2 citations · 7 across the 7 of their papers we have counts for
9 papers
Light Spanners with Small Hop-Diameter
Sujoy Bhore, Lazar Milenkovic
Lightness, sparsity, and hop-diameter are the fundamental parameters of geometric spanners. Arya et al. [STOC'95] showed in their seminal work that there exists a construction of E…
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…
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…
The Magic Permutohedron
Djordje Baralic, Lazar Milenkovic
We present a configuration called a magic permutohedron that shows the placement of the numbers of in the vertices of the permutohedra so that the sum of n…
Sparse Euclidean Spanners with Tiny Diameter: A Tight Lower Bound
Hung Le, Lazar Milenkovic, Shay Solomon
In STOC'95 [ADMSS'95] Arya et al. showed that any set of points in admits a -spanner with hop-diameter at most 2 (respectively, 3) and edges…
Can't See The Forest for the Trees: Navigating Metric Spaces by Bounded Hop-Diameter Spanners
Omri Kahalon, Hung Le, Lazar Milenkovic +1
Spanners for metric spaces have been extensively studied, both in general metrics and in restricted classes, perhaps most notably in low-dimensional Euclidean spaces -- due to thei…
Surprising Examples of Manifolds in Toric Topology!
Djordje Baralic, Lazar Milenkovic
We investigate small covers and quasitoric over the duals of neighborly simplicial polytopes with small number of vertices in dimensions , , and . In the most of the c…