioning method that leverages graph partitioning to optimize both qubit…
Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies…
Consider a set $P$ of $n$ points picked uniformly and independently from $[0,1]^d$ for a constant dimension $d$ -- such a point set is extremely well behaved in many aspects. For example, for a fixed $r \in [0,1]$, we prove a new…
Recently, Aum\"uller and Dietzfelbinger proposed a version of a dual-pivot quicksort, called "Count", which is optimal among dual-pivot versions with respect to the average number of key comparisons required. In this note we provide further…
We derive a stochastic gradient algorithm for semidefinite optimization using randomization techniques. The algorithm uses subsampling to reduce the computational cost of each iteration and the subsampling ratio explicitly controls…
In this note, we describe a simple approach to obtain a differentially private algorithm for k-clustering with nearly the same multiplicative factor as any non-private counterpart at the cost of a large polynomial additive error. The…
This paper develops an efficient algorithm for computing the Euclidean projection onto the top-k-sum constraint, a key operation in financial risk management and matrix optimization problems. Existing projection methods rely on sorting and…
This thesis discusses the young fields of quantum pseudo-randomness and quantum learning algorithms. We present techniques for derandomising algorithms to decrease randomness resource requirements and improve efficiency. One key object in…
The efficient implementation of matrix arithmetic operations underpins the speedups of many quantum algorithms. We develop a suite of methods to perform matrix arithmetics -- with the result encoded in the off-diagonal blocks of a…
The quantum algorithms for Monte Carlo integration (QMCI), which are based on quantum amplitude estimation (QAE), speed up expected value calculation compared with classical counterparts, and have been widely investigated along with their…
Random batch algorithms are constructed for quantum Monte Carlo simulations. The main objective is to alleviate the computational cost associated with the calculations of two-body interactions, including the pairwise interactions in the…
Let $T=(V,E)$ be a tree with associated costs on its subtrees. A minmax $k$-partition of $T$ is a partition into $k$ subtrees, minimizing the maximum cost of a subtree over all possible partitions. In the centered version of the problem,…
The present paper is concerned with a recursive algorithm as a preprocessing step to find the convex hull of $n$ random points uniformly distributed in the plane. For such a set of points, it is shown that eliminating all but $O(\log n)$ of…