Related papers: The Distance Approach to Approximate Combinatorial…
Modern database optimizer relies on cardinality estimator, whose accuracy directly affects the optimizer's ability to choose an optimal execution plan. Recent work on data-driven methods has leveraged probabilistic models to achieve higher…
The $k$-Maximum Dispersion Problem with Cardinality Constraints ($k$-MDCC) asks for a partition of a given item set with pairwise dissimilarities into $k$ cardinality-constrained groups such that the minimum pairwise intra-group…
Cardinality estimation is the task of approximating the number of distinct elements in a large dataset with possibly repeating elements. LogLog and HyperLogLog (c.f. Durand and Flajolet [ESA 2003], Flajolet et al. [Discrete Math Theor.…
We study the problem of estimating the covariance matrix of a high-dimensional distribution when a small constant fraction of the samples can be arbitrarily corrupted. Recent work gave the first polynomial time algorithms for this problem…
We design fast deterministic algorithms for distance computation in the congested clique model. Our key contributions include: -- A $(2+\epsilon)$-approximation for all-pairs shortest paths in $O(\log^2{n} / \epsilon)$ rounds on unweighted…
Comparison to traditionally accurate computing, approximate computing focuses on the rapidity of the satisfactory solution, but not the unnecessary accuracy of the solution. Approximate bisimularity is the approximate one corresponding to…
Partitioning and grouping of similar objects plays a fundamental role in image segmentation and in clustering problems. In such problems a typical goal is to group together similar objects, or pixels in the case of image processing. At the…
The complexity of matrix multiplication is a central topic in computer science. While the focus has traditionally been on exact algorithms, a long line of literature also considers randomized algorithms, which return an approximate solution…
The input to the distant representatives problem is a set of $n$ objects in the plane and the goal is to find a representative point from each object while maximizing the distance between the closest pair of points. When the objects are…
We study the stochastic $p$-Laplace system in a bounded domain. We propose two new space-time discretizations based on the approximation of time-averaged values. We establish linear convergence in space and $1/2$ convergence in time.…
In this paper, we present novel deterministic algorithms for multiplying two $n \times n$ matrices approximately. Given two matrices $A,B$ we return a matrix $C'$ which is an \emph{approximation} to $C = AB$. We consider the notion of…
This paper extends the framework of randomised matrix multiplication to a coarser partition and proposes an algorithm as a complement to the classical algorithm, especially when the optimal probability distribution of the latter one is…
We consider the problem of tracking $n$ targets in the plane using $2n$ cameras. We can use two cameras to estimate the location of a target. We are then interested in forming $n$ camera pairs where each camera belongs to exactly one pair,…
A solution for Smale's 17th problem, for the case of systems with bounded degree was recently given. This solution, an algorithm computing approximate zeros of complex polynomial systems in average polynomial time, assumed infinite…
We present a complete algorithm for finding an exact minimal polynomial from its approximate value by using an improved parameterized integer relation construction method. Our result is superior to the existence of error controlling on…
Consider the problem of finding a point in an ultrametric space with the minimum average distance to all points. We give this problem a Monte Carlo $O((\log^2(1/\epsilon))/\epsilon^3)$-time $(1+\epsilon)$-approximation algorithm for all…
We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…
Cardinality estimation is a fundamental task in database management systems, aiming to predict query results accurately without executing the queries. However, existing techniques either achieve low estimation accuracy or incur high…
Although it has been claimed in two different papers that the maximum cardinality cut problem is polynomial-time solvable for proper interval graphs, both of them turned out to be erroneous. In this paper, we give FPT algorithms for the…
Approximate Bayesian computation performs approximate inference for models where likelihood computations are expensive or impossible. Instead simulations from the model are performed for various parameter values and accepted if they are…