ﻻ يوجد ملخص باللغة العربية
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 recursive calls, we use previous results of Har-Peled and Mendel, and Abam and Har-Peled for computing a sparse annulus that separates the points in a balanced way.
We show that the geodesic diameter of a polygonal domain with n vertices can be computed in O(n^4 log n) time by considering O(n^3) candidate diameter endpoints; the endpoints are a subset of vertices of the overlay of shortest path maps from vertices of the domain.
Tree comparison metrics have proven to be an invaluable aide in the reconstruction and analysis of phylogenetic (evolutionary) trees. The path-length distance between trees is a particularly attractive measure as it reflects differences in tree shape
It is known for some time that a random graph $G(n,p)$ contains w.h.p. a Hamiltonian cycle if $p$ is larger than the critical value $p_{crit}= (log n + log log n + omega_n)/n$. The determination of a concrete Hamiltonian cycle is even for values much
In population protocols, the underlying distributed network consists of $n$ nodes (or agents), denoted by $V$, and a scheduler that continuously selects uniformly random pairs of nodes to interact. When two nodes interact, their states are updated by
Resolving an open question from 2006, we prove the existence of light-weight bounded-degree spanners for unit ball graphs in the metrics of bounded doubling dimension, and we design a simple $mathcal{O}(log^*n)$-round distributed algorithm that given