Faster Minimization of Tardy Processing Time on a Single Machine

This paper is concerned with the 1 | | ∑ p j U j problem, the problem of minimizing the total processing time of tardy jobs on a single machine. This is not only a fundamental scheduling problem, but also an important problem from a theoretical point of view as it generalizes the Subset Sum problem...

Full description

Saved in:

Bibliographic Details
Published in:	Algorithmica Vol. 84; no. 5; pp. 1341 - 1356
Main Authors:	Bringmann, Karl, Fischer, Nick, Hermelin, Danny, Shabtay, Dvir, Wellnitz, Philip
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.05.2022 Springer Nature B.V
Subjects:	Algorithm Analysis and Problem Complexity Algorithms Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Integers Knapsack problem Mathematics of Computing Multiplication Polynomials Run time (computers) Theory of Computation Tardy processing time min)-Convolution max Single machine scheduling Pseudo-polynomial time algorithm Fast polynomial multiplication
ISSN:	0178-4617, 1432-0541
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Abstract	This paper is concerned with the 1 \| \| ∑ p j U j problem, the problem of minimizing the total processing time of tardy jobs on a single machine. This is not only a fundamental scheduling problem, but also an important problem from a theoretical point of view as it generalizes the Subset Sum problem and is closely related to the 0/1-Knapsack problem. The problem is well-known to be NP-hard, but only in a weak sense, meaning it admits pseudo-polynomial time algorithms. The best known running time follows from the famous Lawler and Moore algorithm that solves a more general weighted version in O ( P · n ) time, where P is the total processing time of all n jobs in the input. This algorithm has been developed in the late 60s, and has yet to be improved to date. In this paper we develop two new algorithms for problem, each improving on Lawler and Moore’s algorithm in a different scenario. Our first algorithm runs in O ~ ( P 7 / 4 ) time, and outperforms Lawler and Moore’s algorithm in instances where n = ω ~ ( P 3 / 4 ) . Our second algorithm runs in O ~ ( min { P · D # , P + D } ) time, where D # is the number of different due dates in the instance, and D is the sum of all different due dates. This algorithm improves on Lawler and Moore’s algorithm when n = ω ~ ( D # ) or n = ω ~ ( D / P ) . Further, it extends the known O ~ ( P ) algorithm for the single due date special case of 1 \| \| ∑ p j U j in a natural way. Both algorithms rely on basic primitive operations between sets of integers and vectors of integers for the speedup in their running times. The second algorithm relies on fast polynomial multiplication as its main engine, and can be easily extended to the case of a fixed number of machines. For the first algorithm we define a new “skewed” version of ( max , min ) -Convolution which is interesting in its own right.
AbstractList	This paper is concerned with the 1\|\|∑pjUj problem, the problem of minimizing the total processing time of tardy jobs on a single machine. This is not only a fundamental scheduling problem, but also an important problem from a theoretical point of view as it generalizes the Subset Sum problem and is closely related to the 0/1-Knapsack problem. The problem is well-known to be NP-hard, but only in a weak sense, meaning it admits pseudo-polynomial time algorithms. The best known running time follows from the famous Lawler and Moore algorithm that solves a more general weighted version in O(P·n) time, where P is the total processing time of all n jobs in the input. This algorithm has been developed in the late 60s, and has yet to be improved to date. In this paper we develop two new algorithms for problem, each improving on Lawler and Moore’s algorithm in a different scenario.Our first algorithm runs in O~(P7/4) time, and outperforms Lawler and Moore’s algorithm in instances where n=ω~(P3/4).Our second algorithm runs in O~(min{P·D#,P+D}) time, where D# is the number of different due dates in the instance, and D is the sum of all different due dates. This algorithm improves on Lawler and Moore’s algorithm when n=ω~(D#) or n=ω~(D/P). Further, it extends the known O~(P) algorithm for the single due date special case of 1\|\|∑pjUj in a natural way. Both algorithms rely on basic primitive operations between sets of integers and vectors of integers for the speedup in their running times. The second algorithm relies on fast polynomial multiplication as its main engine, and can be easily extended to the case of a fixed number of machines. For the first algorithm we define a new “skewed” version of (max,min)-Convolution which is interesting in its own right. This paper is concerned with the 1 \| \| ∑ p j U j problem, the problem of minimizing the total processing time of tardy jobs on a single machine. This is not only a fundamental scheduling problem, but also an important problem from a theoretical point of view as it generalizes the Subset Sum problem and is closely related to the 0/1-Knapsack problem. The problem is well-known to be NP-hard, but only in a weak sense, meaning it admits pseudo-polynomial time algorithms. The best known running time follows from the famous Lawler and Moore algorithm that solves a more general weighted version in O ( P · n ) time, where P is the total processing time of all n jobs in the input. This algorithm has been developed