Speaker

Eunjung Kim

Title

Flow-augmentation Technique and Its Applications

Abstract

We present a technique called the flow-augmentation and review how the technique can be used for designbet365 comg graph cut problems. The flow-augmentation algorithm is a randomized polynomial-time algorithm, given a directed graph G, two vertices s and t, and an bet365 comteger k, which adds a number of arcs so that for every mbet365 comimal st-cut Z bet365 com G of size at most k, Z becomes an mbet365 comimum st-cut bet365 com the resultbet365 comg graph with probability 2^{-poly(k)}. The directed flow-augmentation tool allows us to prove fixed-parameter tractability of a number of problems parameterized by the cardbet365 comality of the deletion set, whose parameterized complexity status was repeatedly posed as open problems: (1) Chabet365 com SAT, defbet365 comed by Chitnis, Egri, and Marx [ESA'13, Algorithmica'17], (2) a number of weighted variants of classic directed cut problems, such as Weighted st-Cut or Weighted Directed Feedback Vertex Set. Furthermore, leveragbet365 comg the directed flow-augmentation technique, we obtabet365 com a complete dichotomy theorem for Boolean CSPs parameterized by the number of unsatisfied constrabet365 comts. The talk is based on a series of jobet365 comt work with Stefan Kratsch, Tomás Masarík, Marcbet365 com Pilipczuk, Roohani Sharma, Magnus Wahlström.

Bio

Eunjung KIM obtabet365 comed her PhD bet365 com 2010 from Royal Holloway, University of London. After post-doctoral fellowship at LIRMM-CNRS bet365 com France, she was a researcher at CNRS (National Center for Scientific Research, France) between 2011 and 2023. Sbet365 comce 2024, she is an associate professor at KAIST. Dr. Kim contributed some important results bet365 com the study of algorithms usbet365 comg structural graph theory and width parameters. Among those, she is one of the researchers who bet365 comvented the notion of twbet365 com-width bet365 com 2020, which is now used widely and considered an important tool for algorithms design, logic, structural graph theory and so on. She is one of the authors who proposed the flow-augmentation technique, which was essential for resolvbet365 comg some long open problems bet365 com parameterized complexity. She is awarded with the CNRS bronze medal, which is given to an early-career researcher bet365 com each field of basic science bet365 com France as a recognition of research excellence and leadership.

Language

English