On generating all maximal independent sets
Information Processing Letters
Planar graph coloring is not self-reducible, assuming P≠NP
Theoretical Computer Science
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
On the algebraic structure of combinatorial problems
Theoretical Computer Science
Suboptimal Cuts: Their Enumeration, Weight and Number (Extended Abstract)
ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Efficiently enumerating results of keyword search over data graphs
Information Systems
Parameterized complexity of constraint satisfaction problems
Computational Complexity
On the Hardness of Losing Weight
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Boolean Constraint Satisfaction Problems: When Does Post's Lattice Help?
Complexity of Constraints
Partial Polymorphisms and Constraint Satisfaction Problems
Complexity of Constraints
Introduction to the Maximum Solution Problem
Complexity of Constraints
Lower bounds for three algorithms for transversal hypergraph generation
Discrete Applied Mathematics
Efficient Algorithms for the Problems of Enumerating Cuts by Non-decreasing Weights
Algorithmica - Special Issue: Computation and Combinatorial Optimization; Guest Editors: Xiaodong Hu and Jie Wang
Enumerating all solutions for constraint satisfaction problems
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Nonuniform Boolean constraint satisfaction problems with cardinality constraint
ACM Transactions on Computational Logic (TOCL)
Incrementally computing ordered answers of acyclic conjunctive queries
NGITS'06 Proceedings of the 6th international conference on Next Generation Information Technologies and Systems
On acyclic conjunctive queries and constant delay enumeration
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Enumerating with constant delay the answers to a query
Proceedings of the 16th International Conference on Database Theory
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We address the problem of enumerating all models of Boolean formulæ in order of non-decreasing weight in Schaefer's framework. The weight of a model is the number of variables assigned to 1. Tractability in this context amounts to enumerating all models one after the other in sorted order, with polynomial delay between two successive outputs. The question of model-enumeration has already been studied in Schaefer's framework, but without imposing a specific order. The order of non-decreasing weight changes the complexity considerably. We obtain a new dichotomous complexity classification. On the one hand, we develop new polynomial delay algorithms for Horn and 2-XOR-formulæ to enumerate the models by non-decreasing weight. On the other hand, we prove that in all other cases such a polynomial delay algorithm does not exist, unlessP = NP.