A branch-and-cut approach to physical mapping with end-probes
RECOMB '97 Proceedings of the first annual international conference on Computational molecular biology
An algebra for cyclic ordering of 2D orientations
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
A Geometric Approach to Betweenness
SIAM Journal on Discrete Mathematics
On the satisfiability and maximum satisfiability of random 3-CNF formulas
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Typical random 3-SAT formulae and the satisfiability threshold
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Models and thresholds for random constraint satisfaction problems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
The Efficiency of Resolution and Davis--Putnam Procedures
SIAM Journal on Computing
Cores in random hypergraphs and Boolean formulas
Random Structures & Algorithms
Random Structures & Algorithms - Proceedings of the Eleventh International Conference "Random Structures and Algorithms," August 9—13, 2003, Poznan, Poland
Random $k$-SAT: Two Moments Suffice to Cross a Sharp Threshold
SIAM Journal on Computing
Hardness of fully dense problems
Information and Computation
The complexity of temporal constraint satisfaction problems
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Sharp thresholds for constraint satisfaction problems and homomorphisms
Random Structures & Algorithms
When does the giant component bring unsatisfiability?
Combinatorica
On Random Ordering Constraints
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
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Ordering constraints are formally analogous to instances of the satisfiability problem in conjunctive normal form, but instead of a boolean assignment we consider a linear ordering of the variables in question. A clause becomes true given a linear ordering if and only if the relative ordering of its variables obeys the constraint considered. The naturally arising satisfiability problems are NP-complete for many types of constraints. We look at random ordering constraints. Previous work of the author shows that there is a sharp unsatisfiability threshold for certain types of constraints. The value of the threshold, however, is essentially undetermined. We pursue the problem of approximating the precise value of the threshold. We show that random instances of the betweenness constraint are satisfiable with high probability if the number of randomly picked clauses is ≤0.92n, where n is the number of variables considered. This improves the previous bound, which is n random clauses. The proof is based on a binary relaxation of the betweenness constraint and involves some ideas not used before in the area of random ordering constraints.