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 $(\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 …

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

We consider an incremental variant of the rooted prize-collecting Steiner-tree problem with a
growing budget constraint. While no incremental solution exists that simultaneously …

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 …