Computing the block triangular form of a sparse matrix
ACM Transactions on Mathematical Software (TOMS)
An incremental algorithm for satisfying hierarchies of multiway dataflow constraints
ACM Transactions on Programming Languages and Systems (TOPLAS)
A graph-constructive approach to solving systems of geometric constraints
ACM Transactions on Graphics (TOG)
Generalizing partial order and dynamic backtracking
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Journal of Artificial Intelligence Research
Constraint (Logic) Programming: A Survey on Research and Applications
Selected papers from the Joint ERCIM/Compulog Net Workshop on New Trends in Contraints
A Constraint Programming Approach for Solving Rigid Geometric Systems
CP '02 Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming
A Debugging Scheme for Declarative Equation Based Modeling Languages
PADL '02 Proceedings of the 4th International Symposium on Practical Aspects of Declarative Languages
On bounded block decomposition problems for under-specified systems of equations
Journal of Computer and System Sciences
When interval analysis helps inter-block backtracking
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Inter-block backtracking: exploiting the structure in continuous CSPs
COCOS'03 Proceedings of the Second international conference on Global Optimization and Constraint Satisfaction
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In practice, constraint satisfaction problems are often structured. By exploiting this structure, solving algorithms can make important gains in performance. In this paper, we focus on structured continuous CSPs defined by systems of equations. We use graph decomposition techniques to decompose the constraint graph into a directed acyclic graph of small blocks. We present new algorithms to solve decomposed problems which solve the blocks in partial order and perform intelligent backtracking when a block has no solution. For under-constrained problems, the solution space can be explored by choosing some variables as input parameters. However, in this case, the decomposition is no longer unique and some choices lead to decompositions with smaller blocks than others. We present an algorithm for selecting the input parameters that lead to good decompositions. First experimental results indicate that, even on small problems, significant speedups can be obtained using these algorithms.