A partition of a weighted graph is-sparse if every cluster has diameter at most, and every ball
of radius intersects at most clusters. Similarly, is-scattering if instead for balls, we require that …

A spanning tree T of graph G is a ρ-approximate universal Steiner tree (UST) for root vertex r
if, for any subset of vertices S containing r, the cost of the minimal subgraph of T connecting …

Abstract A partition (C 1, C 2,…, C q) of G=(V, E) into clusters of strong (respectively, weak)
diameter d, such that the supergraph obtained by contracting each C i is ℓ-colorable is …

A $(\beta,\delta,\Delta) $-padded decomposition of an edge-weighted graph $ G=(V, E, w) $
is a stochastic decomposition into clusters of diameter at most $\Delta $ such that for every …

Chan, Har-Peled, and Jones [2020] recently developed locality-sensitive ordering (LSO), a
new tool that allows one to reduce problems in the Euclidean space ℝ d to the 1 …

For a pair of positive parameters D, Χ, a partition P of the vertex set V of an n-vertex graph
G=(V, E) into disjoint clusters of diameter at most D each is called a (D, Χ) network …

Given a weighted graph $ G=(V, E, w) $, a partition of $ V $ is $\Delta $-bounded if the
diameter of each cluster is bounded by $\Delta $. A distribution over $\Delta $-bounded …

Given a metric space $(X, d_X) $, a $(\beta, s,\Delta) $-sparse cover is a collection of
clusters $\mathcal {C}\subseteq P (X) $ with diameter at most $\Delta $, such that for every …

This article presents universal algorithms for clustering problems, including the widely
studied k-median, k-means, and k-center objectives. The input is a metric space containing …

This paper considers correlation clustering on unweighted complete graphs. We give a
combinatorial algorithm that returns a single clustering solution that is simultaneously O (1) …