Continuous Optimization: The “Right” Language for Graph Algorithms? (Invited Talk)

Abstract

Traditionally, we view graphs as purely combinatorial objects and tend to design our graph algorithms to be combinatorial as well. In fact, in the context of algorithms, "combinatorial" became a synonym of "fast".

Recent work, however, shows that a number of such "inherently combinatorial" graph problems can be solved much faster using methods that are very "non-combinatorial". Specifically, by approaching these problems with tools and notions borrowed from linear algebra and, more broadly, from continuous optimization. A notable examples here are the recent lines of work on the maximum flow problem, the bipartite matching problem, and the shortest path problem in graphs with negative-length arcs. 

This raises an intriguing question: Is continuous optimization a more suitable and principled optics for fast graph algorithms than the classic combinatorial view? In this talk, I will discuss this question as well as the developments that motivated it.