Extremal behavior of the Greedy algorithm for a triangle scheduling problem
We study the mixed-criticality scheduling problem, where the goal is to schedule jobs with different criticality levels on a single machine. As shown by Dürr et al. (2018), the problem can be treated as a specific 1-dimensional triangle scheduling problem. In that paper a new Greedy algorithm was de...
Uloženo v:
| Vydáno v: | Computers & operations research Ročník 169; s. 106718 |
|---|---|
| Hlavní autoři: | , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Elsevier Ltd
01.09.2024
|
| Témata: | |
| ISSN: | 0305-0548, 1873-765X |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | We study the mixed-criticality scheduling problem, where the goal is to schedule jobs with different criticality levels on a single machine. As shown by Dürr et al. (2018), the problem can be treated as a specific 1-dimensional triangle scheduling problem. In that paper a new Greedy algorithm was defined, and the authors proved that its approximation ratio lies between 1.05 and 3/2. In this paper we present a quadratic integer programming model, which can be used to computationally analyze the algorithm for inputs with small sizes. The model simulates the behavior of the algorithm and it compares the makespan with the optimal one. Using this model, we found sequences extendable to longer series, giving a lower bound of 1.27 for the Greedy algorithm. Also, the optimum on problem instances consisting of intervals of natural numbers is analyzed and a closed formula is determined. In this way, we detected two input classes where, in one of them, Greedy is far from optimal (we think that this could be the worst case), and in the other one it is optimal.
•A quadratic integer programming model for the analysis of a Greedy algorithm for triangle scheduling.•A new lower bound for the approximation ratio of the Greedy algorithm.•Analysis of the Greedy algorithm for instances consisting of intervals of natural numbers. |
|---|---|
| AbstractList | We study the mixed-criticality scheduling problem, where the goal is to schedule jobs with different criticality levels on a single machine. As shown by Dürr et al. (2018), the problem can be treated as a specific 1-dimensional triangle scheduling problem. In that paper a new Greedy algorithm was defined, and the authors proved that its approximation ratio lies between 1.05 and 3/2. In this paper we present a quadratic integer programming model, which can be used to computationally analyze the algorithm for inputs with small sizes. The model simulates the behavior of the algorithm and it compares the makespan with the optimal one. Using this model, we found sequences extendable to longer series, giving a lower bound of 1.27 for the Greedy algorithm. Also, the optimum on problem instances consisting of intervals of natural numbers is analyzed and a closed formula is determined. In this way, we detected two input classes where, in one of them, Greedy is far from optimal (we think that this could be the worst case), and in the other one it is optimal.
•A quadratic integer programming model for the analysis of a Greedy algorithm for triangle scheduling.•A new lower bound for the approximation ratio of the Greedy algorithm.•Analysis of the Greedy algorithm for instances consisting of intervals of natural numbers. |
| ArticleNumber | 106718 |
