Derandomized Squaring of Graphs
We introduce a “derandomized” analogue of graph squaring. This operation increases the connectivity of the graph (as measured by the second eigenvalue) almost as well as squaring the graph does, yet only increases the degree of the graph by a constant factor, instead of squaring the degree.
One application of this product is an alternative proof of Reingold’s recent breakthrough result that S-T Connectivity in Undirected Graphs can be solved in deterministic logspace.
KeywordsUndirected Graph Regular Graph Input Graph Edge Label Pseudorandom Generator
Unable to display preview. Download preview PDF.
- [INW]Impagliazzo, R., Nisan, N., Wigderson, A.: Pseudorandomness for Network Algorithms. In: Proceedings of the Twenty-Sixth Annual ACM Symposium on the Theory of Computing, Montréal, Québec, Canada, May 23-25, pp. 356–364 (1994)Google Scholar
- [Mih]Mihail, M.: Conductance and convergence of markov chains: a combinatorial treatment of expanders. In: Proc. of the 37th Conf. on Foundations of Computer Science, pp. 526–531 (1989)Google Scholar
- [RTV]Reingold, Trevisan, and Vadhan. Pseudorandom Walks in Biregular Graphs and the RL vs. L Problem. In: ECCCTR: Electronic Colloquium on Computational Complexity, technical reports (2005)Google Scholar
- [RTV]Reingold, O., Trevisan, L., Vadhan, S.: Pseudorandom Walks in Biregular Graphs and the RL vs. L Problem. Electronic Colloquium on Computational Complexity Technical Report TR05-022 (February 2005), http://www.eccc.uni-trier.de/eccc