ECAI '92 Proceedings of the 10th European conference on Artificial intelligence
Fast planning through planning graph analysis
Artificial Intelligence
Approximating clique and biclique problems
Journal of Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Using Auxiliary Variables and Implied Constraints to Model Non-Binary Problems
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Node-and edge-deletion NP-complete problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
The maximum edge biclique problem is NP-complete
Discrete Applied Mathematics
Artificial Intelligence - Special issue on logical formalizations and commonsense reasoning
Solving non-Boolean satisfiability problems with stochastic local search
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Pushing the envelope: planning, propositional logic, and stochastic search
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 2
Mapping problems with finite-domain variables to problems with boolean variables
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
Concise finite-domain representations for PDDL planning tasks
Artificial Intelligence
Understanding planning tasks: domain complexity and heuristic decomposition
Understanding planning tasks: domain complexity and heuristic decomposition
Programming for modular reconfigurable robots
Programming and Computing Software
Towards optimal cooperative path planning in hard setups through satisfiability solving
PRICAI'12 Proceedings of the 12th Pacific Rim international conference on Trends in Artificial Intelligence
Mining-based compression approach of propositional formulae
Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
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We address the problem of representing big sets of binary constraints compactly. Binary constraints in the form of 2-literal clauses are ubiquitous in propositional formulae that represent real-world problems ranging from model-checking problems in computer-aided verification to AI planning problems. Current satisfiability and constraint solvers are applicable to very big problems, and in some cases the physical size of the problem representations prevents solving the problems, not their computational difficulty. Our work is motivated by this observation. We propose graph-theoretic techniques based on cliques and bicliques for compactly representing big sets of binary constraints that have the form of 2-literal clauses. An n, m biclique in a graph associated with the constraints can be very compactly represented with only n+m binary constraints and one auxiliary variable. Cliques in the graph are associated with at-most-one constraints, and can be represented with a logarithmic number of binary constraints. The clique representation turns out to be a special case of the biclique representation. We demonstrate the effectiveness of the biclique representation in making the representation of big planning problems practical.