scholarly journals Better Algorithms for Satisfiability Problems for Formulas of Bounded Rank-width

2013 ◽  
Vol 123 (1) ◽  
pp. 59-76 ◽  
Author(s):  
Robert Ganian ◽  
Petr Hliněný ◽  
Jan Obdržálek
Keyword(s):  
Satisfiability Problems ◽  
Bounded Rank

scholarly journals Isomorphism, canonization, and definability for graphs of bounded rank width

2021 ◽  
Vol 64 (5) ◽  
pp. 98-105
Author(s):  
Martin Grohe ◽  
Daniel Neuen
Keyword(s):  
Fixed Point ◽  
Complexity Theory ◽  
Polynomial Time ◽  
Graph Isomorphism ◽  
Isomorphism Problem ◽  
Descriptive Complexity ◽  
Graph Isomorphism Problem ◽  
Structural Graph ◽  
Graph Classes ◽  
Bounded Rank

We investigate the interplay between the graph isomorphism problem, logical definability, and structural graph theory on a rich family of dense graph classes: graph classes of bounded rank width. We prove that the combinatorial Weisfeiler-Leman algorithm of dimension (3 k + 4) is a complete isomorphism test for the class of all graphs of rank width at most k. A consequence of our result is the first polynomial time canonization algorithm for graphs of bounded rank width. Our second main result addresses an open problem in descriptive complexity theory: we show that fixed-point logic with counting expresses precisely the polynomial time properties of graphs of bounded rank width.

scholarly journals On the Performance of Congestion Games for Optimum Satisfiability Problems

2007 ◽  
pp. 220-231 ◽  
Author(s):  
Aristotelis Giannakos ◽  
Laurent Gourvès ◽  
Jérôme Monnot ◽  
Vangelis Th. Paschos
Keyword(s):  
Congestion Games ◽  
Satisfiability Problems
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