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[theory-seminar] Theory Seminar Today
Shashwat Silas
silas at stanford.edu
Thu Oct 12 11:52:59 PDT 2017
Hi all,
Just a reminder that theory seminar will happen today at 415pm at Gates 463A. Hope to see you all there!
Thatchaphol Saranurak (KTH)
Dynamic Spanning Forest: Techniques and Connections to Other Fields
I will first give an overview of dynamic algorithms and their connections to other fields. Then, I will present our recent progress on the question "is there a dynamic algorithm with small worst-case update time" for the spanning forest problem, which is among central problems in dynamic algorithms on graphs. Our result guarantees an n^{o(1)} worst-case update time with high probability, where n is the number of nodes. The best worst-case bounds prior to our work are (i) the long-standing O(\sqrt{n}) bound of [Frederickson STOC'83, Eppstein, Galil, Italiano and Nissenzweig FOCS'92] (which is slightly improved by a O(\sqrt{\log(n)}) factor by [Kejlberg-Rasmussen, Kopelowitz, Pettie, Thorup ESA'16]) and (ii) the polylogarithmic bound of [Kapron, King and Mountjoy SODA'13] which works under an oblivious adversary assumption (our result does not make such assumption).
The crucial techniques are about expanders: 1) an algorithm for decomposing a graph into a collection of expanders in near-linear time, and 2) an algorithm for "repairing" the expansion property of an expander after deleting some edges of it. These techniques can be of independent interest.
This talk is based on results by [Nanongkai, Saranurak and Wulff-Nilsen, FOCS'17], [Nanongkai and Saranurak, STOC'17] and [Wulff-Nilsen, STOC'17].
Thanks,
Shashwat
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