| Author | Balogh, János Békési, József Tuza, Zsolt Dósa, György Büki, Nóra |
| Author_xml | – sequence: 1 givenname: János surname: Balogh fullname: Balogh, János email: baloghj@inf.u-szeged.hu organization: Department of Computational Optimization, Faculty of Science and Informatics, University of Szeged, Árpád sqr. 2, H-6720 Szeged, Hungary – sequence: 2 givenname: József surname: Békési fullname: Békési, József email: bekesi@inf.u-szeged.hu organization: Department of Computer Algorithms and Artificial Intelligence, Faculty of Science and Informatics, University of Szeged, Árpád sqr. 2, H-6720 Szeged, Hungary – sequence: 3 givenname: Nóra orcidid: 0009-0009-6054-4687 surname: Büki fullname: Büki, Nóra email: bukinora@inf.u-szeged.hu organization: Department of Computational Optimization, Faculty of Science and Informatics, University of Szeged, Árpád sqr. 2, H-6720 Szeged, Hungary – sequence: 4 givenname: György surname: Dósa fullname: Dósa, György email: dosa.gyorgy@mik.uni-pannon.hu organization: Department of Mathematics, Faculty of Information Technology, University of Pannonia, Egyetem str. 10, H-8200 Veszprém, Hungary – sequence: 5 givenname: Zsolt surname: Tuza fullname: Tuza, Zsolt email: tuza.zsolt@mik.uni-pannon.hu organization: HUN-REN Alfréd Rényi Institute of Mathematics, Reáltanoda str. 13–15, H-1053 Budapest, Hungary |
| BookMark | eNp9kM9KAzEQh4NUsK0-gLe8wNZk_2UXT1JqFQteFLyFZDLbTcluSjYW-_ZuqScPncswv-EbmG9GJr3vkZB7zhac8fJhtwAfFilL83EuBa-uyJRXIktEWXxNyJRlrEhYkVc3ZDYMOzaWSPmUvK1-YsBOOaqxVQfrA_UNjS3SdUA0R6rc1gcb2442407RGKzqtw7pAC2ab2f7Ld0Hrx12t-S6UW7Au78-J5_Pq4_lS7J5X78unzYJZGkaE8C8LjQveAmiLEWledqYQtdpqYGpukFdG6wyA3ldMUAwegwE13XRKDQI2Zzw810IfhgCNnIfbKfCUXImTzbkTo425MmGPNsYGfGPARtVtL6PQVl3kXw8kzi-dLAY5AAWe0BjA0KUxtsL9C8t233o |
| CitedBy_id | crossref_primary_10_2478_amns_2024_2913 |
| Cites_doi | 10.1016/j.ejor.2017.03.054 10.1007/s10951-017-0533-1 10.1007/s10951-016-0468-y 10.1145/3585516 10.1016/j.ejor.2019.05.038 |
| ContentType | Journal Article |
| Copyright | 2024 |
| Copyright_xml | – notice: 2024 |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.cor.2024.106718 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Computer Science Business |
| EISSN | 1873-765X |
| ExternalDocumentID | 10_1016_j_cor_2024_106718 S0305054824001904 |
| GroupedDBID | --K --M -~X .DC .~1 0R~ 186 1B1 1OL 1RT 1~. 1~5 29F 4.4 457 4G. 5GY 5VS 6J9 7-5 71M 8P~ 9JN 9JO AAAKF AAAKG AABNK AACTN AAEDT AAEDW AAFJI AAIAV AAIKJ AAKOC AALRI AAOAW AAQXK AARIN AAXUO AAYFN AAYOK ABAOU ABBOA ABEFU ABFNM ABFRF ABJNI ABMAC ABMMH ABUCO ABXDB ACDAQ ACGFO ACGFS ACNCT ACNNM ACRLP ACZNC ADBBV ADEZE ADGUI ADJOM ADMUD AEBSH AEFWE AEHXG AEKER AENEX AFFNX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHZHX AI. AIALX AIEXJ AIGVJ AIKHN AITUG AJOXV AKRWK ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOMHK AOUOD APLSM ARUGR ASPBG AVARZ AVWKF AXJTR AZFZN BKOJK BKOMP BLXMC CS3 DU5 EBS EFJIC EJD EO8 EO9 EP2 EP3 FDB FEDTE FGOYB FIRID FNPLU FYGXN G-Q G8K GBLVA GBOLZ HAMUX HVGLF HZ~ H~9 IHE J1W KOM LY1 M41 MHUIS MO0 MS~ O-L O9- OAUVE OZT P-8 P-9 P2P PC. PQQKQ PRBVW Q38 R2- RIG ROL RPZ RXW SDF SDG SDP SDS SES SEW SPC SPCBC SSB SSD SSO SSV SSW SSZ T5K TAE TN5 U5U UAO UPT VH1 WUQ XPP ZMT ~02 ~G- 9DU AATTM AAXKI AAYWO AAYXX ABDPE ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKYEP ANKPU APXCP CITATION EFKBS EFLBG ~HD |
| ID | FETCH-LOGICAL-c322t-ce495b1516c76678b12fd5b926bc0a9feb9de83dc4980cecdbb9d71b95faedec3 |
