Algorithms and complexity for the almost equal maximum flow problem
In the equal maximum flow problem (EMFP), we aim for a maximum flow where we require the same flow value on all arcs in some given subsets of the arc set, so called homologous arc sets. In this article, we study the closely related almost equal maximum flow problems (AEMFP) where the flow values on...
Gespeichert in:
| Veröffentlicht in: | Networks Jg. 83; H. 4; S. 642 - 652 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
New York
Wiley Subscription Services, Inc
01.06.2024
|
| Schlagworte: | |
| ISSN: | 0028-3045, 1097-0037 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | In the equal maximum flow problem (EMFP), we aim for a maximum flow where we require the same flow value on all arcs in some given subsets of the arc set, so called homologous arc sets. In this article, we study the closely related almost equal maximum flow problems (AEMFP) where the flow values on arcs of one homologous arc set differ at most by the valuation of a so called deviation function . We prove that the integer AEMFP is in general ‐complete, and show that even the problem of finding a fractional maximum flow in the case of convex deviation functions is also ‐complete. This is in contrast to the EMFP, which is polynomial time solvable in the fractional case. Additionally, we provide inapproximability results for the integral AEMFP. For the (fractional) concave AEMFP we state a strongly polynomial algorithm for the linear and concave piecewise polynomial deviation function case for a fixed number of homologous sets using a parametric search approach. |
|---|---|
| AbstractList | In the equal maximum flow problem (EMFP), we aim for a maximum flow where we require the same flow value on all arcs in some given subsets of the arc set, so called homologous arc sets. In this article, we study the closely related almost equal maximum flow problems (AEMFP) where the flow values on arcs of one homologous arc set differ at most by the valuation of a so called deviation function Δ$$ \Delta $$. We prove that the integer AEMFP is in general ð'©ð'«‐complete, and show that even the problem of finding a fractional maximum flow in the case of convex deviation functions is also ð'©ð'«‐complete. This is in contrast to the EMFP, which is polynomial time solvable in the fractional case. Additionally, we provide inapproximability results for the integral AEMFP. For the (fractional) concave AEMFP we state a strongly polynomial algorithm for the linear and concave piecewise polynomial deviation function case for a fixed number of homologous sets using a parametric search approach. In the equal maximum flow problem (EMFP), we aim for a maximum flow where we require the same flow value on all arcs in some given subsets of the arc set, so called homologous arc sets. In this article, we study the closely related almost equal maximum flow problems (AEMFP) where the flow values on arcs of one homologous arc set differ at most by the valuation of a so called deviation function . We prove that the integer AEMFP is in general ‐complete, and show that even the problem of finding a fractional maximum flow in the case of convex deviation functions is also ‐complete. This is in contrast to the EMFP, which is polynomial time solvable in the fractional case. Additionally, we provide inapproximability results for the integral AEMFP. For the (fractional) concave AEMFP we state a strongly polynomial algorithm for the linear and concave piecewise polynomial deviation function case for a fixed number of homologous sets using a parametric search approach. |
| Author | Haese, Rebekka Heller, Till Krumke, Sven O. |
