{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/41540"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/41540","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Extracting the K best solutions from a valued and-or acyclic graph","abstract":"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).","abstract_html":"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).","abstract_has_math":false,"creators":["Elliott, Paul Harrison, 1979-"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.","school":null,"contributors":[],"advisors":["Howard Shrobe and Brian C. 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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)."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["M.Eng."]},{"key":"dc:title","label":"Title","values":["Extracting the K best solutions from a valued and-or acyclic graph"]}]}],"canonical_facts":{"dc:contributor.advisor":["Howard Shrobe and Brian C. Williams."],"dc:contributor.department":["Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science."],"dc:contributor.other":["Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science."],"dc:creator":["Elliott, Paul Harrison, 1979-"],"dc:date.accessioned":["2008-05-19T14:58:21Z"],"dc:date.available":["2008-05-19T14:58:21Z"],"dc:date.issued":["2007"],"dc:description":["Thesis (M. 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