• Login
    View Item 
    •   Treasures Home
    • Electronic Theses and Dissertations
    • UTD Theses and Dissertations
    • View Item
    •   Treasures Home
    • Electronic Theses and Dissertations
    • UTD Theses and Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Computation of Cycle Bases in Surface Embedded Graphs

    Thumbnail
    View/Open
    STANLEY-PRIMARY-2022-1.pdf (284.7Kb)
    Date
    2021-12-01
    Author
    Stanley, Thomas
    Metadata
    Show full item record
    Abstract
    Abstract
    We study the problem of finding a cycle basis, a minimum weight set of independent cycles that form a basis of the cycle space for a given graph. We focus on finding the minimum cycle basis of directed graphs. This is a more complicated problem compared to the undirected case as the underlying field is Q for directed graphs instead of Z2 for undirected, which causes problems in the speed of calculations. Previously the fastest known deterministic algorithm to find the minimum cycle basis of a directed graph runs in O(m3n + m2n 2 log n) time [11]. We concentrate on graphs embedded on a surface of genus g. We modify algorithms for undirected graphs to work on directed graphs. We present an O(mn2 g 2 log g + mω+1) time algorithm to find the minimum cycle basis of a directed graph embedded on a surface of genus g. We also give an improvement on the minimum cycle basis in the undirected case
    URI

    https://hdl.handle.net/10735.1/9622
    Collections
    • UTD Theses and Dissertations

    DSpace software copyright © 2002-2016  DuraSpace
    Contact Us | Send Feedback
    Theme by 
    Atmire NV
     

     

    Browse

    All of TreasuresCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

    My Account

    Login

    DSpace software copyright © 2002-2016  DuraSpace
    Contact Us | Send Feedback
    Theme by 
    Atmire NV