Related papers: Random Rates for 0-Extension and Low-Diameter Deco…

Many high-dimensional uncertainty quantification problems are solved by polynomial dimensional decomposition (PDD), which represents Fourier-like series expansion in terms of random orthonormal polynomials with increasing dimensions. This…

While the standard unweighted Voronoi diagram in the plane has linear worst-case complexity, many of its natural generalizations do not. This paper considers two such previously studied generalizations, namely multiplicative and semi…

Power diagrams, a type of weighted Voronoi diagrams, have many applications throughout operations research. We study the problem of power diagram detection: determining whether a given finite partition of $\mathbb{R}^d$ takes the form of a…

For statistics of rare events in systems obeying a large-deviation principle, the rate function is a key quantity. When numerically estimating the rate function one is always restricted to finite system sizes. Thus, if the interest is in…

We have implemented different algorithms for generating Poissonian and vectorizable random lattices. The random lattices fulfil the Voronoi/Delaunay construction. We measure the performance of our algorithms for the two types of random…

We present an algorithm to compute the geodesic $L_1$ farthest-point Voronoi diagram of $m$ point sites in the presence of $n$ rectangular obstacles in the plane. It takes $O(nm+n \log n + m\log m)$ construction time using $O(nm)$ space.…

We solve the graph bi-partitioning problem in dense graphs with arbitrary degree distribution using the replica method. We find the cut-size to scale universally with <k^1/2>. In contrast, earlier results studying the problem in graphs with…

This is an expository note answering a question posed to us by Richard Stanley, in which we prove a limit shape theorem for partitions of $n$ which maximize the number of subpartitions. The limit shape and the growth rate of the number of…

We propose a method to derive the stationary size distributions of a system, and the degree distributions of networks, using maximisation of the Gibbs-Shannon entropy. We apply this to a preferential attachment-type algorithm for systems of…

We study polynomial-time approximation algorithms for (edge/vertex) Sparsest Cut and Small Set Expansion in terms of $k$, the number of edges or vertices cut in the optimal solution. Our main results are $\mathcal{O}(\text{polylog}\,…

We consider the $0$-Extension problem, where we are given an undirected graph $\mathcal{G}=(V,E)$ equipped with non-negative edge weights $w:E\rightarrow \mathbb{R}^+$, a collection $ T=\{ t_1,\ldots,t_k\}\subseteq V$ of $k$ special…

A fast new algorithm is proposed for numerical computation of (approximate) D-optimal designs. This "cocktail algorithm" extends the well-known vertex direction method (VDM; Fedorov 1972) and the multiplicative algorithm (Silvey,…

For a metric $\mu$ on a finite set $T$, the minimum 0-extension problem 0-Ext$[\mu]$ is defined as follows: Given $V\supseteq T$ and $\ c:{V \choose 2}\rightarrow \mathbf{Q_+}$, minimize $\sum c(xy)\mu(\gamma(x),\gamma(y))$ subject to…

Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…

This paper gives poly-logarithmic-round, distributed D-approximation algorithms for covering problems with submodular cost and monotone covering constraints (Submodular-cost Covering). The approximation ratio D is the maximum number of…

We propose extensions and improvements of the statistical analysis of distributed multipoles (SADM) algorithm put forth by Chipot et al. in [6] for the derivation of distributed atomic multipoles from the quantum-mechanical electrostatic…

Voronoi diagrams are essential geometrical structures with numerous applications, particularly astrophysics-driven finite volume methods. While serial algorithms for constructing these entities are well-established, parallel construction…

We consider a natural generalization of the Partial Vertex Cover problem. Here an instance consists of a graph G = (V,E), a positive cost function c: V-> Z^{+}, a partition $P_1,..., P_r$ of the edge set $E$, and a parameter $k_i$ for each…

Given a set $S$ of $m$ point sites in a simple polygon $P$ of $n$ vertices, we consider the problem of computing the geodesic farthest-point Voronoi diagram for $S$ in $P$. It is known that the problem has an $\Omega(n+m\log m)$ time lower…

Statistical inference from high-dimensional data with low-dimensional structures has recently attracted lots of attention. In machine learning, deep generative modeling approaches implicitly estimate distributions of complex objects by…