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Theory Seminar: On Parameterized Analysis and the Disjoint Paths Problem
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Meirav Zehavi (Ben-Gurion University)
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Wednesday, 17.11.2021, 12:30
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Taub 201 Taub Bld.
Parameterized Analysis leads both to a deeper understanding of intractability results and to practical solutions for many NP-hard problems. Informally speaking, Parameterized Analysis is a mathematical paradigm to answer the following fundamental question: What makes an NP-hard problem hard? Specifically, how do different parameters (being formal quantifications of structure) of an NP-hard problem relate to its inherent difficulty? Can we exploit these relations algorithmically, and to what extent? Over the past three decades, Parameterized Analysis has grown to be a mature field of outstandingly broad scope with significant impact from both theoretical and practical perspectives on computation. In this talk, I will first give a brief introduction to the field of Parameterized Analysis. Additionally, I will zoom in to a specific result, namely, the first single-exponential time parameterized algorithm for the Disjoint Paths problem on planar graphs. An efficient algorithm for the Disjoint Paths problem in general, and on “almost planar” graphs in particular, is a critical part in the quest for the establishment of an Efficient Graph Minors Theory. As the Graph Minors Theory is the origin of Parameterized Analysis and is ubiquitous in the design of parameterized algorithms, making this theory efficient is a holy grail in the field.
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