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

Date and Time: Tuesday, April 18, 2023, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Nicolas El Maalouly

Equivalency Classes of Certain Constrained Matching Problems

In the Exact Matching problem, we are given a graph with edges colored red and blue, and an integer k. 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 study of EM resulted in the definition of several new matching problems. In this talk I will introduce some of these problems and show how they are related.

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