Georgia Institute of Technology College of Sciences

Tree-width is a well-known metric on undirected graphs that measures how tree-like a graph is and gives a notion of graph decomposition that proves useful in fixed-parameter tractable (FPT) algorithm development. In the directed setting, many similar notions have been proposed - none of which has been accepted widely as a natural generalization of tree-width. Among the many suggested equivalent parameters were the "directed tree-width" by Johnson et al, and DAG-width by Berwanger et al and Odbrzalek. In this talk, I will present a recent paper by Hunter and Kreutzer, that defines another such directed width parameter, celled "kelly-width". I will discuss the equivalent complexity measures for graphs such as elimination orderings, k-trees and cops and robber games and study their natural generalizations to digraphs. I will discuss its usefulness by discussing potential applications including polynomial-time algorithms for NP-complete problems on graphs of bounded Kelly-width (FPT). I will also briefly discuss our work in progress (joint with Shiva Kintali) towards designing an approximation algorithm for Kelly Width.