2019-01-17 | Thatchaphol Saranurak:Dynamic Spanning Forest: Techniques and Connections to Other Fields

2019-01-17   


Abstract

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].

 

Time

117日(周四)14:00-15:00

 

Speaker

Thatchaphol Saranurak is a research assistant professor at Toyota Technological Institute at Chicago. He currently works on two topics in theoretical computer science.

 i).Barriers in dynamic graph problems: some dynamic graph problems have resisted many attempts to improve their running time for decades. He investigates those barriers and try to either break them or prove a (conditional) lower bound explaining why it is hard to improve.

 ii).Optimal self-adjusting binary search tree algorithms: a famous 30-year-old conjecture called "dynamic optimality conjecture" states that splay tree is an optimal binary search tree algorithm. By formulating related easier questions, solving them, and making connections to many related areas in combinatorics, he is trying to make progress in proving this conjecture.

 

Venue

信息管理与工程学院602

上海财经大学(第三教学楼西侧)

上海市杨浦区武东路100