Scattering and sparse partitions, and their applications
A Filtser - ACM Transactions on Algorithms, 2024 - dl.acm.org
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 …
of radius intersects at most clusters. Similarly, is-scattering if instead for balls, we require that …
One tree to rule them all: Poly-logarithmic universal steiner tree
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 …
if, for any subset of vertices S containing r, the cost of the minimal subgraph of T connecting …
Near-Optimal Fully-Dynamic All-Pairs Shortest Paths in Planar Graphs
We study the fully-dynamic all-pair shortest paths (APSP) problem on planar graphs: given
an n-vertex planar graph G=(V,E) undergoing edge insertions and deletions, the goal is to …
an n-vertex planar graph G=(V,E) undergoing edge insertions and deletions, the goal is to …
An Lower Bound for Steiner Point Removal
In the Steiner point removal (SPR) problem, we are given a (weighted) graph G and a subset
T of its vertices called terminals, and the goal is to compute a (weighted) graph H on T that is …
T of its vertices called terminals, and the goal is to compute a (weighted) graph H on T that is …
[PDF][PDF] Near-Optimal (1+ ϵ)-Approximate Fully-Dynamic All-Pairs Shortest Paths in Planar Graphs
We study the fully-dynamic all-pair shortest paths (APSP) problem on planar graphs: given
an n-vertex planar graph G=(V, E) undergoing edge insertions and deletions, the goal is to …
an n-vertex planar graph G=(V, E) undergoing edge insertions and deletions, the goal is to …
An Lower Bound for Steiner Point Removal
In the Steiner point removal (SPR) problem, we are given a (weighted) graph $ G $ and a
subset $ T $ of its vertices called terminals, and the goal is to compute a (weighted) graph …
subset $ T $ of its vertices called terminals, and the goal is to compute a (weighted) graph …
[PDF][PDF] One Tree to Rule Them All: Poly-Logarithmic Universal Steiner Tree
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 …
if, for any subset of vertices S containing r, the cost of the minimal subgraph of T connecting …