Special Section On The Forty-Third Annual Acm Symposium On Theory Of Computing (Stoc 2011)

This section of SIAM Journal on Computing contains extended versions of selected papers from the 43rd ACM Symposium on Theory of Computing (STOC), held June 6--8, 2011, in San Jose, California, as part of the fifth Federated Computing Research Conference (FCRC). The STOC proceedings contained 84 papers, which were selected from 304 submissions by the program committee, consisting of Ittai Abraham, Alexandr Andoni, Avrim Blum, Allan Borodin, Kousha Etessami, Lisa Fleischer, Venkatesan Guruswami, David Kempe, Frederic Magniez, Dieter van Melkebeek, Daniele Micciancio, Moni Naor, Kobbi Nissim, Seth Pettie, Ronitt Rubinfeld, Amir Shpilka, Ravi Sundaram, Eva Tardos, Prasad Tetali, Salil Vadhan (chair), Kasturi Varadarajan, Nisheeth Vishnoi, John Watrous, and Ryan Williams. Five of the STOC papers appear in this special section, each one expanded and fully refereed according to the high standards of the journal. They cover a diverse collection of topics: In “Distributed Verification and Hardness of Distributed Approximation,” Das Sarma, Holzer, Kor, Korman, Nanongkai, Pandurangan, Peleg, and Wattenhofer prove strong lower bounds on the power of distributed networks to verify their own properties (such as connectivity) and solve optimization problems such as computing approximate shortest paths or approximate min-cuts. They establish new connections between distributed computation and two-party communication complexity. The paper “Pareto Optimal Solutions for Smoothed Analysts” by Moitra and O'Donnell considers the smoothed complexity of discrete multi-objective optimization problems with $d+1$ linear objectives and with a solution space consisting of binary $n$-vectors. The authors show that, in a suitable smoothed analysis framework for such problems, the expected number of Pareto optimal solutions is at most $n^{2d}$. This improves greatly, as a function of the dimension d, an earlier upper bound established by Roeglin and Teng, which had roughly the form $n^{d^d}$. The paper “Blackbox Identity Testing for Bounded Top-Fanin Depth-3 Circuits: The Field Doesn't Matter” by Saxena and Seshadhri provides the first deterministic polynomial-time identity test for depth-3 arithmetic circuits with bounded top-fanin that only needs blackbox access to the circuit. Their construction has the feature that it works for arbitrary fields. In their paper “An Optimal Lower Bound on the Communication Complexity of Gap-Hamming-Distance,” Chakrabarti and Regev prove a lower bound establishing that the randomized communication complexity of the gap-Hamming-distance problem is linear. In obtaining this result, they have resolved an important and well-studied communication complexity problem having a fundamental connection to the data stream model of computation. Svensson's paper “Santa Claus Schedules Jobs on Unrelated Machines” breaks the barrier of 2 for efficiently approximating the minimum makespan for scheduling jobs on unrelated machines in the setting where all machines on which a given job can run take the same amount of time for that job. We thank the authors, the referees, and the full program committee for all their work, which made this special section possible.