On the complexity of H-coloring
Journal of Combinatorial Theory Series B
Approximating treewidth, pathwidth, frontsize, and shortest elimination tree
Journal of Algorithms
The hardest constraint problems: a double phase transition
Artificial Intelligence
Easy problems are sometimes hard
Artificial Intelligence
Phase transitions and the search problem
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
Simple Markov-chain algorithms for generating bipartite graphs and tournaments
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Random regular graphs of high degree
Random Structures & Algorithms
A High Girth Graph Construction
SIAM Journal on Discrete Mathematics
A spectral lower bound for the treewidth of a graph and its consequences
Information Processing Letters
The Complexity of Homomorphism and Constraint Satisfaction Problems Seen from the Other Side
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Generating Random Regular Graphs Quickly
Combinatorics, Probability and Computing
Journal of Combinatorial Theory Series B
On the Laplacian Eigenvalues of Gn,p
Combinatorics, Probability and Computing
Sparse constraint graphs and exceptionally hard problems
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Balance and filtering in structured satisfiable problems
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
The structure of tractable constraint satisfaction problems
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
From High Girth Graphs to Hard Instances
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Generating highly balanced sudoku problems as hard problems
Journal of Heuristics
Large hinge width on sparse random hypergraphs
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
| Hi-index | 0.00 |
Tractable cases of the binary CSP are mainly divided in two classes: constraint language restrictions and constraint graph restrictions. To better understand and identify the hardest binary CSPs, in this work we propose methods to increase their hardness by increasing the balance of both the constraint language and the constraint graph. The balance of a constraint is increased by maximizing the number of domain elements with the same number of occurrences. The balance of the graph is defined using the classical definition from graph theory. In this sense we present two graph models; a first graph model that increases the balance of a graph maximizing the number of vertices with the same degree, and a second one that additionally increases the girth of the graph, because a high girth implies a high treewidth, an important parameter for binary CSPs hardness. Our results show that our more balanced graph models and constraints result in harder instances when compared to typicaI random binary CSP instances, by several orders of magnitude. Also we detect, at least for sparse constraint graphs, a higher treewidth for our graph models.