Efficient Algorithms for Shortest Paths in Sparse Networks
Journal of the ACM (JACM)
PPCP '94 Proceedings of the Second International Workshop on Principles and Practice of Constraint Programming
Negative-Cycle Detection Algorithms
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Fully Dynamic Shortest Paths and Negative Cycles Detection on Digraphs with Arbitrary Arc Weights
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
O-Trees: A Constraint-Based Index Structure
ADC '00 Proceedings of the Australasian Database Conference
Higher-Order and Symbolic Computation
QUICKXPLAIN: preferred explanations and relaxations for over-constrained problems
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
An efficient decision procedure for UTVPI constraints
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
Fast and flexible difference constraint propagation for DPLL(T)
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Minimum clique cover in claw-free perfect graphs and the weak Edmonds-Johnson property
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
Lossless horizontal decomposition with domain constraints on interpreted attributes
BNCOD'13 Proceedings of the 29th British National conference on Big Data
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Unit two-variable-per-inequality (UTVPI) constraints form one of the largest class of integer constraints that are polynomial time solvable (unless P = NP). There is considerable interest in their use for constraint solving, abstract interpretation, spatial database algorithms, and theorem proving. In this paper we develop new incremental algorithms for UTVPI constraint satisfaction and implication checking that require ℴ(m + n log n + p) time and ℴ(n + m + p) space to incrementally check satisfiability of m UTVPI constraints on n variables, and we check the implication of p UTVPI constraints. The algorithms can be straightforwardly extended to create nonincremental implication checking and generation of all (nonredundant) implied constraints, as well as generate minimal unsatisfiable subsets and minimal implicants.