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What and Who
Title:Fine-Grained Complexity of Exists^k-Forall-Quantified First-Order Graph Properties: Optimization and Approximability (Master Thesis)
Speaker:Alejandro Cassis
coming from:Fachrichtung Informatik - Saarbrücken
Speakers Bio:
Event Type:AG1 Mittagsseminar (own work)
Visibility:D1
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Level:AG Audience
Language:English
Date, Time and Location
Date:Tuesday, 25 February 2020
Time:13:00
Duration:30 Minutes
Location:Saarbrücken
Building:E1 4
Room:024
Abstract
The model-checking problem of first-order properties over relational structures constitutes one of the largest natural classes of problems for which we have a fine-grained characterization of its hardness. In particular, consider a first-order property psi defined by k existential quantifiers followed by a universal one (Exists^k Forall), and a graph G on m edges. For the problem of model checking psi over G, Bringmann, Fischer and Künnemann [CCC 19'] gave a dichotomy: they either give a polynomial-time improvement over the O(m^k)-baseline algorithm, or show that it requires time m^{k - o(1)} assuming the MAX3SAT hypothesis.

In this work we consider a natural optimization variant: instead of asking for k vertices which make the predicate true for all vertices y, we ask for the k vertices which maximize or minimize the number of y's which satisfy the predicate. In the same spirit, we give a dichotomy characterizing the hardness of all such predicates. Moreover, we extend the results to a characterization of predicates that admit a constant factor approximation.

Contact
Name(s):Karl Bringmann
Video Broadcast
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Attachments, File(s):
  • Karl Bringmann, 02/04/2020 05:03 PM
  • Karl Bringmann, 02/04/2020 05:03 PM -- Created document.