相关论文: Further Results on Arithmetic Filters for Geometri…
When classical particle filtering algorithms are used for maximum likelihood parameter estimation in nonlinear state-space models, a key challenge is that estimates of the likelihood function and its derivatives are inherently noisy. The…
It is well known that, under very weak assumptions, multiobjective optimization problems admit $(1+\varepsilon,\dots,1+\varepsilon)$-approximation sets (also called $\varepsilon$-Pareto sets) of polynomial cardinality (in the size of the…
Polynomial approximations of functions are widely used in scientific computing. In certain applications, it is often desired to require the polynomial approximation to be non-negative (resp. non-positive), or bounded within a given range,…
If several independent algorithms for a computer-calculated quantity exist, then one can expect their results (which differ because of numerical errors) to follow approximately Gaussian distribution. The mean of this distribution,…
We consider the classical $k$-means clustering problem in the setting bi-criteria approximation, in which an algoithm is allowed to output $\beta k > k$ clusters, and must produce a clustering with cost at most $\alpha$ times the to the…
We study dense packings of a large number of congruent non-overlapping circles inside a square by looking for configurations which maximize the packing density, defined as the ratio between the area occupied by the disks and the area of the…
This paper considers the arbitrary-proportional finite-set-partitioning problem which involves partitioning a finite set into multiple subsets with respect to arbitrary nonnegative proportions. This is the core art of many fundamental…
In this paper we introduce a projection method for the space of probability distributions based on the differential geometric approach to statistics. This method is based on a direct L2 metric as opposed to the usual Hellinger distance and…
The margin of victory of an election is a useful measure to capture the robustness of an election outcome. It also plays a crucial role in determining the sample size of various algorithms in post election audit, polling etc. In this work,…
In this paper we analyze O'Hara's partition bijection. We present three type of results. First, we show that O'Hara's bijection can be viewed geometrically as a certain scissor congruence type result. Second, we obtain a number of new…
Implicit particle filters for data assimilation update the particles by first choosing probabilities and then looking for particle locations that assume them, guiding the particles one by one to the high probability domain. We provide a…
We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…
For interior-point algorithms in linear programming, it is well-known that the selection of the centering parameter is crucial for proving polynomility in theory and for efficiency in practice. However, the selection of the centering…
A modification of the standard Boris algorithm, called filtered Boris algorithm, is proposed for the numerical integration of the equations of motion of charged particles in a strong non-uniform magnetic field in the asymptotic scaling…
We improve upon the running time for finding a point in a convex set given a separation oracle. In particular, given a separation oracle for a convex set $K\subset \mathbb{R}^n$ contained in a box of radius $R$, we show how to either find a…
In this paper, we investigate the learning-augmented $k$-median clustering problem, which aims to improve the performance of traditional clustering algorithms by preprocessing the point set with a predictor of error rate $\alpha \in [0,1)$.…
First, we study geometric variants of the standard set cover motivated by assignment of directional antenna and shipping with deadlines, providing the first known polynomial-time exact solutions. Next, we consider the following general…
Papadimitriou and Yannakakis show that the polynomial-time solvability of a certain singleobjective problem determines the class of multiobjective optimization problems that admit a polynomial-time computable $(1+\varepsilon, \dots ,…
We present an algorithm for efficiently approximating of qubit unitaries over gate sets derived from totally definite quaternion algebras. It achieves $\varepsilon$-approximations using circuits of length $O(\log(1/\varepsilon))$, which is…
The theory of multidimensional persistence captures the topology of a multifiltration -- a multiparameter family of increasing spaces. Multifiltrations arise naturally in the topological analysis of scientific data. In this paper, we give a…