Integer and combinatorial optimization
Integer and combinatorial optimization
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Fundamental concepts of qualitative probabilistic networks
Artificial Intelligence
Completeness in approximation classes
Information and Computation
Approximate solution of NP optimization problems
Theoretical Computer Science
Scheduling independent tasks to reduce mean finishing time
Communications of the ACM
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
A Short Guide To Approximation Preserving Reductions
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
Monotonicity in Bayesian networks
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Probabilities for a probabilistic network: a case study in oesophageal cancer
Artificial Intelligence in Medicine
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It is often desirable that a probabilistic network is monotone, e.g., more severe symptoms increase the likeliness of a more serious disease. Unfortunately, determining whether a network is monotone is highly intractable. Often, approximation algorithms are employed that work on a local scale. For these algorithms, the monotonicity of the arcs (rather than the network as a whole) is determined. However, in many situations monotonicity depends on the ordering of the values of the nodes, which is sometimes rather arbitrary. Thus, it is desirable to order the values of these variables such that as many arcs as possible are monotone. We introduce the concept of local monotonicity, discuss the computational complexity of finding an optimal ordering of the values of the nodes in a network, and sketch a branch-and-bound exact algorithm to find such an optimal solution.