scholarly journals Complexity classification of the six-vertex model

2018 ◽  
Vol 259 ◽  
pp. 130-141 ◽  
Author(s):  
Jin-Yi Cai ◽  
Zhiguo Fu ◽  
Mingji Xia
Keyword(s):  
Vertex Model ◽  
Complexity Classification

Computer-Aided complexity classification of combinational problems

1982 ◽  
Vol 25 (11) ◽  
pp. 817-822 ◽  
Author(s):  
B. J. Lageweg ◽  
J. K. Lenstra ◽  
E. L. Lawler ◽  
A. H. G. Rinnooy Kan
Keyword(s):  
Computer Aided ◽  
Complexity Classification

Complexity classification of the edge coloring problem for a family of graph classes

2017 ◽  
Vol 27 (2) ◽  
Author(s):  
Dmitriy S. Malyshev
Keyword(s):  
Edge Coloring ◽  
Complete Classification ◽  
Chromatic Index ◽  
Forbidden Subgraphs ◽  
Coloring Problem ◽  
Graph Classes ◽  
Complexity Classification ◽  
Index Problem

AbstractA class of graphs is called monotone if it is closed under deletion of vertices and edges. Any such class may be defined in terms of forbidden subgraphs. The chromatic index of a graph is the smallest number of colors required for its edge-coloring such that any two adjacent edges have different colors. We obtain a complete classification of the complexity of the chromatic index problem for all monotone classes defined in terms of forbidden subgraphs having at most 6 edges or at most 7 vertices.

scholarly journals A Compendium of Parameterized Problems at Higher Levels of the Polynomial Hierarchy

Algorithms ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 188 ◽  
Author(s):  
Ronald de Haan ◽  
Stefan Szeider
Keyword(s):  
Polynomial Hierarchy ◽  
Fixed Parameter Tractable ◽  
Fixed Parameter ◽  
Complexity Classification

We present a list of parameterized problems together with a complexity classification of whether they allow a fixed-parameter tractable reduction to SAT or not. These problems are parameterized versions of problems whose complexity lies at the second level of the Polynomial Hierarchy or higher.

TAXONOMY OF THE SIXTEEN-VERTEX MODELS

1992 ◽  
Vol 06 (14) ◽  
pp. 2559-2574 ◽  
Author(s):  
S. BOUKRAA ◽  
J.-M. MAILLARD
Keyword(s):  
Symmetry Group ◽  
Parameter Space ◽  
Vertex Model ◽  
Vertex Models ◽  
Exact Calculations ◽  
Inversion Relations

A classification of the subcases of the sixteen-vertex model compatible with the infinite symmetry group generated by the inversion relations of the model is performed. The elliptic parameterization of these models is recalled, emphasizing the subvarieties of the parameter space for which this parameterization degenerates into a rational one. This situation corresponds to the vanishing of some discriminant and is deeply related to the critical and disorder manifolds for these models. We concentrate on subcases of the sixteen-vertex model for which factorizations of this discriminant occur, allowing further exact calculations.

A Complete 4-parametric complexity classification of short shop scheduling problems

2011 ◽  
Vol 15 (4) ◽  
pp. 427-446 ◽  
Author(s):  
Alexander Kononov ◽  
Sergey Sevastyanov ◽  
Maxim Sviridenko
Keyword(s):  
Scheduling Problems ◽  
Shop Scheduling ◽  
Complexity Classification

scholarly journals A complexity classification of spin systems with an external field

2015 ◽  
Vol 112 (43) ◽  
pp. 13161-13166 ◽  
Author(s):  
Leslie Ann Goldberg ◽  
Mark Jerrum
Keyword(s):  
Ising Model ◽  
External Field ◽  
Spin System ◽  
Spin Systems ◽  
Ferromagnetic Ising Model ◽  
Complexity Classification ◽  
Antiferromagnetic Ising Model ◽  
Computational Difficulty ◽  
State Spin

We study the computational complexity of approximating the partition function of a q-state spin system with an external field. There are just three possible levels of computational difficulty, depending on the interaction strengths between adjacent spins: (i) efficiently exactly computable, (ii) equivalent to the ferromagnetic Ising model, and (iii) equivalent to the antiferromagnetic Ising model. Thus, every nontrivial q-state spin system, irrespective of the number q of spins, is computationally equivalent to one of two fundamental two-state spin systems.

scholarly journals Computer-Aided Complexity Classification of Dial-a-Ride Problems

2004 ◽  
Vol 16 (2) ◽  
pp. 120-132 ◽  
Author(s):  
Willem E. de Paepe ◽  
Jan Karel Lenstra ◽  
Jiri Sgall ◽  
René A. Sitters ◽  
Leen Stougie
Keyword(s):  
Computer Aided ◽  
Complexity Classification
Sign in / Sign up

Export Citation Format

Share Document