Skip to content
University of Maryland LibrariesDigital Repository at the University of Maryland
    • Login
    View Item 
    •   DRUM
    • College of Computer, Mathematical & Natural Sciences
    • Computer Science
    • Technical Reports from UMIACS
    • View Item
    •   DRUM
    • College of Computer, Mathematical & Natural Sciences
    • Computer Science
    • Technical Reports from UMIACS
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Fault Tolerant K-Center Problems

    Thumbnail
    View/Open
    CS-TR-3652.ps (182.1Kb)
    No. of downloads: 248

    Auto-generated copy of CS-TR-3652.ps (206.3Kb)
    No. of downloads: 886

    Date
    1998-10-15
    Author
    Khuller, Samir
    Pless, Robert
    Sussmann, Yoram J.
    Metadata
    Show full item record
    Abstract
    The basic $K$-center problem is a fundamental facility location problem, where we are asked to locate $K$ facilities in a graph, and to assign vertices to facilities, so as to minimize the maximum distance from a vertex to the facility to which it is assigned. This problem is known to be NP-hard, and several optimal approximation algorithms that achieve a factor of $2$ have been developed for it. We focus our attention on a generalization of this problem, where each vertex is required to have a set of $\alpha$ ($\alpha \le K$) centers close to it. In particular, we study two different versions of this problem. In the first version, each vertex is required to have at least $\alpha$ centers close to it. In the second version, each vertex that {\em does not have a center placed on it} is required to have at least $\alpha$ centers close to it. For both these versions we are able to provide polynomial time approximation algorithms that achieve constant approximation factors for {\em any} $\alpha$. For the first version we give an algorithm that achieves an approximation factor of $3$ for any $\alpha$, and achieves an approximation factor of $2$ for $\alpha < 4$. For the second version, we provide algorithms with approximation factors of $2$ for any $\alpha$. The best possible approximation factor for even the basic $K$-center problem is 2. In addition, we give a polynomial time approximation algorithm for a generalization of the $K$-supplier problem where a subset of at most $K$ supplier nodes must be selected as centers so that every demand node has at least $\alpha$ centers close to it. We also provide polynomial time approximation algorithms for all the above problems for generalizations when cost and weight functions are defined on the set of vertices. (Also cross-referenced as UMIACS-TR-96-40)
    URI
    http://hdl.handle.net/1903/823
    Collections
    • Technical Reports from UMIACS
    • Technical Reports of the Computer Science Department

    DRUM is brought to you by the University of Maryland Libraries
    University of Maryland, College Park, MD 20742-7011 (301)314-1328.
    Please send us your comments.
    Web Accessibility
     

     

    Browse

    All of DRUMCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

    My Account

    LoginRegister
    Pages
    About DRUMAbout Download Statistics

    DRUM is brought to you by the University of Maryland Libraries
    University of Maryland, College Park, MD 20742-7011 (301)314-1328.
    Please send us your comments.
    Web Accessibility