Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Thursday, October 27, 2022, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Saeed Ilchi

Deterministic Distributed Sparse and Ultra-Sparse Spanners and Connectivity Certificates

We present efficient distributed algorithms for a number of fundamental problems in the area of graph sparsification: We provide the first deterministic distributed algorithm that computes an ultra-sparse spanner in polylog(n) rounds in weighted graphs. Concretely, our algorithm outputs a spanning subgraph with only n+o(n) edges in which the pairwise distances are stretched by a factor of at most O(log n⋅2O(log∗n)).

We provide a polylog(n)-round deterministic distributed algorithm that computes a spanner with stretch (2k−1) and O(nk+n1+1/klog k) edges in unweighted graphs and with O(n1+1/kk) edges in weighted graphs.

We present the first polylog(n)-round randomized distributed algorithm that computes a sparse connectivity certificate. For an n-node graph G, a certificate for connectivity k is a spanning subgraph H that is k-edge-connected if and only if G is k-edge-connected, and this subgraph H is called sparse if it has O(nk) edges. Our algorithm achieves a sparsity of (1+o(1))nk edges, which is within a 2(1+o(1)) factor of the best possible.

This talk is based on a joint work with Marcel Bezdrighin, Michael Elkin, Mohsen Ghaffari, Christoph Grunau, Bernhard Haeupler, and Václav Rozhoň:
https://arxiv.org/abs/2204.14086


Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2024  2023  2022  2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks


Automatic MiSe System Software Version 1.4803M   |   admin login