Related papers: Fast computation of the circular map
Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good…
The purpose of this paper is to introduce a new numerical method to solve multi-marginal optimal transport problems with pairwise interaction costs. The complexity of multi-marginal optimal transport generally scales exponentially in the…
We present a simple, accurate method for computing singular or nearly singular integrals on a smooth, closed surface, such as layer potentials for harmonic functions evaluated at points on or near the surface. The integral is computed with…
In this article we present an efficient algorithm to compute rotation intervals of circle maps of degree one. It is based on the computation of the rotation number of a monotone circle map of degree one with a constant section. The main…
We consider the problem of computing the data-cube marginals of a fixed order $k$ (i.e., all marginals that aggregate over $k$ dimensions), using a single round of MapReduce. The focus is on the relationship between the reducer size (number…
Finding sparse cuts is an important tool in analyzing large-scale distributed networks such as the Internet and Peer-to-Peer networks, as well as large-scale graphs such as the web graph, online social communities, and VLSI circuits. In…
In this paper, we introduce a novel algorithm for segmentation of imperfect boundary probability maps (BPM) in connectomics. Our algorithm can be a considered as an extension of spectral clustering. Instead of clustering the diffusion maps…
This paper proposes a new parallel approach to solve connected components on a 2D binary image implemented with CUDA. We employ the following strategies to accelerate neighborhood exploration after dividing an input image into independent…
Computing the simulation preorder of a given Kripke structure (i.e., a directed graph with $n$ labeled vertices) has crucial applications in model checking of temporal logic. It amounts to solving a specific two-players reachability game,…
Motion planning seeks a collision-free path in a configuration space (C-space), representing all possible robot configurations in the environment. As it is challenging to construct a C-space explicitly for a high-dimensional robot, we…
Multi-access Edge Computing (MEC) facilitates the deployment of critical applications with stringent QoS requirements, latency in particular. This paper considers the problem of jointly planning the availability of computational resources…
A continuous map from R^m to R^N or from C^m to C^N is called k-regular if the images of any $k$ points are linearly independent. Given integers m and k a problem going back to Chebyshev and Borsuk is to determine the minimal value of N for…
The boundary integral method is an efficient approach for solving time-harmonic acoustic obstacle scattering problems. The main computational task is the evaluation of an oscillatory boundary integral at each discretization point of the…
We describe a new sampling-based method to determine cuts in an undirected graph. For a graph (V, E), its cycle space is the family of all subsets of E that have even degree at each vertex. We prove that with high probability, sampling the…
The communication cost of algorithms (also known as I/O-complexity) is shown to be closely related to the expansion properties of the corresponding computation graphs. We demonstrate this on Strassen's and other fast matrix multiplication…
Simulating large quantum circuits on hardware with limited qubit counts is often attempted through methods like circuit knitting, which typically incur sample costs that grow exponentially with the number of connections cut. In this work,…
We present improved distributed algorithms for triangle detection and its variants in the CONGEST model. We show that Triangle Detection, Counting, and Enumeration can be solved in $\tilde{O}(n^{1/2})$ rounds. In contrast, the previous…
We represent planning as a set of loosely coupled network flow problems, where each network corresponds to one of the state variables in the planning domain. The network nodes correspond to the state variable values and the network arcs…
This paper concerns with iterative schemes for the perfect reconstruction of functions belonging to multiresolution spaces on bounded manifolds from nonuniform sampling. The schemes have optimal complexity in the sense that the…
Let $\mathscr O$ be a set of $n$ disjoint obstacles in $\mathbb{R}^2$, $\mathscr M$ be a moving object. Let $s$ and $l$ denote the starting point and maximum path length of the moving object $\mathscr M$, respectively. Given a point $p$ in…