How to construct random functions
Journal of the ACM (JACM)
How to construct pseudorandom permutations from pseudorandom functions
SIAM Journal on Computing - Special issue on cryptography
Property testing in bounded degree graphs
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Fast, small-space algorithms for approximate histogram maintenance
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On the Implementation of Huge Random Objects
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Implementing Huge Sparse Random Graphs
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Derandomized constructions of k-wise (almost) independent permutations
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Efficiently constructible huge graphs that preserve first order properties of random graphs
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Implementing Huge Sparse Random Graphs
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
On the Implementation of Huge Random Objects
SIAM Journal on Computing
| Hi-index | 0.00 |
Consider a scenario where one desires to simulate the execution of some graph algorithm on huge random G(N,p) graphs, where N= 2nvertices are fixed and each edge independently appears with probability p= pn. Sampling and storing these graphs is infeasible, yet Goldreich et al. [7], and Naor et al. [12] considered emulating dense G(N,p) graphs by efficiently computable `random looking' graphs. We emulate sparseG(N,p) graphs - including the densities of the G(N,p) threshold for containing a giant component (p~1 / N), and for achieving connectivity (p茂戮驴 ~ln N/ N). The reasonable model for accessing sparse graphs is neighborhood queries where on query-vertex v, the entire neighbor-set Γ(v) is efficiently retrieved (without sequentially deciding adjacency for each vertex). Our emulation is faithful in the sense that our graphs are indistinguishable from G(N,p) graphs from the view of any efficient algorithm that inspects the graph by neighborhood queries of its choice. In particular, the G(N,p) degree sequence is sufficiently well approximated.