• Login
    View Item 
    •   Home
    • Faculty/ Researcher Works
    • Faculty/ Researcher Works
    • View Item
    •   Home
    • Faculty/ Researcher Works
    • Faculty/ Researcher Works
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of TUScholarShareCommunitiesDateAuthorsTitlesSubjectsGenresThis CollectionDateAuthorsTitlesSubjectsGenres

    My Account

    LoginRegister

    Help

    AboutPeoplePoliciesHelp for DepositorsData DepositFAQs

    Statistics

    Most Popular ItemsStatistics by CountryMost Popular Authors

    A dense hierarchy of sublinear time approximation schemes for bin packing

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Thumbnail
    Name:
    1007.1260v3.pdf
    Size:
    515.3Kb
    Format:
    PDF
    Download
    Genre
    Pre-print
    Date
    2012-05-23
    Author
    Beigel, R
    Fu, B
    Subject
    cs.CC
    cs.CC
    cs.DS
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/4220
    
    Metadata
    Show full item record
    DOI
    10.1007/978-3-642-29700-7_16
    Abstract
    The bin packing problem is to find the minimum number of bins of size one to pack a list of items with sizes a 1,..., a n in (0,1]. Using uniform sampling, which selects a random element from the input list each time, we develop a randomized (Formula Presented) time (1 + ε)- approximation scheme for the bin packing problem. We show that every randomized algorithm with uniform random sampling needs (Formula Presented) time to give an (1 + ε)-approximation. For each function s(n): N → N, define Σ(s(n)) to be the set of all bin packing problems with the sum of item sizes equal to s(n). We show that Σ(n b) is NP-hard for every b ∈ (0,1]. This implies a dense sublinear time hierarchy of approximation schemes for a class of NP-hard problems, which are derived from the bin packing problem. We also show a randomized streaming approximation scheme for the bin packing problem such that it needs only constant updating time and constant space, and outputs an (1 + ε)-approximation in time. Let S(δ)-bin packing be the class of bin packing problems with each input item of size at least δ. This research also gives a natural example of NP-hard problem (S(δ)-bin packing) that has a constant time approximation scheme, and a constant time and space sliding window streaming approximation scheme, where δ is a positive constant. © 2012 Springer-Verlag.
    Citation to related work
    Springer Berlin Heidelberg
    Has part
    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    ADA compliance
    For Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu
    ae974a485f413a2113503eed53cd6c53
    http://dx.doi.org/10.34944/dspace/4202
    Scopus Count
    Collections
    Faculty/ Researcher Works

    entitlement

     
    DSpace software (copyright © 2002 - 2023)  DuraSpace
    Temple University Libraries | 1900 N. 13th Street | Philadelphia, PA 19122
    (215) 204-8212 | scholarshare@temple.edu
    Open Repository is a service operated by 
    Atmire NV
     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    By default, clicking on the export buttons will result in a download of the allowed maximum amount of items.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.