| Author_xml | – sequence: 1 givenname: Rebekka surname: Haese fullname: Haese, Rebekka organization: Department of Mathematics Optimization Research Group, RPTU Kaiserslautern‐Landau Kaiserslautern Germany – sequence: 2 givenname: Till orcidid: 0000-0002-8227-9353 surname: Heller fullname: Heller, Till organization: Department of Optimization Fraunhofer Institute for Industrial Mathematics ITWM Kaiserslautern Germany – sequence: 3 givenname: Sven O. surname: Krumke fullname: Krumke, Sven O. organization: Department of Mathematics Optimization Research Group, RPTU Kaiserslautern‐Landau Kaiserslautern Germany |
| BookMark | eNotkE9LAzEQxYNUsK0e_AYBTx62TpL9kz2WolUoeNFzSLOJ3ZJs2iSL7bc3WmHgHebNe8xvhiaDHzRC9wQWBIA-DTotKKXQXqEpgbYpAFgzQdO84wWDsrpBsxj3AIRUhE_Ramm_fOjTzkUshw4r7w5Wn_p0xsYHnHYaS-t8TFgfR2mxk6fejQ4b67_xIfit1e4WXRtpo7771zn6fHn-WL0Wm_f122q5KRStaCpo1bUcGrpVteqkUbLpdFVq3hBJpKprzYBJ0nFWA5im5qXhTBnS5WGcKMLm6OGSm3uPo45J7P0Yhlwp8mmbnwNKs-vx4lLBxxi0EYfQOxnOgoD4ZSQyI_HHiP0AtSZbXg |
| Cites_doi | 10.1145/800133.804326 10.21236/ADA594171 10.1016/j.orl.2009.03.006 10.1287/opre.34.2.250 10.1007/s11269-010-9625-9 10.1002/net.22094 10.1007/s10479-021-04426-0 10.1016/0377-2217(88)90012-4 10.1007/3-540-45655-4_55 10.1109/SFCS.1981.11 10.1287/mnsc.45.10.1440 10.1016/S0377-2217(02)00505-2 10.1142/9789814354363_0019 |
| ContentType | Journal Article |
| Copyright | 2024. This article is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| Copyright_xml | – notice: 2024. This article is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| DBID | AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D |
| DOI | 10.1002/net.22209 |
| DatabaseName | CrossRef Computer and Information Systems Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Computer and Information Systems Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Advanced Technologies Database with Aerospace ProQuest Computer Science Collection Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Computer and Information Systems Abstracts CrossRef |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 1097-0037 |
| EndPage | 652 |
| ExternalDocumentID | 10_1002_net_22209 |
| GroupedDBID | -~X .3N .DC .GA .Y3 05W 0R~ 10A 123 1L6 1OB 1OC 1ZS 31~ 33P 3SF 3WU 4.4 4ZD 50Y 50Z 51W 51X 52M 52N 52O 52P 52S 52T 52U 52W 52X 5VS 66C 6TJ 6TU 702 7PT 8-0 8-1 8-3 8-4 8-5 8UM 930 A03 AAESR AAEVG AAHQN AAMMB AAMNL AANHP AANLZ AAONW AASGY AAXRX AAYCA AAYXX AAZKR ABCQN ABCUV ABDPE ABEFU ABEML ABIJN ACAHQ ACBWZ ACCZN ACGFS ACIWK ACPOU ACRPL ACSCC ACXBN ACXQS ACYXJ ADBBV ADEOM ADIZJ ADKYN ADMGS ADMLS ADNMO ADOZA ADZMN AEFGJ AEIGN AEIMD AENEX AEUYR AEYWJ AFBPY AFFPM AFGKR AFWVQ AFZJQ AGHNM AGQPQ AGXDD AGYGG AHBTC AIDQK AIDYY AIQQE AITYG AIURR AJXKR ALAGY ALMA_UNASSIGNED_HOLDINGS ALUQN ALVPJ AMBMR AMVHM AMYDB ARCSS ASPBG ATUGU AUFTA AVWKF AZBYB AZFZN AZVAB BAFTC BDRZF BFHJK BHBCM BMNLL BNHUX BROTX BRXPI BY8 CITATION CS3 D-E D-F DCZOG DPXWK DR2 DRFUL DRSTM DU5 EBS EJD F00 F01 F04 FEDTE FSPIC G-S G.N GODZA H.T H.X HBH HF~ HGLYW HHY HHZ HVGLF HZ~ H~9 IX1 J0M JPC KQQ LATKE LAW LC2 LC3 LEEKS LH4 LITHE LOXES LP6 LP7 LUTES LW6 LYRES M6L MEWTI MK4 MRFUL MRSTM MSFUL MSSTM MVM MXFUL MXSTM N04 N05 N9A NF~ NHB NNB O66 O8X O9- OIG P2P P2W P2X P4D PALCI PQQKQ Q.N Q11 QB0 QRW R.K RIWAO RJQFR ROL RX1 RXW SAMSI SUPJJ TAE TN5 TUS TWZ UB1 V2E W8V W99 WBKPD WH7 WIB WIH WIK WJL WOHZO WQJ WXSBR WYISQ XBAML XG1 XPP XV2 ZCA ZY4 ZZTAW ~IA ~WT 7SC 8FD JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c252t-25d98072bc6cdafca7de54e871a1ac66e303a1d83600f7684f83cf1df1d381c13 |
| ISICitedReferencesCount | 0 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001147113000001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0028-3045 |
| IngestDate | Fri Jul 25 12:22:49 EDT 2025 Sat Nov 29 04:29:59 EST 2025 |
| IsDoiOpenAccess | false |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 4 |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c252t-25d98072bc6cdafca7de54e871a1ac66e303a1d83600f7684f83cf1df1d381c13 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0002-8227-9353 |
| OpenAccessLink | https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/net.22209 |
| PQID | 3039045022 |
| PQPubID | 1016413 |
| PageCount | 11 |
