SIAM Journal on Algebraic and Discrete Methods
Combinatorica
Deterministic simulation in LOGSPACE
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Better expanders and superconcentrators
Journal of Algorithms
Expanders obtained from affine transformations
Combinatorica - Theory of Computing
Explicit construction of linear sized tolerant networks
Discrete Mathematics - First Japan Conference on Graph Theory and Applications
Sorting in c log n parallel steps
Combinatorica
An O(logN) deterministic packet routing scheme
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
On-line algorithms for path selection in a nonblocking network
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Better expansion for Ramanujan graphs
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
SIAM Journal on Computing
On the second eigenvalue of a graph
Discrete Mathematics
Self-routing superconcentrators
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Expander graphs
Near-perfect Token Distribution
ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
Improved routing and sorting on multibutterflies
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Loss-less condensers, unbalanced expanders, and extractors
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Randomness conductors and constant-degree lossless expanders
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Local majorities, coalitions and monopolies in graphs: a review
Theoretical Computer Science
Load balancing of unit size tokens and expansion properties of graphs
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
A Randomness-Efficient Sampler for Matrix-valued Functions and Applications
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Linear degree extractors and the inapproximability of max clique and chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Slow emergence of cooperation for win-stay lose-shift on trees
Machine Learning
On the Expansion of the Giant Component in Percolated (n, d,λ) Graphs
Combinatorics, Probability and Computing
A combinatorial construction of almost-ramanujan graphs using the zig-zag product
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
From High Girth Graphs to Hard Instances
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Unbalanced expanders and randomness extractors from Parvaresh--Vardy codes
Journal of the ACM (JACM)
Pseudo-random graphs and bit probe schemes with one-sided error
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
An introduction to randomness extractors
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
A sample of samplers: a computational perspective on sampling
Studies in complexity and cryptography
Basic facts about expander graphs
Studies in complexity and cryptography
A Combinatorial Construction of Almost-Ramanujan Graphs Using the Zig-Zag Product
SIAM Journal on Computing
Randomised broadcasting: memory vs. randomness
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Tight bounds on computing error-correcting codes by bounded-depth circuits with arbitrary gates
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Randomised broadcasting: Memory vs. randomness
Theoretical Computer Science
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The spectral method is the best currently known technique to prove lower bounds on expansion. Ramanujan graphs, which have asymptotically optimal second eigenvalue, are the best-known explicit expanders. The spectral method yielded a lower bound of k/4 on the expansion of linear-sized subsets of k-regular Ramanujan graphs. We improve the lower bound on the expansion of Ramanujan graphs to approximately k/2. Moreover, we construct a family of k-regular graphs with asymptotically optimal second eigenvalue and linear expansion equal to k/2. This shows that k/2 is the best bound one can obtain using the second eigenvalue method. We also show an upper bound of roughly 1+k-1 on the average degree of linear-sized induced subgraphs of Ramanujan graphs. This compares positively with the classical bound 2k-1 . As a byproduct, we obtain improved results on random walks on expanders and construct selection networks (respectively, extrovert graphs) of smaller size (respectively, degree) than was previously known.