相关论文: Deterministic Sparse Pattern Matching via the Baur…
Computing the convolution $A\star B$ of two length-$n$ integer vectors $A,B$ is a core problem in several disciplines. It frequently comes up in algorithms for Knapsack, $k$-SUM, All-Pairs Shortest Paths, and string pattern matching…
Computing the convolution $A\star B$ of two length-$n$ vectors $A,B$ is an ubiquitous computational primitive. Applications range from string problems to Knapsack-type problems, and from 3SUM to All-Pairs Shortest Paths. These applications…
In sparse convolution-type problems, a common technique is to hash the input integers modulo a random prime $p\in [Q/2,Q]$ for some parameter $Q$, which reduces the range of the input integers while preserving their additive structure.…
A geometrical pattern is a set of points with all pairwise distances (or, more generally, relative distances) specified. Finding matches to such patterns has applications to spatial data in seismic, astronomical, and transportation…
This paper presents new and efficient algorithms for matching stellar catalogues where the transformation between the coordinate systems of the two catalagoues is unknown and may include shearing. Finding a given object whether a star or…
Probabilistic cross-identification has been successfully applied to a number of problems in astronomy from matching simple point sources to associating stars with unknown proper motions and even radio observations with realistic morphology.…
We present a new deterministic algorithm for the sparse Fourier transform problem, in which we seek to identify k << N significant Fourier coefficients from a signal of bandwidth N. Previous deterministic algorithms exhibit quadratic…
We present and implement a probabilistic (Bayesian) method for producing catalogs from images of stellar fields. The method is capable of inferring the number of sources N in the image and can also handle the challenges introduced by noise,…
We propose a new method to infer the star formation histories of resolved stellar populations. With photometry one may plot observed stars on a colour-magnitude diagram (CMD) and then compare with synthetic CMDs representing different star…
We present a new approach for solving (minimum disagreement) correlation clustering that results in sublinear algorithms with highly efficient time and space complexity for this problem. In particular, we obtain the following algorithms for…
Information in the time distribution of points in a state space reconstructed from observed data yields a test for ``nonstationarity''. Framed in terms of a statistical hypothesis test, this numerical algorithm can discern whether some…
We consider the problem of querying a string (or, a database) of length $N$ bits to determine all the locations where a substring (query) of length $M$ appears either exactly or is within a Hamming distance of $K$ from the query. We assume…
We propose a new pattern-matching algorithm for matching CCD images to a stellar catalogue based statistical method in this paper. The method of constructing star pairs can greatly reduce the computational complexity compared with the…
Computing the convolution $A \star B$ of two vectors of dimension $n$ is one of the most important computational primitives in many fields. For the non-negative convolution scenario, the classical solution is to leverage the Fast Fourier…
Star clusters are often hard to find, as they may lie in a dense field of background objects or, because in the case of embedded clusters, they are surrounded by a more dispersed population of young stars. This paper discusses four…
The observable macroscopic properties of relativistic stars (whose equations of state are known) can be predicted by solving the stellar structure equations that follow from Einstein's equation. For neutron stars, however, our knowledge of…
This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…
Perturbing a deterministic $n$-dimensional matrix with small Gaussian noise is a cornerstone of smoothed analysis of algorithms [Spielman and Teng, JACM 2004], as it reduces the condition number of the input to $O(n)$, and with it the…
Given two vectors $u,v \in \mathbb{Q}^D$ over a finite domain $D$ and a function $f : D\times D\to D$, the convolution problem asks to compute the vector $w \in \mathbb{Q}^D$ whose entries are defined by $w(d) = \sum_{\substack{x,y \in D \\…
Pattern matching is one of the fundamental problems in Computer Science. Both the classic version of the problem as well as the more sophisticated version where wildcards can also appear in the input can be solved in almost linear time…