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: Tuesday, September 26, 2023, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Nicolas El Maalouly

Top-k Perfect Matching: Motivation and LP Relaxation

In the Top-k Perfect Matching (TkPM) we are given a weighted graph and an integer k and the goal is to output a perfect matching that maximizes the top-k weight function (the top-k weight function is the sum of the k highest weights in a given set of edges). Such an objective function has been studied for problems like k-Clustering and load balancing but not yet for matching problems. The main motivation to study this problem however, is that it relates to the Exact Matching problem. Here we are given a graph with edges colored red and blue, and an integer k and the goal is to output a perfect matching with exactly k red edges. After introducing the problem in 1982, Papadimitriou and Yannakakis conjectured it to be NP-hard. Soon after however, Mulmuley et al. proved in 1987 that it can be solved in randomized polynomial time, which makes it unlikely to be NP-hard. Determining whether Exact Matching is in P remains an open problem and very little progress has been made towards that goal. The hope is that by studying Top-k perfect matching we can gain more insight into Exact Matching. The main focus of this talk will be the LP relaxation of the problem and its properties.

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