Gabow’s O( √ nm) General Matching Algorithm Background, Implementation, Engineering, Experiments - Kurt Mehlhorn (Max Planck)

Title: Gabow’s O( √ nm) General Matching Algorithm Background, Implementation, Engineering, Experiments - Kurt Mehlhorn (Max Planck)

Speaker: Kurt Mehlhorn (Director Emeritus of the Max Planck Institute for Informatics, The Max Planck Society for the Advancement of Science, Germany and Senior Professor of Computer Science at Saarland University, Germany) 

Abstract: A matching M in a undirected graph G is a subset of the edges such that no two edges in M share an endpoint. Algorithms for computing maximum cardinality matchings were studied since the infancy of combinatorial computing. For bipartite graphs, an O( √ nm) algorithm was found in the ’70, and near-linear time algorithms in the last decade. The former algorithm is discussed in several textbooks. For general graphs, the problem seems harder, and algorithms with time O( √ nm) were obtained later (Micali/Vazirani ’80, Vazirani ’94, ’12, ’20, ’24, Goldberg/Karzanov ’04, Gabow/Tarjan ’91, Gabow ’17), required several refinements, and are not discussed in textbooks yet. We discuss an implementation of Gabow’s algorithm, heuristic refinements of the algorithm, and experimentation with the algorithm. The talk is based on joint work with Martin Ansaripour and Alireza Danaei.

Short bio: Kurt Mehlhorn is Director Emeritus of the MPI for Informatics and Senior Professor of Computer Science at Saarland University. He headed the algorithms and complexity group at the MPI for Informatics. He co-authored some 300 publications in the field, published six books, and is one of the people behind the LEDA software library. Recently, he produced a series of video lectures ``Ideas and Concepts of Computer Science’’ (in German) for a general audience. He supervised more than 90 students, many of whom have now faculty positions. He has received several prizes (Leibniz Award, EATCS Award, Zuse Medal, ACM Paris Kanellakis Theory and Practice Award, Erasmus Medal of the Academia Europaea) for his work. He holds Honorary Doctorate Degrees from Magdeburg, Aalto, Waterloo, Aarhus, Gothenburg and Patras universities and is an ACM Fellow. He is a member of the German Academy of Sciences Leopoldina, Academia Europaea, the German Academy of Science and Engineering acatech, the US Academy of Engineering, the Indian Academy of Engineering, and the US Academy of Science. From 2002 to 2008, he was vice president of the Max Planck Society. He is a co-founder of Algorithmic Solutions Software GmbH. He currently serves on the Research Advisory Board of Tata Consultancy, and the advisory board of Carnegie Mellon, Qatar.