Special Section On The Forty-Second Annual Acm Symposium On Theory Of Computing (Stoc 2010)

This issue of SICOMP contains eight selected papers from the Forty-Second Annual ACM Symposium on Theory of Computing (STOC 2010), held June 6--8, 2010, in Cambridge, Massachusetts. The STOC proceedings contained 78 papers, which the program committee selected from 279 submissions. The program committee consisted of Timothy Chan, Ken Clarkson, Constantinos Daskalakis, Irit Dinur, Faith Ellen, Alan Frieze, Parikshit Gopalan, Piotr Indyk, Valentine Kabanets, Yael Tauman Kalai, Howard Karloff, Robert Kleinberg, Assaf Naor, Noam Nisan, Chris Peikert, Jaikumar Radhakrishnan, Oded Regev, Alexander Russell, Leonard Schulman (chair), Aravind Srinivasan, Santosh Vempala, and Andrew Yao. Eight of the STOC papers appear in this special section, each expanded and subjected to the standard thorough reviewing process of the journal. They cover a diverse collection of topics: In “Improving Exhaustive Search Implies Superpolynomial Lower Bounds," R. Ryan Williams shows that there are natural problems in NP and BPP for which algorithms that improve over the naïve deterministic simulation even quite slightly, imply lower bounds such as NEXP $\not\in$ P/poly and LOGSPACE $\neq$ NP. Williams also proves certain unconditional time-space lower bounds for improving on exhaustive search; the length of the witness-string in some standard verification protocol is a key parameter here. In “An Effective Dichotomy for the Counting Constraint Satisfaction Problem," Martin Dyer and David Richerby consider the counting constraint satisfaction problem (\#CSP). This problem asks how many ways there are to satisfy a system of constraints on a set of variables, where a constraint is a relation chosen from a fixed finite set. This class is shown to have a decidable dichotomy, depending on the form of the relations. The dichotomy is that each problem in the class either is in FP or is \#P-complete, with no intermediate cases. In “Pseudorandom Generators for Polynomial Threshold Functions," Raghu Meka and David Zuckerman develop improved (and in many cases the first nontrivial) pseudorandom generators for low-degree polynomial threshold functions; related explicit constructions are also developed. A key ingredient is the use of invariance principles to construct pseudorandom generators. In “Local List-Decoding and Testing of Random Linear Codes from High Error," Swastik Kopparty and Shubhangi Saraf give efficient local list-decoding and testing algorithms for “sparse" random linear codes, and subexponential time algorithms for list-decoding random linear codes, which tolerate error rates approaching $1/2$. In “How to Compress Interactive Communication," Boaz Barak, Mark Braverman, Xi Chen, and Anup Rao attack the important direct sum problem in communication complexity: is the complexity of evaluating $n$ copies of a function ever significantly less than $n$ times the complexity of evaluating it once? By defining a new notion of information cost for protocols --- the so-called internal information cost --- and providing new protocol compression schemes, they prove that computing $n$ copies of any function requires communicating at least $\sqrt{n}$ times as many bits as computing one copy of the function. In “A Deterministic Single Exponential Time Algorithm for Most Lattice Problems based on Voronoi Cell Computations," Daniele Micciancio and Panagiotis Voulgaris provide the first $\exp(O(n))$-time algorithms for the closest vector problem (CVP) and shortest independent vectors problem (SIVP); their algorithm is, moreover, deterministic. Likewise they provide a deterministic algorithm for the shortest vector problem (SVP), whose $\exp(O(n))$ runtime is an improvement over the best known bounds for randomized algorithms. In “Perfect Matchings in $O(n \log n)$ Time in Regular Bipartite Graphs," Ashish Goel, Michael Kapralov, and Sanjeev Khanna provide a randomized algorithm that finds a perfect matching in a $d$-regular $n$-node bipartite graph in time $O(n \log n)$, notably, within time that may be sublinear in the input size and is independent of the degree. In “Efficiency Improvements in Constructing Pseudorandom Generators from One-Way Functions," Iftach Haitner, Omer Reingold, and Salil Vadhan give a new construction of pseudorandom generators from one-way functions that both simplifies and tightens the acclaimed original construction of Hastad, Impagliazzo, Levin, and Luby. We thank the authors, the STOC program committee, the STOC external reviewers, and the journal referees for all their work to make this special issue possible.