Extracting the K best solutions from a valued and-or acyclic graph

• Main Author: Elliott, Paul Harrison, 1979-
• Other Authors: Howard Shrobe and Brian C. Williams.
• Format: Others
• Language: English
• Published: Massachusetts Institute of Technology 2008
• Subjects: Electrical Engineering and Computer Science.
• Online Access: http://hdl.handle.net/1721.1/41540

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007. === This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. === Includes bibliographical references (p. 117-118). === In this thesis, we are interested in solving a problem that arises in model-based programming, specifically in the estimation of the state a system described by a probabilistic model. Some model-based estimators, such as the MEXEC algorithm and the DNNF-based Belief State Estimation algorithm, use a valued and-or acyclic graph to represent the possible estimates. These algorithms specifically use a valued smooth deterministic decomposable negation normal form (sd-DNNF) representation, a type of and-or acyclic graph. Prior work has focused on extracting either all or only the best solution from the sd-DNNF. This work develops an efficient algorithm that is able to extract the k best solutions, where k is a parameter to the algorithm. For a graph with -E- edges, -V - nodes and -Ev- children per non-leaf node, the algorithm presented in this thesis has a time complexity of O(-E-k log k +-E- log -Ev-+-V -k log -Ev-) and a space complexity O(-E-k). === by Paul Harrison Elliott. === M.Eng.