Tail bounds for occupancy and the satisfiability threshold conjecture
Random Structures & Algorithms
New methods to color the vertices of a graph
Communications of the ACM
The scaling window of the 2-SAT transition
Random Structures & Algorithms
Frozen development in graph coloring
Theoretical Computer Science - Phase transitions in combinatorial problems
Generating Satisfiable Problem Instances
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Backbone fragility and the local search cost peak
Journal of Artificial Intelligence Research
From approximate to optimal solutions: a case study of number partitioning
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Linear time near-optimal planning in the blocks world
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 2
Clustering at the phase transition
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Problem difficulty for tabu search in job-shop scheduling
Artificial Intelligence
Phase Transitions and Backbones of 3-SAT and Maximum 3-SAT
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Learning the Empirical Hardness of Optimization Problems: The Case of Combinatorial Auctions
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Searching for backbones and fat: a limit-crossing approach with applications
Eighteenth national conference on Artificial intelligence
A two-phase backbone-based search heuristic for partial MAX-SAT: an initial investigation
IEA/AIE'2005 Proceedings of the 18th international conference on Innovations in Applied Artificial Intelligence
Discrete Applied Mathematics - Special issue: Typical case complexity and phase transitions
Evolving combinatorial problem instances that are difficult to solve
Evolutionary Computation
Cross-disciplinary perspectives on meta-learning for algorithm selection
ACM Computing Surveys (CSUR)
Empirical hardness models: Methodology and a case study on combinatorial auctions
Journal of the ACM (JACM)
Effective Tour Searching for TSP by Contraction of Pseudo Backbone Edges
AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
The backdoor key: a path to understanding problem hardness
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Backbones and backdoors in satisfiability
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 3
Phase transitions and backbones of the asymmetric traveling salesman problem
Journal of Artificial Intelligence Research
Journal of Artificial Intelligence Research
How the landscape of random job shop scheduling instances depends on the ratio of jobs to machines
Journal of Artificial Intelligence Research
Phase transitions of the asymmetric traveling salesman
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
The backbone of the travelling salesperson
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Discrete Applied Mathematics
On Computing Backbones of Propositional Theories
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Review: Measuring instance difficulty for combinatorial optimization problems
Computers and Operations Research
Is computational complexity a barrier to manipulation?
Annals of Mathematics and Artificial Intelligence
A backbone-based co-evolutionary heuristic for partial MAX-SAT
EA'05 Proceedings of the 7th international conference on Artificial Evolution
Reasoning over biological networks using maximum satisfiability
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
A backbone based TSP heuristic for large instances
Journal of Heuristics
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We study the impact of backbones in optimization and approximation problems. We show that some optimization problems like graph coloring resemble decision problems, with problem hardness positively correlated with backbone size. For other optimization problems like blocks world planning and traveling salesperson problems, problem hardness is weakly and negatively correlated with backbone size, while the cost of finding optimal and approximate solutions is positively correlated with backbone size. A third class of optimization problems like number partitioning have regions of both types of behavior. We find that to observe the impact of backbone size on problem hardness, it is necessary to eliminate some symmetries, perform trivial reductions and factor out the effective problem size.