scholarly journals Constant delay traversal of grammar-compressed graphs with bounded rank

2020 ◽  
Vol 273 ◽  
pp. 104520
Author(s):  
Sebastian Maneth ◽  
Fabian Peternek
Keyword(s):  
Constant Delay ◽  
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.

NUMERICAL BIFURCATION ANALYSIS OF DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

2001 ◽  
Vol 11 (03) ◽  
pp. 737-753 ◽  
Author(s):  
TATYANA LUZYANINA ◽  
KOEN ENGELBORGHS ◽  
DIRK ROOSE
Keyword(s):  
Differential Equations ◽  
Bifurcation Analysis ◽  
Delay Differential Equations ◽  
Constant Delay ◽  
State Dependent ◽  
State Dependent Delay ◽  
Numerical Bifurcation ◽  
Delay Differential ◽  
Steady State Solutions ◽  
Numerical Bifurcation Analysis

In this paper we apply existing numerical methods for bifurcation analysis of delay differential equations with constant delay to equations with state-dependent delay. In particular, we study the computation, continuation and stability analysis of steady state solutions and periodic solutions. We collect the relevant theory and describe open theoretical problems in the context of bifurcation analysis. We present computational results for two examples and compare with analytical results whenever possible.

Periodic Solutions for a Class of Functional Differential Equations with State-Dependent Delay Close to Zero

2003 ◽  
Vol 13 (06) ◽  
pp. 807-841 ◽  
Author(s):  
R. Ouifki ◽  
M. L. Hbid
Keyword(s):  
Differential Equation ◽  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Delay Equation ◽  
Constant Delay ◽  
State Dependent ◽  
State Dependent Delay ◽  
Existence Of Periodic Solutions ◽  
Functional Differential

The purpose of the paper is to prove the existence of periodic solutions for a functional differential equation with state-dependent delay, of the type [Formula: see text] Transforming this equation into a perturbed constant delay equation and using the Hopf bifurcation result and the Poincaré procedure for this last equation, we prove the existence of a branch of periodic solutions for the state-dependent delay equation, bifurcating from r ≡ 0.

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
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