On Light Spanners, Low-Treewidth Embeddings and Efficient Traversing in Minor-Free Graphs

Explore cutting-edge graph theory concepts in this 24-minute IEEE conference talk covering light spanners, low-treewidth embeddings, and efficient traversing in minor-free graphs. Delve into Capacitated Vehicle Routing, Subset TSP, and techniques for designing Polynomial-Time Approximation Schemes (PTAS). Learn about light preservers, local spanners, and their applications in planar graphs with vortices. Examine tree structures of clique-sums in nearly-embedded graphs and discover open problems in the field. Gain insights from researchers Vincent Cohen-Addad, Arnold Filtser, Philip N. Klein, and Hung Le as they present advanced algorithms and graph theory applications.

Intro
Capacitated Vehicle Routing (CVR)
"Approximable" Instances.
"Approximable" means
Results for Subset TSP
Two techniques to design a PTAS
PTAS from Light Preservers
PTAS from Low Treewdith Embedding
The Framework
Light Preservers from Local Spanners
The rest of the talk: find L-local spanners.
Planar graph + One Vortex and D = 0(L)
Removing Diameter Constraint
Planar graph + O(1) Vortices
Tree of Clique-sums of Nearly-embed. Graphs
Open problems