| ISICitedReferencesCount | 0 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001255525400001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0305-0548 |
| IngestDate | Sat Nov 29 03:23:47 EST 2025 Tue Nov 18 22:12:44 EST 2025 Sat Jul 13 15:31:44 EDT 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Mixed-criticality scheduling Algorithm analysis Triangle scheduling |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c322t-ce495b1516c76678b12fd5b926bc0a9feb9de83dc4980cecdbb9d71b95faedec3 |
| ORCID | 0009-0009-6054-4687 |
| ParticipantIDs | crossref_primary_10_1016_j_cor_2024_106718 crossref_citationtrail_10_1016_j_cor_2024_106718 elsevier_sciencedirect_doi_10_1016_j_cor_2024_106718 |
| PublicationCentury | 2000 |
| PublicationDate | 2024-09-01 |
| PublicationDateYYYYMMDD | 2024-09-01 |
| PublicationDate_xml | – month: 09 year: 2024 text: 2024-09-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationTitle | Computers & operations research |
| PublicationYear | 2024 |
| Publisher | Elsevier Ltd |
| Publisher_xml | – name: Elsevier Ltd |
| References | Hanzálek, Tunys, Šucha (b6) 2016; 19 Bestuzheva, Besançon, Chen (b7) 2023; 49 Novak, Sucha, Hanzalek (b4) 2019; 279 Dürr, Hanzálek, Konrad, Seddik, Sitters, Vásquez, Woeginger (b1) 2018; 21 Seddik, Hanzálek (b5) 2017; 262 Alt, Buchin, Chaplick, Cheong, Kindermann, Knauer, Stehn (b3) 2018; 9 Burns, Davis (b2) 2017; 50 Hanzálek (10.1016/j.cor.2024.106718_b6) 2016; 19 Dürr (10.1016/j.cor.2024.106718_b1) 2018; 21 Novak (10.1016/j.cor.2024.106718_b4) 2019; 279 Alt (10.1016/j.cor.2024.106718_b3) 2018; 9 Seddik (10.1016/j.cor.2024.106718_b5) 2017; 262 Burns (10.1016/j.cor.2024.106718_b2) 2017; 50 Bestuzheva (10.1016/j.cor.2024.106718_b7) 2023; 49 |
| References_xml | – volume: 50 start-page: ARTICLE 82 year: 2017 ident: b2 article-title: A survey of research into mixed criticality systems publication-title: ACM Comput. Surv. – volume: 19 start-page: 601 year: 2016 end-page: 607 ident: b6 article-title: An analysis of the non-preemptive mixed-criticality match-up scheduling problem publication-title: J. Sched. – volume: 9 start-page: 312 year: 2018 end-page: 327 ident: b3 article-title: Placing your coins on a shelf publication-title: J. Comput. Geom. – volume: 21 start-page: 305 year: 2018 end-page: 312 ident: b1 article-title: The triangle scheduling problem publication-title: J. Sched. – volume: 262 start-page: 46 year: 2017 end-page: 59 ident: b5 article-title: Match-up scheduling of mixed-criticality jobs: Maximizing the probability of jobs execution publication-title: European J. Oper. Res. – volume: 279 start-page: 687 year: 2019 end-page: 703 ident: b4 article-title: Scheduling with uncertain processing times in mixed-criticality systems publication-title: European J. Oper. Res. – volume: 49 start-page: 1 year: 2023 end-page: 21 ident: b7 article-title: Enabling research through the SCIP optimization suite 8.0 publication-title: ACM Trans. Math. Software – volume: 262 start-page: 46 issue: 1 year: 2017 ident: 10.1016/j.cor.2024.106718_b5 article-title: Match-up scheduling of mixed-criticality jobs: Maximizing the probability of jobs execution publication-title: European J. Oper. Res. doi: 10.1016/j.ejor.2017.03.054 – volume: 21 start-page: 305 year: 2018 ident: 10.1016/j.cor.2024.106718_b1 article-title: The triangle scheduling problem publication-title: J. Sched. doi: 