Online algorithms and other conceptually simple algorithms
Abstract:What can and cannot be computed by “conceptually simple algorithms”? In this regard, my primary interest is on approximation algorithms for combinatorial optimization problems and the relation of such problems to areas such as algorithmic game theory and computational social choice. Why do we care about conceptual simplicity and can we formalize such a concept? For some problems, simple algorithmic ideas provide the best known solution or are reasonably competitive with the best known algorithms. Moreover, “in practice”, it is often the case that users will opt for a quick understandable algorithm. While it is arguably impossible to precisely define a useful general definition of “simplicity”, we can study well used (albeit rarely precisely defined) combinatorial algorithmic paradigms such as various forms and extensions of online and greedy algorithms, primal dual algorithms, and “simple” dynamic programming. We can provide definitions for such paradigms that are sufficiently expressive so as to capture many or most existing algorithms, but still allow us to prove impossibiity results that do not rely on computational complexity assumptions. More generally, in addition to competitive and approximation ratios for online and greedy algorithms, we are led to what might be called the price of simplicity for different objectives such as fairness or distortion in social choice applications.
Short Bio:Allan Borodin is a University Professor at the University of Toronto in the Department of Computer Science. He joined the University of Toronto in 1969 and was the chair of the Department 1980-1985. His research areas include computational complexity and algorithm analysis and design.
He has been a visiting professor at Cornell, ETH-Zurich, University of Nice, Hebrew University, and the Weizmann Institute. He is a Fellow of the Royal Society of Canada, an ACM Fellow and a Member, Order of Canada.