Shortcut partitions in minor-free graphs: Steiner point removal, distance oracles, tree covers, and more

HC Chang, J Conroy, H Le, L Milenković… - Proceedings of the 2024 …, 2024 - SIAM
The notion of shortcut partition, introduced recently by Chang, Conroy, Le, Milenković,
Solomon, and Than [CCL+ 23], is a new type of graph partition into low-diameter clusters …

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 …

Resolving the steiner point removal problem in planar graphs via shortcut partitions

HC Chang, J Conroy, H Le, L Milenkovic… - arXiv preprint arXiv …, 2023 - arxiv.org
Recently the authors [CCLMST23] introduced the notion of shortcut partition of planar
graphs and obtained several results from the partition, including a tree cover with $ O (1) …

Optimal padded decomposition for bounded treewidth graphs

A Filtser, T Friedrich, D Issac, N Kumar, H Le… - arXiv preprint arXiv …, 2024 - arxiv.org
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 …

An Lower Bound for Steiner Point Removal

Y Chen, Z Tan - Proceedings of the 2024 Annual ACM-SIAM …, 2024 - SIAM
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 …

An Lower Bound for Steiner Point Removal

Y Chen, Z Tan - arXiv preprint arXiv:2310.07862, 2023 - arxiv.org
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 …

[PDF][PDF] Compact Representations of Graphs and Their Metrics

DE Hershkowitz - 2020 - reports-archive.adm.cs.cmu.edu
Graphs and metrics are two of the most ubiquitous, versatile and powerful tools in modern
computing. Both are general enough to be widely applicable but structured enough to …