A fast parallel algorithm for the maximal independent set problem
Journal of the ACM (JACM)
A fast and simple randomized parallel algorithm for the maximal independent set problem
Journal of Algorithms
A simple parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
On the complexity of H-coloring
Journal of Combinatorial Theory Series B
Simulating (logcn)-wise independence in NC
Journal of the ACM (JACM)
Sample spaces uniform on neighborhoods
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Small-bias probability spaces: efficient constructions and applications
SIAM Journal on Computing
Removing randomness in parallel computation without a processor penalty
Journal of Computer and System Sciences
Constructing Small Sample Spaces Satisfying Given Constants
SIAM Journal on Discrete Mathematics
The probabilistic method yields deterministic parallel algorithms
Proceedings of the 30th IEEE symposium on Foundations of computer science
Randomized graph products, chromatic numbers, and Lovasz j-function
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Approximate graph coloring by semidefinite programming
Journal of the ACM (JACM)
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Almost k-wise independence versus k-wise independence
Information Processing Letters
Pairwise independence and derandomization
Foundations and Trends® in Theoretical Computer Science
Index Coding with Side Information
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Testing k-wise and almost k-wise independence
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Approximation Algorithms Using Hierarchies of Semidefinite Programming Relaxations
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
The bit extraction problem or t-resilient functions
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Simple construction of almost k-wise independent random variables
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
A constructive proof of the Lovász local lemma
Proceedings of the forty-first annual ACM symposium on Theory of computing
Conditional Hardness for Approximate Coloring
SIAM Journal on Computing
Testing non-uniform k-wise independent distributions over product spaces
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
On the conditional hardness of coloring a 4-colorable graph with super-constant number of colors
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
A parallel algorithmic version of the local lemma
Random Structures & Algorithms
On the Shannon capacity of a graph
IEEE Transactions on Information Theory
On Some Problems of Lovász Concerning the Shannon Capacity of a Graph
IEEE Transactions on Information Theory
Combinatorial Coloring of 3-Colorable Graphs
FOCS '12 Proceedings of the 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
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For a hypergraph H on the vertex set {1,...,n}, a distribution D = (D_1,...,D_n) over {0,1}^n is H-wise independent if every restriction of D to indices which form an edge in H is uniform. This generalizes the notion of k-wise independence obtained by taking H to be the complete n vertex k-uniform hypergraph. This generalization was studied by Schulman (STOC 1992), who presented constructions of H-wise independent distributions that are linear, i.e., the samples are strings of inner products (over F2) of a fixed set of vectors with a uniformly chosen random vector. Let l(H) denote the minimum possible size of a sample space of a uniform H-wise independent distribution. The l parameter is well understood for the special case of k-wise independence. In this work we study the notion of H-wise independence and the l parameter for general graphs and hypergraphs. For graphs, we show how the l parameter relates to standard graph parameters (e.g., clique number, chromatic number, Lovasz theta function, minrank). We derive algorithmic and hardness results for this parameter as well as an explicit construction of graphs G for which l(G) is exponentially smaller than the size of the sample space of any linear G-wise independent distribution. For hypergraphs, we study the problem of testing whether a given distribution is H-wise independent, generalizing results of Alon et al. (STOC 2007).