| ParticipantIDs | proquest_journals_3039045022 crossref_primary_10_1002_net_22209 |
| PublicationCentury | 2000 |
| PublicationDate | 2024-06-00 20240601 |
| PublicationDateYYYYMMDD | 2024-06-01 |
| PublicationDate_xml | – month: 06 year: 2024 text: 2024-06-00 |
| PublicationDecade | 2020 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | Networks |
| PublicationYear | 2024 |
| Publisher | Wiley Subscription Services, Inc |
| Publisher_xml | – name: Wiley Subscription Services, Inc |
| References | e_1_2_8_13_1 e_1_2_8_14_1 e_1_2_8_15_1 e_1_2_8_16_1 e_1_2_8_3_1 e_1_2_8_2_1 e_1_2_8_5_1 e_1_2_8_4_1 e_1_2_8_6_1 e_1_2_8_9_1 e_1_2_8_8_1 e_1_2_8_10_1 e_1_2_8_11_1 e_1_2_8_12_1 Garey M. R. (e_1_2_8_7_1) 1979 |
| References_xml | – ident: e_1_2_8_11_1 doi: 10.1145/800133.804326 – ident: e_1_2_8_2_1 doi: 10.21236/ADA594171 – ident: e_1_2_8_13_1 doi: 10.1016/j.orl.2009.03.006 – ident: e_1_2_8_15_1 doi: 10.1287/opre.34.2.250 – ident: e_1_2_8_10_1 doi: 10.1007/s11269-010-9625-9 – ident: e_1_2_8_9_1 doi: 10.1002/net.22094 – ident: e_1_2_8_5_1 doi: 10.1007/s10479-021-04426-0 – ident: e_1_2_8_4_1 doi: 10.1016/0377-2217(88)90012-4 – ident: e_1_2_8_8_1 – ident: e_1_2_8_14_1 doi: 10.1007/3-540-45655-4_55 – volume-title: Computers and intractability year: 1979 ident: e_1_2_8_7_1 – ident: e_1_2_8_12_1 doi: 10.1109/SFCS.1981.11 – ident: e_1_2_8_3_1 doi: 10.1287/mnsc.45.10.1440 – ident: e_1_2_8_6_1 doi: 10.1016/S0377-2217(02)00505-2 – ident: e_1_2_8_16_1 doi: 10.1142/9789814354363_0019 |
| SSID | ssj0011518 |
| Score | 2.3613539 |
| Snippet | In the equal maximum flow problem (EMFP), we aim for a maximum flow where we require the same flow value on all arcs in some given subsets of the arc set, so... |
| SourceID | proquest crossref |
| SourceType | Aggregation Database Index Database |
| StartPage | 642 |
| SubjectTerms | Algorithms Deviation Homology Mathematical analysis Polynomials |
| Title | Algorithms and complexity for the almost equal maximum flow problem |
| URI | https://www.proquest.com/docview/3039045022 |
| Volume | 83 |
| WOSCitedRecordID | wos001147113000001&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 | |
| journalDatabaseRights | – providerCode: PRVWIB databaseName: Wiley Online Library - Journals customDbUrl: eissn: 1097-0037 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0011518 issn: 0028-3045 databaseCode: DRFUL dateStart: 19960101 isFulltext: true titleUrlDefault: https://onlinelibrary.wiley.com providerName: Wiley-Blackwell |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1bS-NAFB607oM-iLq7eGcQ2Zcyu8kkzeVRvCAoVSRC38I4mVmLTXpJqv35nslMLiKIPggllLS0yTlfz6XnnO8gdAw5j5TSo0Q6jiQuFw4JIBMirgT_wiVT3Ljlsgm_3w8Gg_DWlAvycp2An2XBYhFOvlXVcA6UrUZnv6Du-kPhBDwHpcMR1A7HTyn-ZPR_DBn_Y5pXM2sTRXppOjNVnMlG6TgvumJajo6wxTCdp105Gr90zXqZdsTa133ieWOqhN7FqBTz9FRb9UtRDRVGw1HdtnE1m6em_Qesavem_ScDdZtmqE-asraNpQFR9VftYbRZtRTnq6XpXSq7qxfYGHy5LSPqab4t4489zXD7ztQb6lhR_IUQxwobf1bV8Ps38cX99XUcnQ-iP5MpUZvGVEXerF1ZRivU74VgCVfO7uCNde0JYqCg4u5W91HxUVn0X_1tb6OYt068jEyiDbRuUgp8oqGwiZZEtoXWWkSTP9FpAwoMoMANKDCAAgMosAYFLkGBDSiwAgU2oPiF7i_Oo9NLYtZnEE57tCC0l4SB5dMH7vGESc78RPRcARkysxn3PAHRC7MTNcVjSVWPlYHDpZ3AA8I4bju_UScbZ2IbYW5zYXslO6VaWQchqfBCyiR1hfUQJP4OOqrEEU80S0qs-bBpDDKLS5ntoP1KULH5veQxXEMIMoZIcvfjl_fQagPMfdQpZnNxgH7w52KYzw6NDl8BrFRoIg |
| linkProvider | Wiley-Blackwell |
| 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%3Ajournal&rft.genre=article&rft.atitle=Algorithms+and+complexity+for+the+almost+equal+maximum+flow+problem&rft.jtitle=Networks&rft.au=Haese%2C+Rebekka&rft.au=Heller%2C+Till&rft.au=Krumke%2C+Sven+O&rft.date=2024-06-01&rft.pub=Wiley+Subscription+Services%2C+Inc&rft.issn=0028-3045&rft.eissn=1097-0037&rft.volume=83&rft.issue=4&rft.spage=642&rft.epage=652&rft_id=info:doi/10.1002%2Fnet.22209&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0028-3045&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0028-3045&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0028-3045&client=summon |