Abstract
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.
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Rozenman, E., Vadhan, S. (2005). Derandomized Squaring of Graphs. In: Chekuri, C., Jansen, K., Rolim, J.D.P., Trevisan, L. (eds) Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2005 2005. Lecture Notes in Computer Science, vol 3624. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11538462_37
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DOI: https://doi.org/10.1007/11538462_37
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