A Constant Factor Approximation Algorithm for Unsplittable Flow on Paths

In this paper, we present a constant-factor approximation algorithm for the unsplittable flow problem on a path. This improves on the previous best known approximation factor of O(log n). The approximation ratio of our algorithm is 7+e for any e>;0. In the unsplittable flow problem on a path, we...

Full description

Saved in:
Bibliographic Details
Published in:2011 IEEE 52nd Annual Symposium on Foundations of Computer Science pp. 47 - 56
Main Authors: Bonsma, P., Schulz, J., Wiese, A.
Format: Conference Proceeding
Language:English
Published: IEEE 01.10.2011
Subjects:
Algorithm design and analysis
Approximation algorithms
Approximation methods
constant factor approximation
Heuristic algorithms
maximum weight independent set
Partitioning algorithms
Polynomials
resource allocation
Resource management
strong NP-hardness
unsplittable flow
ISBN:145771843X, 9781457718434
ISSN:0272-5428
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract In this paper, we present a constant-factor approximation algorithm for the unsplittable flow problem on a path. This improves on the previous best known approximation factor of O(log n). The approximation ratio of our algorithm is 7+e for any e>;0. In the unsplittable flow problem on a path, we are given a capacitated path P and n tasks, each task having a demand, a profit, and start and end vertices. The goal is to compute a maximum profit set of tasks, such that for each edge e of P, the total demand of selected tasks that use e does not exceed the capacity of e. This is a well-studied problem that occurs naturally in various settings, and therefore it has been studied under alternative names, such as resource allocation, bandwidth allocation, resource constrained scheduling, temporal knapsack and interval packing. Polynomial time constant factor approximation algorithms for the problem were previously known only under the no-bottleneck assumption (in which the maximum task demand must be no greater than the minimum edge capacity). We introduce several novel algorithmic techniques, which might be of independent interest: a framework which reduces the problem to instances with a bounded range of capacities, and a new geometrically inspired dynamic program which solves a special case of the maximum weight independent set of rectangles problem to optimality. In addition, we show that the problem is strongly NP-hard even if all edge capacities are equal and all demands are either 1, 2, or 3.
AbstractList In this paper, we present a constant-factor approximation algorithm for the unsplittable flow problem on a path. This improves on the previous best known approximation factor of O(log n). The approximation ratio of our algorithm is 7+e for any e>;0. In the unsplittable flow problem on a path, we are given a capacitated path P and n tasks, each task having a demand, a profit, and start and end vertices. The goal is to compute a maximum profit set of tasks, such that for each edge e of P, the total demand of selected tasks that use e does not exceed the capacity of e. This is a well-studied problem that occurs naturally in various settings, and therefore it has been studied under alternative names, such as resource allocation, bandwidth allocation, resource constrained scheduling, temporal knapsack and interval packing. Polynomial time constant factor approximation algorithms for the problem were previously known only under the no-bottleneck assumption (in which the maximum task demand must be no greater than the minimum edge capacity). We introduce several novel algorithmic techniques, which might be of independent interest: a framework which reduces the problem to instances with a bounded range of capacities, and a new geometrically inspired dynamic program which solves a special case of the maximum weight independent set of rectangles problem to optimality. In addition, we show that the problem is strongly NP-hard even if all edge capacities are equal and all demands are either 1, 2, or 3.
Author Bonsma, P.
Wiese, A.
Schulz, J.
Author_xml – sequence: 1
  givenname: P.
  surname: Bonsma
  fullname: Bonsma, P.
  email: bonsma@informatik.hu-berlin.de
  organization: Comput. Sci. Dept., Humboldt Univ. zu Berlin, Berlin, Germany
– sequence: 2
  givenname: J.
  surname: Schulz
  fullname: Schulz, J.
  email: jschulz@math.tu-berlin.de
  organization: Inst. of Math., Tech. Univ. Berlin, Berlin, Germany
– sequence: 3
  givenname: A.
  surname: Wiese
  fullname: Wiese, A.
  email: wiese@math.tu-berlin.de
  organization: Inst. of Math., Tech. Univ. Berlin, Berlin, Germany
