论文信息 - Erdős-Rényi Sequences and Deterministic Construction of Expanding Cayley Graphs

Erdős-Rényi Sequences and Deterministic Construction of Expanding Cayley Graphs

Given a finite group G by its multiplication table, we give a deterministic polynomial-time construction of a directed O(log|G|) degree Cayley expander for G. Our construction exploits the connection between rapid mixing random walks and spectral expansion. Our main group-theoretic tool is Erdős-Renyi sequences. We give a similar construction of O(log|G|) degree undirected Cayley expanders for G, which is an alternative proof of Wigderson and Xiao's derandomization [WX08] of the Alon-Roichman randomized construction.

Vikraman Arvind | Partha Mukhopadhyay | Prajakta Nimbhorkar

[1] Omer Reingold,et al. Undirected connectivity in log-space , 2008, JACM.

[2] Satyen Kale. Efficient algorithms using the multiplicative weights update method , 2007 .

[3] Jaroslav Nešetřil. Algorithms - ESA’ 99 , 2003, Lecture Notes in Computer Science.

[4] M. Murty. Ramanujan Graphs , 1965 .

[5] Avi Wigderson,et al. Derandomizing the Ahlswede-Winter matrix-valued Chernoff bound using pessimistic estimators, and applications , 2008, Theory Comput..

[6] A. Rényi,et al. Probabilistic methods in group theory , 1965 .

[7] Martin Hildebrand. A survey of results on random random walks on finite groups , 2004 .

[8] Noga Alon,et al. Random Cayley Graphs and Expanders , 1994, Random Struct. Algorithms.

[9] Anastasios Zouzias,et al. A Matrix Hyperbolic Cosine Algorithm and Applications , 2011, ICALP.

[10] Igor Pak,et al. Random Cayley Graphs with O(log[G]) Generators Are Expanders , 1999, ESA.

[11] Ravi Montenegro,et al. Mathematical Aspects of Mixing Times in Markov Chains , 2006, Found. Trends Theor. Comput. Sci..

[12] Dana Randall,et al. Rapidly mixing Markov chains with applications in computer science and physics , 2006, Computing in Science & Engineering.

[13] N. Linial,et al. Expander Graphs and their Applications , 2006 .