Related papers: Gravitational allocation for uniform points on the…
We study fair resource allocation under a connectedness constraint wherein a set of indivisible items are arranged on a path and only connected subsets of items may be allocated to the agents. An allocation is deemed fair if it satisfies…
A balanced configuration of points on the sphere $S^2$ is a (finite) set of points which are in equilibrium if they act on each other according any force law dependent only on the distance between two points. The configuration is…
We consider the following distributed pursuit-evasion problem. A team of mobile agents called searchers starts at an arbitrary node of an unknown $n$-node network. Their goal is to execute a search strategy that guarantees capturing a fast…
We calculate the total gravitational energy and the gravitational energy density of the de Sitter space using the definition of localized energy that arises in the framework of the teleparallel equivalent of general relativity. We find that…
This paper develops a systematic and geometric theory of optimal quantization on the unit sphere $\mathbb S^2$, focusing on finite uniform probability distributions supported on the spherical surface - rather than on lower-dimensional…
We investigate fairness in the allocation of indivisible items among groups of agents using the notion of maximin share (MMS). While previous work has shown that no nontrivial multiplicative MMS approximation can be guaranteed in this…
This paper describes novel and fast, simple and robust algorithm with O(N) expected complexity which enables to decrease run-time needed to find an exact maximum distance of two points in E2. The proposed algorithm has been evaluated…
Properly estimating correlations between objects at different spatial scales necessitates $\mathcal{O}(n^2)$ distance calculations. For this reason, most widely adopted packages for estimating correlations use clustering algorithms to…
We study the problem of fairly allocating $m$ indivisible goods to $n$ agents, where agents may have different preferences over the goods. In the traditional setting, agents' valuations are provided as inputs to the algorithm. In this…
We present an $O(n\sqrt{\log n})$ time and linear space algorithm for sorting real numbers. This breaks the long time illusion that real numbers have to be sorted by comparison sorting and take $\Omega (n\log n)$ time to be sorted.
The formation of self-gravitating systems is studied by simulating the collapse of a set of N particles which are generated from several distribution functions. We first establish that the results of such simulations depend on N for small…
We present three new approximation algorithms with improved constant ratios for selecting $n$ points in $n$ disks such that the minimum pairwise distance among the points is maximized. (1) A very simple $O(n\log n)$-time algorithm with…
We consider a setting where we have a ground set $M$ together with real-valued set functions $f_1, \dots, f_n$, and the goal is to partition $M$ into two sets $S_1,S_2$ such that $|f_i(S_1) - f_i(S_2)|$ is small for every $i$. Many results…
The paper concerns the uniform polynomial approximation of a function $f$, continuous on the unit Euclidean sphere of ${\mathbb R}^3$ and known only at a finite number of points that are somehow uniformly distributed on the sphere. First we…
We discuss the exact solution of Einstein's equation corresponding to a static and plane symmetric distribution of matter with constant positive density located below $z=0$ matched to vacuum solutions.
The average distance from a node to all other nodes in a graph, or from a query point in a metric space to a set of points, is a fundamental quantity in data analysis. The inverse of the average distance, known as the (classic) closeness…
We study different ways of determining the mean distance $ < r_n >$ between a reference point and its $n$-th neighbour among random points distributed with uniform density in a $D$-dimensional Euclidean space. First we present a heuristic…
Arrangement field theory is a theory of everything which describes all particles as different manifestations of an unique field, the gauge field Sp(12,C). All fields (bosons and fermions in three families) fill up the adjoint representation…
In this paper, we consider the symmetric KL-divergence between the sum of independent variables and a Gaussian distribution, and obtain a convergence rates of order $O\left( \frac{\ln n}{\sqrt{n}}\right)$. The proof is based on Stein's…
In a combinatorial exchange setting, players place sell (resp. buy) bids on combinations of traded goods. Besides the question of finding an optimal selection of winning bids, the question of how to share the obtained profit is of high…