Related papers: How To Place a Point to Maximize Angles
Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their…
We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…
Maximum likelihood iteration is one of the most commonly used reconstruction algorithms in quantum tomography. The main appeal of the method is that it is easy to implement and that it converges reliably to a physically meaningful density…
We present an algorithm that enumerates all the minimal triangulations of a graph in incremental polynomial time. Consequently, we get an algorithm for enumerating all the proper tree decompositions, in incremental polynomial time, where…
This paper studies the problem of mapping optimization in decentralized control problems. A global optimization algorithm is proposed based on the ideas of ``deterministic annealing" - a powerful non-convex optimization framework derived…
Consider a weighted graph G where vertices are points in the plane and edges are line segments. The weight of each edge is the Euclidean distance between its two endpoints. A routing algorithm on G has a competitive ratio of c if the length…
The article is devoted to the problem of applying the maximum principle for finding optimal control parameters in simulation tasks of interest for a variety of engineering and industrial systems and processes. Especially important is the…
This paper introduces a special family of randomized algorithms for Max DICUT that we call oblivious algorithms. Let the bias of a vertex be the ratio between the total weight of its outgoing edges and the total weight of all its edges. An…
We introduce the Voronoi functional of a triangulation of a finite set of points in the Euclidean plane and prove that among all geometric triangulations of the point set, the Delaunay triangulation maximizes the functional. This result…
This paper presents the formulation and analysis of a novel distributed maximum likelihood algorithm that utilizes a first-order optimization scheme. The proposed approach utilizes a static average consensus algorithm to reach agreement on…
This paper describes a node relocation algorithm based on nonlinear optimization which delivers excellent results for both unstructured and structured plane triangle meshes over convex as well as non-convex domains with high curvature. The…
UAV trajectory planning is often done in a two-step approach, where a low-dimensional path is refined to a dynamic trajectory. The resulting trajectories are only locally optimal, however. On the other hand, direct planning in…
In the study of depth functions it is important to decide whether we want such a function to be sensitive to multimodality or not. In this paper we analyze the Delaunay depth function, which is sensitive to multimodality and compare this…
Clustering is a fundamental problem, aiming to partition a set of elements, like agents or data points, into clusters such that elements in the same cluster are closer to each other than to those in other clusters. In this paper, we present…
We propose a technique called Rotate-and-Kill for solving the polygon inclusion and circumscribing problems. By applying this technique, we obtain $O(n)$ time algorithms for computing (1) the maximum area triangle in a given $n$-sided…
Consider a metric space $(P,dist)$ with $N$ points whose doubling dimension is a constant. We present a simple, randomized, and recursive algorithm that computes, in $O(N \log N)$ expected time, the closest-pair distance in $P$. To generate…
We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the…
We introduce a modified model of random walk, and then develop two novel clustering algorithms based on it. In the algorithms, each data point in a dataset is considered as a particle which can move at random in space according to the…
In this paper, "chance optimization" problems are introduced, where one aims at maximizing the probability of a set defined by polynomial inequalities. These problems are, in general, nonconvex and computationally hard. With the objective…
The local angle property of the (order-$1$) Delaunay triangulations of a generic set in $\mathbb{R}^2$ asserts that the sum of two angles opposite a common edge is less than $\pi$. This paper extends this property to higher order and uses…