scholarly journals Stochastic Constraint Propagation for Mining Probabilistic Networks

2019 ◽  
Author(s):  
Anna Louise D. Latour ◽  
Behrouz Babaki ◽  
Siegfried Nijssen
Keyword(s):  
Data Mining ◽  
Probability Distributions ◽  
Constraint Propagation ◽  
Mixed Integer ◽  
Test Cases ◽  
Decision Diagrams ◽  
Probabilistic Networks ◽  
Ordered Binary Decision Diagrams ◽  
Binary Decision ◽  
Domain Consistency

A number of data mining problems on probabilistic networks can be modeled as Stochastic Constraint Optimization and Satisfaction Problems, i.e., problems that involve objectives or constraints with a stochastic component. Earlier methods for solving these problems used Ordered Binary Decision Diagrams (OBDDs) to represent constraints on probability distributions, which were decomposed into sets of smaller constraints and solved by Constraint Programming (CP) or Mixed Integer Programming (MIP) solvers. For the specific case of monotonic distributions, we propose an alternative method: a new propagator for a global OBDD-based constraint. We show that this propagator is (sub-)linear in the size of the OBDD, and maintains domain consistency. We experimentally evaluate the effectiveness of this global constraint in comparison to existing decomposition-based approaches, and show how this propagator can be used in combination with another data mining specific constraint present in CP systems. As test cases we use problems from the data mining literature.

scholarly journals An exponential lower bound for a constraint propagation proof system based on ordered binary decision diagrams

2008 ◽  
Vol 73 (1) ◽  
pp. 227-237 ◽  
Author(s):  
Jan Krajíček
Keyword(s):  
Lower Bound ◽  
Binary Decision Diagrams ◽  
Constraint Propagation ◽  
Proof System ◽  
Decision Diagrams ◽  
Ordered Binary Decision Diagrams ◽  
Binary Decision ◽  
System Operating ◽  
Exponential Lower Bound

AbstractWe prove an exponential lower bound on the size of proofs in the proof system operating with ordered binary decision diagrams introduced by Atserias, Kolaitis and Vardi [2]. In fact, the lower bound applies to semantic derivations operating with sets defined by OBDDs. We do not assume any particular format of proofs or ordering of variables, the hard formulas are in CNF. We utilize (somewhat indirectly) feasible interpolation.We define a proof system combining resolution and the OBDD proof system.

NC-ALGORITHMS FOR OPERATIONS ON BINARY DECISION DIAGRAMS

1993 ◽  
Vol 03 (01) ◽  
pp. 3-12 ◽  
Author(s):  
DETLEF SIELING ◽  
INGO WEGENER
Keyword(s):  
Binary Decision Diagrams ◽  
Pattern Generation ◽  
Decision Diagrams ◽  
Equivalence Test ◽  
Ordered Binary Decision Diagrams ◽  
Binary Decision ◽  
Verification Test ◽  
Logical Synthesis ◽  
Redundancy Test ◽  
Nc Algorithms

(Ordered) binary decision diagrams are a powerful representation for Boolean functions and are widely used in logical synthesis, verification, test pattern generation or as part of CAD tools. NC-algorithms are presented for the most important operations on this representation, e.g. evaluation for a given input, minimization, satisfiability, redundancy test, replacement of variables by constants or functions, equivalence test and synthesis. The algorithms have logarithmic run time on CRCW COMMON PRAMs with a polynomial number of processors.

scholarly journals Optimal ordered binary decision diagrams for read-once formulas

2000 ◽  
Vol 103 (1-3) ◽  
pp. 237-258 ◽  
Author(s):  
Martin Sauerhoff ◽  
Ingo Wegener ◽  
Ralph Werchner
Keyword(s):  
Binary Decision Diagrams ◽  
Decision Diagrams ◽  
Ordered Binary Decision Diagrams ◽  
Binary Decision

ORDERED BINARY DECISION DIAGRAMS AND THEIR SIGNIFICANCE IN COMPUTER-AIDED DESIGN OF VLSI CIRCUITS

1999 ◽  
Vol 09 (03n04) ◽  
pp. 181-198 ◽  
Author(s):  
CHRISTOPH MEINEL ◽  
THORSTEN THEOBALD
Keyword(s):  
Integrated Circuits ◽  
Computer Aided Design ◽  
Binary Decision Diagrams ◽  
Basic Research ◽  
Vlsi Circuits ◽  
Decision Diagrams ◽  
Ordered Binary Decision Diagrams ◽  
Binary Decision ◽  
Computer Aided ◽  
Aided Design

Many problems in computer-aided design of highly integrated circuits (CAD for VLSI) can be transformed to the task of manipulating objects over finite domains. The efficiency of these operations depends substantially on the chosen data structures. In the last years, ordered binary decision diagrams (OBDDs) have proven to be a very efficient data structure in this context. Here, we give a survey on these developments and stress the deep interactions between basic research and practically relevant applied research with its immediate impact on the performance improvement of modern CAD design and verification tools.

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