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dc.contributor.advisorMcConnell, Ross M.
dc.contributor.authorChaturvedi, Mmanu
dc.contributor.committeememberKirby, Michael J.
dc.contributor.committeememberRajopadhye, Sanjay V.
dc.contributor.committeememberOprea, Iuliana
dc.date.accessioned2017-09-14T16:04:44Z
dc.date.available2017-09-14T16:04:44Z
dc.date.issued2017
dc.description2017 Summer.
dc.descriptionIncludes bibliographical references.
dc.description.abstractWe consider four NP-hard optimization problems on directed acyclic graphs (DAGs), namely, max clique, min coloring, max independent set and min clique cover. It is well-known that these four problems can be solved in polynomial time on transitive DAGs. It is also known that there can be no polynomial O(n1-ϵ)-approximation algorithms for these problems on the general class of DAGs unless P = NP. We propose a new parameter, β, as a measure of departure from transitivity for DAGs. We define β to be the number of vertices in a longest path in a DAG such that there is no edge from the first to the last vertex of the path, and 2 if the graph is transitive. Different values of β define a hierarchy of classes of DAGs, starting with the class of transitive DAGs. We give a polynomial time algorithm for finding a max clique when β is bounded by a fixed constant. The algorithm is exponential in β, but we also give a polynomial β-approximation algorithm. We prove that the other three decision problems are NP-hard even for β ≥ 4 and give polynomial algorithms with approximation bounds of β or better in each case. Furthermore, generalizing the definition of quasi-transitivity introduced by Ghouilà-Houri, we define β-quasi-transitivity and prove a more generalized version their theorem relating quasi-transitive orientation and transitive orientation.
dc.format.mediumborn digital
dc.format.mediummasters theses
dc.identifierChaturvedi_colostate_0053N_14288.pdf
dc.identifier.urihttps://hdl.handle.net/10217/183921
dc.languageEnglish
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019 - CSU Theses and Dissertations
dc.rightsCopyright of the original work is retained by the author.
dc.subjectgraph theory
dc.subjectalgorithms
dc.titleParametric classification of directed acyclic graphs, A
dc.typeText
dcterms.rights.dplaThe copyright and related rights status of this item has not been evaluated (https://rightsstatements.org/vocab/CNE/1.0/). Please refer to the organization that has made the Item available for more information.
thesis.degree.disciplineComputer Science
thesis.degree.grantorColorado State University
thesis.degree.levelMasters
thesis.degree.nameMaster of Science (M.S.)


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