Succinct representations of graphs
Information and Control
Almost optimal lower bounds for small depth circuits
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
On the complexity of the parity argument and other inefficient proofs of existence
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
Interactive proofs and the hardness of approximating cliques
Journal of the ACM (JACM)
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Randomness conductors and constant-degree lossless expanders
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Fast Monte-Carlo Algorithms for finding low-rank approximations
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Entropy waves, the zig-zag graph product, and new constant-degree expanders and extractors
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Random sampling and approximation of MAX-CSPs
Journal of Computer and System Sciences - STOC 2002
A combinatorial characterization of the testable graph properties: it's all about regularity
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
On Approximate Majority and Probabilistic Time
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
An elementary construction of constant-degree expanders
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Every minor-closed property of sparse graphs is testable
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Computational Complexity: A Modern Approach
Computational Complexity: A Modern Approach
Random dot product graph models for social networks
WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
Extractors and Lower Bounds for Locally Samplable Sources
ACM Transactions on Computation Theory (TOCT)
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We propose the study of graphs that are defined by low-complexity distributed and deterministic agents. We suggest that this viewpoint may help introduce the element of individual choice in models of large scale social networks. This viewpoint may also provide interesting new classes of graphs for which to design algorithms. We focus largely on the case where the "low complexity" computation is AC 0. We show that this is already a rich class of graphs that includes examples of lossless expanders and power-law graphs. We give evidence that even such low complexity graphs present a formidable challenge to algorithms designers. On the positive side, we show that many algorithms from property testing and data sketching can be adapted to give meaningful results for low-complexity graphs.