Related papers: Longest minimal length partitions
In this paper we are concerned with finding the vertices of the Voronoi cell of a Euclidean lattice. Given a basis of a lattice, we prove that computing the number of vertices is a #P-hard problem. On the other hand we describe an algorithm…
The project of physics discovery is often equivalent to finding the most concise description of a physical system. The description with optimum predictive capability for a dataset generated by a physical system is one that minimizes both…
Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the…
We introduce a novel approach to reduce the computational effort of solving mixed-integer convex chance constrained programs through the scenario approach. Instead of reducing the number of required scenarios, we directly minimize the…
We study the problem of differentially private optimization with linear constraints when the right-hand-side of the constraints depends on private data. This type of problem appears in many applications, especially resource allocation.…
We consider the {\em Shaped Partition Problem} of partitioning $n$ given vectors in real $k$-space into $p$ parts so as to maximize an arbitrary objective function which is convex on the sum of vectors in each part, subject to arbitrary…
In this paper, we propose to compute Voronoi diagrams over mesh surfaces driven by an arbitrary geodesic distance solver, assuming that the input is a triangle mesh as well as a collection of sites $P=\{p_i\}_{i=1}^m$ on the surface. We…
The deletion channel is the simplest point-to-point communication channel that models lack of synchronization. Input bits are deleted independently with probability d, and when they are not deleted, they are not affected by the channel.…
Various methods have been proposed in the literature to determine an optimal partitioning of the set of actors in a network into core and periphery subsets. However, these methods either work only for relatively small input sizes, or do not…
In this paper we study the extraction of representative elements in the data stream model in the form of submodular maximization. Different from the previous work on streaming submodular maximization, we are interested only in the recent…
We study a general smallest intersecting ball problem and its soft-margin variant in high-dimensional Euclidean spaces for input objects that are compact and convex. These two problems link and unify a series of fundamental problems in…
In this work we are interested in the construction of numerical methods for high dimensional constrained nonlinear optimization problems by particle-based gradient-free techniques. A consensus-based optimization (CBO) approach combined with…
Cardinality-constrained diameter partitioning asks for a partition of $n$ items into two classes of prescribed sizes that minimizes the larger of the two class diameters. We give an $O(n^2)$ algorithm and a matching $\Omega(n^2)$ lower…
We study algorithms for construction of composable coresets for the task of Determinant Maximization under partition constraint. Given a point set $V\subset \mathbb{R}^d$ that is partitioned into $s$ groups $V_1,\cdots, V_s$, and integers…
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…
We derive asymptotic formulas for the number of integer partitions with given sums of $j$th powers of the parts for $j$ belonging to a finite, non-empty set $J \subset \mathbb N$. The method we use is based on the `principle of maximum…
We study the problem of maximizing R{\'e}nyi entropy of order $2$ (equivalently, minimizing the index of coincidence) over the set of joint distributions with prescribed marginals. A closed-form optimizer is known under a feasibility…
We describe an approach for finding upper bounds on an ODE dynamical system's maximal Lyapunov exponent among all trajectories in a specified set. A minimization problem is formulated whose infimum is equal to the maximal Lyapunov exponent,…
We propose a novel approach for navigating in polygonal environments by synthesizing controllers that take as input relative displacement measurements with respect to a set of landmarks. Our algorithm is based on solving a sequence of…
We establish some bounds on the number of higher-dimensional partitions by volume. In particular, we give bounds via vector partitions and MacMahon's numbers.