We present randomized algorithms for two sorting problems. In the local sorting problem, a graph is given in which each vertex is assigned an element of a total order, and the task...
The task of selecting and ordering information appears in multiple contexts in text generation and summarization. For instance, methods for title generation construct a headline b...
We study the expected topological properties of ˇCech and Vietoris-Rips complexes built on random points in Rd . We find higher dimensional analogues of known results for connect...
While it is exponentially unlikely that a sparse random graph or hypergraph is connected, with probability 1 − o(1) such a graph has a “giant component” that, given its numbe...
Coloring a k-colorable graph using k colors (k ≥ 3) is a notoriously hard problem. Considering average case analysis allows for better results. In this work we consider the unif...
Amin Coja-Oghlan, Michael Krivelevich, Dan Vilench...