BookMark eNotjk9LxDAUxCOu4Hbdmzcv-QKt76Xpv2Mp1hUWVtAFb0uavriBblPagPrtDehpfsMMw0RsNbqRGLtHSBChemwPzVsiADFBuGIRFHmVyazA8ppFGCCQTD9WbA2iEHEmRXnLtstiO8CsTEUOcs12NW_cuHg1et4q7d3M62ma3be9KG_dyOvh083Wny_chOw4LtNgvVfdQLwd3BcPlVflz8sduzFqWGj7rxt2bJ_em128Pzy_NPU-tlhkPu5T0wvTK4UkukIaVUhJlGnVIZXaEOky1RWISoHuO6UhN70M1WByMj2kG_bwt2uJ6DTN4ef8c8oRSpRV-guVkVIW
ContentType Conference Proceeding
DBID 6IE
6IH
CBEJK
RIE
RIO
DOI 10.1109/FOCS.2011.10
DatabaseName IEEE Electronic Library (IEL) Conference Proceedings
IEEE Proceedings Order Plan (POP) 1998-present by volume
IEEE Xplore All Conference Proceedings
IEEE Electronic Library (IEL)
IEEE Proceedings Order Plans (POP) 1998-present
DatabaseTitleList
Database_xml – sequence: 1
  dbid: RIE
  name: IEEE Electronic Library (IEL)
  url: https://ieeexplore.ieee.org/
  sourceTypes: Publisher
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISBN 0769545718
9780769545714
EndPage 56
ExternalDocumentID 6108149
Genre orig-research
GroupedDBID -~X
23M
6IE
6IF
6IH
6IK
6IL
6IM
6IN
AAJGR
AAWTH
ACNCT
ADZIZ
AFFNX
AI.
ALMA_UNASSIGNED_HOLDINGS
BEFXN
BFFAM
BGNUA
BKEBE
BPEOZ
CBEJK
CHZPO
IPLJI
OCL
RIE
RIL
RIO
RNS
VH1
ID FETCH-LOGICAL-i175t-d3fd2fdaa1e2b74fa744ee5cab1e8cfeec83c9029a0cdbac06fd4e2bcdb6efd03
IEDL.DBID RIE
ISBN 145771843X
9781457718434
ISICitedReferencesCount 22
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000298962700007&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0272-5428
IngestDate Wed Aug 27 03:21:16 EDT 2025
IsPeerReviewed false
IsScholarly false
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-i175t-d3fd2fdaa1e2b74fa744ee5cab1e8cfeec83c9029a0cdbac06fd4e2bcdb6efd03
PageCount 10
ParticipantIDs ieee_primary_6108149
PublicationCentury 2000
PublicationDate 2011-Oct.
PublicationDateYYYYMMDD 2011-10-01
PublicationDate_xml – month: 10
  year: 2011
  text: 2011-Oct.
PublicationDecade 2010
PublicationTitle 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
PublicationTitleAbbrev focs
PublicationYear 2011
Publisher IEEE
Publisher_xml – name: IEEE
SSID ssib015832604
ssj0040503
ssj0000669372
Score 1.6344327
Snippet In this paper, we present a constant-factor approximation algorithm for the unsplittable flow problem on a path. This improves on the previous best known...
SourceID ieee
SourceType Publisher
StartPage 47
SubjectTerms Algorithm design and analysis
Approximation algorithms
Approximation methods
constant factor approximation
Heuristic algorithms
maximum weight independent set
Partitioning algorithms
Polynomials
resource allocation
Resource management
strong NP-hardness
unsplittable flow
Title A Constant Factor Approximation Algorithm for Unsplittable Flow on Paths
URI https://ieeexplore.ieee.org/document/6108149
WOSCitedRecordID wos000298962700007&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV27TsMwFLXaigEWHi3iLQ-MhObhxM5YVUQdoFSCom6VHzcQCRLUpMDnYztNYGBhsy3LspyrnCP7nnMRujQswk8D7oBwQ0fjceDEJCSOp0ImlHlLs1m-T7d0OmWLRTzroKtWCwMANvkMrk3TvuWrQq7NVdlQQz3TjL6LupRGtVariR0v1KHZ-IzUf-FII29rJUWM74m9b6HG-99nVuQVUmrqnSwa76dNn7QZ8vEwuR8_1E6fRmT7qwKLBaBk939b30ODHyUfnrUYtY86kB-gnbvWq7Xso8kIj2uSWOHEVt_BI2M0_pXVqkY8en0uVln18oY1wcXzvNS8taqM5Aonr8Un1lNmesFygObJzeN44mzqKziZJg2Vo4JU-ani3ANfUJJySghAKLnwgMkUQLJAxq4fc1cqwaUbpYroqboTQarc4BD18iKHI4SpkgJiLj1FIyIpjUMaMOEFiulYiCQco745k-V7baGx3BzHyd_Dp2jbb1LtvDPUq1ZrOEdb8qPKytWF_e7fVgqnJg
linkProvider IEEE
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1dS8MwFA1zCuqLH5v4bR58tK4faZM-jmGZuM2Bm-xtpMmtFuYqa6f-fJN0qz74IvQhKSGUcOk53NxzLkLXmkW4icctiG3fUnjsWSHxieVIn8VS36WZKt_nHh0M2GQSDmvoptLCAIApPoNbPTR3-TITS50qaymoZ4rRb6BNnxDXLtVa6-hxfBWca6eR8j8cKOytzKSIdj4xGReq3f9dZmRePqW648lk7f60mpOqRj5sRY-dp9LrU8tsf_VgMRAU7f3v4_dR80fLh4cVSh2gGswP0W6_cmvNG6jbxp2SJhY4Mv13cFtbjX-lpa4Rt2cv2SItXt-worh4PM8Vcy0KLbrC0Sz7xGrJUG2YN9E4uht1utaqw4KVKtpQWNJLpJtIzh1wY0oSTgkB8AWPHWAiARDME6HthtwWMubCDhJJ1FI1CSCRtneE6vNsDscIUyliCLlwJA2IoDT0qcdix5NMRUMg4AQ19JlM30sTjenqOE7_fn2Ftrujfm_aux88nKGdMpGrn3NULxZLuEBb4qNI88WliYFvO_yqbQ
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=proceeding&rft.title=2011+IEEE+52nd+Annual+Symposium+on+Foundations+of+Computer+Science&rft.atitle=A+Constant+Factor+Approximation+Algorithm+for+Unsplittable+Flow+on+Paths&rft.au=Bonsma%2C+P.&rft.au=Schulz%2C+J.&rft.au=Wiese%2C+A.&rft.date=2011-10-01&rft.pub=IEEE&rft.isbn=9781457718434&rft.issn=0272-5428&rft.spage=47&rft.epage=56&rft_id=info:doi/10.1109%2FFOCS.2011.10&rft.externalDocID=6108149
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0272-5428&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0272-5428&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0272-5428&client=summon