CATS-Apr-12-2013
Title[edit]
The Combinatorics of Hidden Diversity
Speaker[edit]
David Johnson is Head of the Algorithms and Optimization Department at AT&T Labs-Research in Florham Park, NJ, and has been a researcher at the Labs (in its many incarnations) since 1973, when he received his PhD from MIT. He is perhaps best known as the co-author of COMPUTERS AND INTRACTABILITY: A GUIDE TO THE THEORY OF NP-COMPLETENESS, for which he and his co-author M. R. Garey won the INFORMS Lanchester Prize. His research interests include approximation algorithms for combinatorial problems, a subject on which he had several of the first key papers, starting with his PhD thesis on the infamous "bin packing" problem. In recent years he has become a leader in the experimental analysis of algorithms, and has been the creator and lead organizer for the series of DIMACS Implementation Challenges, covering topics from Network Flows to the Traveling Salesman Problem. He also founded the ACM-SIAM Symposium on Discrete Algorithms (SODA), and served as its Steering Committee Chair for its first 23 years. He is an ACM Fellow, a SIAM Fellow, an AT&T Fellow, and the winner of the 2010 Knuth Prize for outstanding contributions to the foundations of computer science.
Abstract[edit]
Suppose we are given n buckets with varying integral sizes, and wish to fill some fraction alpha of them will balls, with a bucket of size k being filled as soon as it receives k balls. Our goal is to minimize the number of balls used.
If we know the sizes of the buckets, this is a trivial problem: Just identify the (alpha)n smallest buckets, and fill them. But what if we do not know the sizes of the buckets in advance, and after each ball placement only find out whether the bucket is now full or not?
This problem models a cryptographic question. Suppose an adversary wishes to prevent a multiparty protocol from succeeding. Typically with such protocols, the adversary need only corrupt half (or a third) of the parties to attain its goal. But suppose each party is protected by a sequence of some number of cryptographic walls, each of which requires a certain amount of computation to break through. If parties have differing numbers of walls, and the adversary does not know how many walls a given party has until it breaks through the last one, we get our balls-and-buckets problem.
This cryptographic connection is formalized in a paper I've written with Juan Garay, Aggelos Kiayis, and Moti Yung. Here I will concentrate on the combinatorial side, giving algorithms for the adversary (bucket filler) in the presence various levels of partial information about the sizes, and near-matching lower bounds on what is possible, both for deterministic and randomized algorithms. I also address the question of how a system-designer can best spend his security dollars (in wall building) in the hidden diversity setting.
