Theory Seminar

Dynamic Spanning Forest: Techniques and Connections to Other Fields

Thatchophol Saranurak

Research Asst. Professor
Friday, November 16, 2018
10:30am - 11:30am
BBB 3725

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About the Event

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 STOCྏ, Eppstein, Galil, Italiano and Nissenzweig FOCS྘] (which is slightly improved by a O(\sqrt{\log(n)}) factor by [Kejlberg-Rasmussen, Kopelowitz, Pettie, Thorup ESAཌ]) and (ii) the polylogarithmic bound of [Kapron, King and Mountjoy SODAཉ] which works under an oblivious adversary assumption (our result does not make such an 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, FOCSཌྷ], [Nanongkai and Saranurak, STOCཌྷ] and [Wulff-Nilsen, STOCཌྷ].

Additional Information

Sponsor(s): Theory Group

Faculty Sponsor: Seth Pettie

Open to: Public

Web Page: https://sites.google.com/site/thsaranurak/home