View in EDS

FRACTIONALLY SUBADDITIVE MAXIMIZATION UNDER AN INCREMENTAL KNAPSACK CONSTRAINT WITH APPLICATIONS TO INCREMENTAL FLOWS.

Saved in:
Bibliographic Details
Title: FRACTIONALLY SUBADDITIVE MAXIMIZATION UNDER AN INCREMENTAL KNAPSACK CONSTRAINT WITH APPLICATIONS TO INCREMENTAL FLOWS.
Authors: DISSER, YANN1 disser@mathematik.tu-darmstadt.de, KLIMM, MAX2 klimm@math.tu-berlin.de, LUTZ, ANNETTE1 lutz@mathematik.tu-darmstadt.de, WECKBECKER, DAVID1 weckbecker@mathematik.tu-darmstadt.de
Source: SIAM Journal on Discrete Mathematics. 2024, Vol. 38 Issue 1, p764-789. 26p.
Subjects: Backpacks, Algorithms
Abstract: We consider the problem of maximizing a fractionally subadditive function under an increasing knapsack constraint. An incremental solution to this problem is given by an order in which to include the elements of the ground set, and the competitive ratio of an incremental solution is defined by the worst ratio over all capacities relative to an optimum solution of the corresponding capacity. We present an algorithm that finds an incremental solution of competitive ratio at most max\{ 3.293 M, 2M\}, under the assumption that the values of singleton sets are in the range [1,M], and we give a lower bound of max\{ 2.618,M\} on the attainable competitive ratio. In addition, we establish that our framework captures potential-based flows between two vertices, and we give a lower bound of max\{ 2,M\} and an upper bound of 2M for the incremental maximization of classical flows with capacities in [1,M] which is tight for the unit capacity case. [ABSTRACT FROM AUTHOR]
Copyright of SIAM Journal on Discrete Mathematics is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
FullText Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 177075466
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: FRACTIONALLY SUBADDITIVE MAXIMIZATION UNDER AN INCREMENTAL KNAPSACK CONSTRAINT WITH APPLICATIONS TO INCREMENTAL FLOWS.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22DISSER%2C+YANN%22">DISSER, YANN</searchLink><relatesTo>1</relatesTo><i> disser@mathematik.tu-darmstadt.de</i><br /><searchLink fieldCode="AR" term="%22KLIMM%2C+MAX%22">KLIMM, MAX</searchLink><relatesTo>2</relatesTo><i> klimm@math.tu-berlin.de</i><br /><searchLink fieldCode="AR" term="%22LUTZ%2C+ANNETTE%22">LUTZ, ANNETTE</searchLink><relatesTo>1</relatesTo><i> lutz@mathematik.tu-darmstadt.de</i><br /><searchLink fieldCode="AR" term="%22WECKBECKER%2C+DAVID%22">WECKBECKER, DAVID</searchLink><relatesTo>1</relatesTo><i> weckbecker@mathematik.tu-darmstadt.de</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Discrete+Mathematics%22">SIAM Journal on Discrete Mathematics</searchLink>. 2024, Vol. 38 Issue 1, p764-789. 26p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Backpacks%22">Backpacks</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We consider the problem of maximizing a fractionally subadditive function under an increasing knapsack constraint. An incremental solution to this problem is given by an order in which to include the elements of the ground set, and the competitive ratio of an incremental solution is defined by the worst ratio over all capacities relative to an optimum solution of the corresponding capacity. We present an algorithm that finds an incremental solution of competitive ratio at most max\{ 3.293 M, 2M\}, under the assumption that the values of singleton sets are in the range [1,M], and we give a lower bound of max\{ 2.618,M\} on the attainable competitive ratio. In addition, we establish that our framework captures potential-based flows between two vertices, and we give a lower bound of max\{ 2,M\} and an upper bound of 2M for the incremental maximization of classical flows with capacities in [1,M] which is tight for the unit capacity case. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of SIAM Journal on Discrete Mathematics is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=177075466
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1137/23M1569265
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 26
        StartPage: 764
    Subjects:
      – SubjectFull: Backpacks
        Type: general
      – SubjectFull: Algorithms
        Type: general
    Titles:
      – TitleFull: FRACTIONALLY SUBADDITIVE MAXIMIZATION UNDER AN INCREMENTAL KNAPSACK CONSTRAINT WITH APPLICATIONS TO INCREMENTAL FLOWS.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: DISSER, YANN
      – PersonEntity:
          Name:
            NameFull: KLIMM, MAX
      – PersonEntity:
          Name:
            NameFull: LUTZ, ANNETTE
      – PersonEntity:
          Name:
            NameFull: WECKBECKER, DAVID
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Text: 2024
              Type: published
              Y: 2024
          Identifiers:
            – Type: issn-print
              Value: 08954801
          Numbering:
            – Type: volume
              Value: 38
            – Type: issue
              Value: 1
          Titles:
            – TitleFull: SIAM Journal on Discrete Mathematics
              Type: main
ResultId 1