- Star Splaying - 

To quote the abstract from the paper itself: "I propose a new paradigm 
that will revolutionize the way paradigms are revolutionized. Synergy 
will take place too." 

I will present Jonathan 
Shewchuk's recent paper that presents a technique that solves a 
number of problems among which is the Delaunay repair problem: 
"Suppose the vertices of a Delaunay triangulation move by small 
distances, rendering the triangulation no longer Delaunay. The goal 
is to restore the Delaunay property, with the vertices fixed in their 
new positions."