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Full-Text Articles in Industrial Organization
Tight Representation Of Logical Constraints As Cardinality Rules, John Hooker, Hong Yan
Tight Representation Of Logical Constraints As Cardinality Rules, John Hooker, Hong Yan
John Hooker
We address the problem of finding a "tight" representation of complex logical constraints in a mixed integer programming model by describing a convex hull representation of cardinality rules.
A Linear Programming Framework For Logics Of Uncertainty, K. Andersen, John Hooker
A Linear Programming Framework For Logics Of Uncertainty, K. Andersen, John Hooker
John Hooker
Several logics for reasoning under uncertainty distribute “probability mass” over sets in some sense. These include probabilistic logic, Dempster-Shafer theory, other logics based on belief functions, and second-order probabilistic logic. We show that these logics are instances of a certain type of linear programming model, typically with exponentially many variables. We also show how a single linear programming package can implement these logics computationally if one “plugs in” a different column generation subroutine for each logic, although the practicality of this approach has been demonstrated so far only for probabilistic logic.
Solving The Incremental Satisfiability Problem, John Hooker
Solving The Incremental Satisfiability Problem, John Hooker
John Hooker
Given a set of clauses in propositional logic that have been found satisfiable, we wish to check whether satisfiability is preserved when the clause set is incremented with a new clause. We describe an efficient implementation of the Davis-Putnam-Loveland algorithm for checking the satisfiability of the original set. We then show how to modify the algorithm for efficient solution of the incremental problem, which is NP-complete. We also report computational results.
Resolution And The Integrality Of Satisfiability Problems, John Hooker
Resolution And The Integrality Of Satisfiability Problems, John Hooker
John Hooker
No abstract provided.