[Colloquium] Theoretical Seminar Today

[Donna Brooms via Colloquium]

The University of Chicago

Department of Computer Science & Mathematics

Combinatorics & Theoretical Seminar

Thatchaphol Saranurak (TTIC)

Tuesday, November 20, 2018

Ry. 251 @ 3:30 pm

Title: “Dynamic Spanning Forest: Techniques and Connections to Other Fields”

Abstract: I will talk about 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], [Wulff-Nilsen, STOC'17], and [Saranurak and Wang SODA'19].






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