2 citations · 4 across the 12 of their papers we have counts for
15 papers
Three trees suffice for a constant stretch in minor-free graphs
Hung Le, Huy Pham, Cuong Than +1
In this short note, we show that -minor-free graphs have a tree cover with trees and constant stretch for any fixed graph . The number of trees matches the recent lower b…
Improved Euclidean Shallow Light Trees
Hung Le, Shay Solomon, Cuong Than +2
For parameters , a spanning tree of a weighted graph rooted at a designated vertex is called an -shallow-light tree (SLT) if (i) for every vertex ,…
Approximating Euclidean Shallow-Light Trees
Hung Le, Shay Solomon, Cuong Than +2
For a weighted graph and a designated source vertex , a spanning tree that simultaneously approximates a shortest-path tree w.r.t. source and a minimum…
Tree-Like Shortcuttings of Trees
Hung Le, Lazar Milenković, Shay Solomon +1
Sparse shortcuttings of trees -- equivalently, sparse 1-spanners for tree metrics with bounded hop-diameter -- have been studied extensively (under different names and settings), s…
Optimal Bounds for Spanners and Tree Covers in Doubling Metrics
An La, Hung Le, Shay Solomon +4
It is known that any -point set in the -dimensional Euclidean space , for , admits: 1) a -spanner with maximum degree and…
Approximate Light Spanners in Planar Graphs
Hung Le, Shay Solomon, Cuong Than +2
In their seminal paper, Althöfer et al. (DCG 1993) introduced the {\em greedy spanner} and showed that, for any weighted planar graph , the weight of the greedy -spanner…
Light Tree Covers, Routing, and Path-Reporting Oracles via Spanning Tree Covers in Doubling Graphs
Hsien-Chih Chang, Jonathan Conroy, Hung Le +2
A -stretch tree cover of an edge-weighted -vertex graph is a collection of trees, where every pair of vertices has a -stretch path in one o…
Towards Instance-Optimal Euclidean Spanners
Hung Le, Shay Solomon, Cuong Than +2
Euclidean spanners are important geometric objects that have been extensively studied since the 1980s. The two most basic "compactness'' measures of a Euclidean spanner are the…
Optimal Euclidean Tree Covers
Hsien-Chih Chang, Jonathan Conroy, Hung Le +3
A of a metric space is a collection of trees, where every pair of points has a -stretch path in one of the trees. The…
Shortcut Partitions in Minor-Free Graphs: Steiner Point Removal, Distance Oracles, Tree Covers, and More
Hsien-Chih Chang, Jonathan Conroy, Hung Le +3
The notion of shortcut partition, introduced recently by Chang, Conroy, Le, Milenković, Solomon, and Than [CCLMST23], is a new type of graph partition into low-diameter clusters. R…
Optimal Fault-Tolerant Spanners in Euclidean and Doubling Metrics: Breaking the Lightness Barrier
Hung Le, Shay Solomon, Cuong Than
An essential requirement of spanners in many applications is to be fault-tolerant: a -spanner of a metric space is called (vertex) -fault-tolerant (-FT) if it remains…
Resolving the Steiner Point Removal Problem in Planar Graphs via Shortcut Partitions
Hsien-Chih Chang, Jonathan Conroy, Hung Le +3
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 tre…
Covering Planar Metrics (and Beyond): O(1) Trees Suffice
Hsien-Chih Chang, Jonathan Conroy, Hung Le +3
While research on the geometry of planar graphs has been active in the past decades, many properties of planar metrics remain mysterious. This paper studies a fundamental aspect of…
Greedy Spanners in Euclidean Spaces Admit Sublinear Separators
Hung Le, Cuong Than
The greedy spanner in a low dimensional Euclidean space is a fundamental geometric construction that has been extensively studied over three decades as it possesses the two most ba…
Clades and clans: a comparison study of two evolutionary models
Sha Zhu, Cuong Than, Taoyang Wu
The Yule-Harding-Kingman (YHK) model and the proportional to distinguishable arrangements (PDA) model are two binary tree generating models that are widely used in evolutionary bio…