10.1007/s10951-017-0533-1 – volume: 9 start-page: 312 issue: 1 year: 2018 ident: 10.1016/j.cor.2024.106718_b3 article-title: Placing your coins on a shelf publication-title: J. Comput. Geom. – volume: 19 start-page: 601 issue: 5 year: 2016 ident: 10.1016/j.cor.2024.106718_b6 article-title: An analysis of the non-preemptive mixed-criticality match-up scheduling problem publication-title: J. Sched. doi: 10.1007/s10951-016-0468-y – volume: 49 start-page: 1 issue: 2 year: 2023 ident: 10.1016/j.cor.2024.106718_b7 article-title: Enabling research through the SCIP optimization suite 8.0 publication-title: ACM Trans. Math. Software doi: 10.1145/3585516 – volume: 50 start-page: ARTICLE 82 issue: 6 year: 2017 ident: 10.1016/j.cor.2024.106718_b2 article-title: A survey of research into mixed criticality systems publication-title: ACM Comput. Surv. – volume: 279 start-page: 687 issue: 3 year: 2019 ident: 10.1016/j.cor.2024.106718_b4 article-title: Scheduling with uncertain processing times in mixed-criticality systems publication-title: European J. Oper. Res. doi: 10.1016/j.ejor.2019.05.038 |
| SSID | ssj0000721 |
| Score | 2.4366727 |
| Snippet | We study the mixed-criticality scheduling problem, where the goal is to schedule jobs with different criticality levels on a single machine. As shown by Dürr... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 106718 |
| SubjectTerms | Algorithm analysis Mixed-criticality scheduling Triangle scheduling |
| Title | Extremal behavior of the Greedy algorithm for a triangle scheduling problem |
| URI | https://dx.doi.org/10.1016/j.cor.2024.106718 |
| Volume | 169 |
| WOSCitedRecordID | wos001255525400001&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: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1873-765X dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000721 issn: 0305-0548 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1bb9MwFLbKhtB44FJAGzf5gSeqTLk4cfK4jnIZUoXEkPoWxY49OrqkSsLU8Rv40Rzf0pabAImXtHXtuvL5dPz5-FwQeiYDGaWxiIC5ydQjIiEeKyj3goJkFBhxRCKpi03Q6TSdzbJ3g8FXFwtzuaBVla5W2fK_ihraQNgqdPYvxN3_KDTAexA6PEHs8PwjwU9WXSMuYOVdBL5zA1AuNuXVqFic1c28-3hhHChHqm5HdbYQIzjnwr5jw9N1mZlN5urKP7QaLPVSNNaJzqYL6s3KY2UO0saaE30LH1T12hRv7uU_mZd23vcaR19aIbe6jY9NRe2p-b7p948XpqHVtPfVlf6UNPZuwBowQtJ7aFmrmousWbsx6Wgu5VQYmyych8Io55QCppJ4tqW9TaWXH3YCY5Q4B0GqrK8hOVS58qyq306w_V7NpaZS7rTAj8g1tBvSOAM1v3v0ZjI7We_sVMfx9f_N3ZJrf8HvJvo5z9ngLqd30C176MBHBix30UBUQ3TDxTwM0W0nXGxV_RDd3EhUeQ-9daDCDlS4lhhAhQ2ocA8qDKDCBXagwmtQYQuq--jDy8np8WvPluHwOGj7zuMCDtEMmGHCaQLchgWhLGOWhQnjfpFJwbJSpFHJSZb6XPCSQQMNWBbLQpSCRw_QTlVXYh_hxOdFkQpfxpFPijJknPAyLglnKRdUhgfId4uWc5ujXpVKWeTOGfE8h3XO1TrnZp0P0PN-yNIkaPldZ-IkkVuGaZhjDrD59bCH_zbsEdpb4_0x2umaz-IJus4vu3nbPLXg-gYAI5oO |
| linkProvider | Elsevier |
| 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=Extremal+behavior+of+the+Greedy+algorithm+for+a+triangle+scheduling+problem&rft.jtitle=Computers+%26+operations+research&rft.au=Balogh%2C+J%C3%A1nos&rft.au=B%C3%A9k%C3%A9si%2C+J%C3%B3zsef&rft.au=B%C3%BCki%2C+N%C3%B3ra&rft.au=D%C3%B3sa%2C+Gy%C3%B6rgy&rft.date=2024-09-01&rft.pub=Elsevier+Ltd&rft.issn=0305-0548&rft.eissn=1873-765X&rft.volume=169&rft_id=info:doi/10.1016%2Fj.cor.2024.106718&rft.externalDocID=S0305054824001904 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0305-0548&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0305-0548&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0305-0548&client=summon |