in the late 60s, and has yet to be improved to date. In this paper we develop two new algorithms for problem, each improving on Lawler and Moore’s algorithm in a different scenario. Our first algorithm runs in O ~ ( P 7 / 4 ) time, and outperforms Lawler and Moore’s algorithm in instances where n = ω ~ ( P 3 / 4 ) . Our second algorithm runs in O ~ ( min { P · D # , P + D } ) time, where D # is the number of different due dates in the instance, and D is the sum of all different due dates. This algorithm improves on Lawler and Moore’s algorithm when n = ω ~ ( D # ) or n = ω ~ ( D / P ) . Further, it extends the known O ~ ( P ) algorithm for the single due date special case of 1 \| \| ∑ p j U j in a natural way. Both algorithms rely on basic primitive operations between sets of integers and vectors of integers for the speedup in their running times. The second algorithm relies on fast polynomial multiplication as its main engine, and can be easily extended to the case of a fixed number of machines. For the first algorithm we define a new “skewed” version of ( max , min ) -Convolution which is interesting in its own right.
Author	Hermelin, Danny Fischer, Nick Bringmann, Karl Wellnitz, Philip Shabtay, Dvir
Author_xml	– sequence: 1 givenname: Karl surname: Bringmann fullname: Bringmann, Karl organization: Saarland University, Saarland Informatics Campus (SIC), Max Planck Institute for Informatics, Saarland Informatics Campus (SIC) – sequence: 2 givenname: Nick surname: Fischer fullname: Fischer, Nick organization: Saarland University, Saarland Informatics Campus (SIC), Max Planck Institute for Informatics, Saarland Informatics Campus (SIC) – sequence: 3 givenname: Danny surname: Hermelin fullname: Hermelin, Danny organization: Department of Industrial Engineering and Management, Ben-Gurion University of the Negev – sequence: 4 givenname: Dvir surname: Shabtay fullname: Shabtay, Dvir email: dvirs@bgu.ac.il organization: Department of Industrial Engineering and Management, Ben-Gurion University of the Negev – sequence: 5 givenname: Philip surname: Wellnitz fullname: Wellnitz, Philip organization: Max Planck Institute for Informatics, Saarland Informatics Campus (SIC)
BookMark	eNp9kE9LAzEQxYMo2Fa_gKeA59X82yS9KcWq0KJgPYfs7qSmtNmabCn10xtbQfDQ0zDM-828eX10GtoACF1RckMJUbeJEFHygjBWEDJkutieoB4VPLeloKeoR6jShZBUnaN-SgtCKFND2UN3Y5s6iHjqg1_5L9v5NuDW4ZmNzQ6_xraGlHyY45lfAc4zi99yuwQ8tfWHD3CBzpxdJrj8rQP0Pn6YjZ6Kycvj8-h-UtRc8q6oKqKFglpV2inZNIqWwjnQQjSV4LKRwjYlgaqhTDonrK60cDU4KLmA7JQP0PVh7zq2nxtInVm0mxjyScNkKTUbCsaySh9UdWxTiuBM7bv9U120fmkoMT95mUNeJudl9nmZbUbZP3Qd_crG3XGIH6CUxWEO8c_VEeobgi5_4w
CitedBy_id	crossref_primary_10_1007_s00453_023_01176_2
Cites_doi	10.1007/978-1-4684-2001-2_9 10.1137/1.9781611975482.3 10.1109/SFCS.1989.63475 10.1137/0117039 10.1006/jsco.1994.1042 10.1145/3293465 10.1137/1.9781611974782.69 10.1287/mnsc.16.1.77 10.1137/1.9781611974782.68
ContentType	Journal Article
Copyright	The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022.
Copyright_xml	– notice: The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 – notice: The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022.
DBID	AAYXX CITATION JQ2
DOI	10.1007/s00453-022-00928-w
DatabaseName	CrossRef ProQuest Computer Science Collection
DatabaseTitle	CrossRef ProQuest Computer Science Collection
DatabaseTitleList	ProQuest Computer Science Collection
DeliveryMethod	fulltext_linktorsrc
Discipline	Computer Science
EISSN	1432-0541
EndPage	1356
ExternalDocumentID	10_1007_s00453_022_00928_w
GrantInformation_xml	– fundername: FP7 Ideas: European Research Council grantid: 850979 funderid: http://dx.doi.org/10.13039/100011199 – fundername: Israel Science Foundation grantid: 1070/20) funderid: http://dx.doi.org/10.13039/501100003977
GroupedDBID	-4Z -59 -5G -BR -EM -Y2 -~C -~X .86 .DC .VR 06D 0R~ 0VY 199 1N0 1SB 203 23M 28- 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 78A 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AAOBN AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDPE ABDZT ABECU ABFSI ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABLJU ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTAH ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFGCZ AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AI. AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BBWZM BDATZ BGNMA BSONS CAG COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP E.L EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ H~9 I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV KOW LAS LLZTM M4Y MA- N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM P19 P9O PF- PT4 PT5 QOK QOS R4E R89 R9I RHV RIG RNI RNS ROL RPX RSV RZK S16 S1Z S26 S27 S28 S3B SAP SCJ SCLPG SCO SDH SDM SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TN5 TSG TSK TSV TUC U2A UG4 UOJIU UQL UTJUX UZXMN VC2 VFIZW VH1 VXZ W23 W48 WK8 YLTOR Z45 Z7X Z83 Z88 Z8R Z8W Z92 ZMTXR ZY4 ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP ATHPR AYFIA CITATION JQ2
ID	FETCH-LOGICAL-c363t-bb0847ec7b8f76dd7154ffe844db436d64ad50ebd126ff4a8b84fcefe534e7963
IEDL.DBID	RSV
ISICitedReferencesCount	7
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000749006400001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0178-4617
IngestDate	Thu Oct 02 15:07:04 EDT 2025 Sat Nov 29 02:20:32 EST 2025 Tue Nov 18 22:33:02 EST 2025 Fri Feb 21 02:45:57 EST 2025
IsDoiOpenAccess	false
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Issue	5
Keywords	Tardy processing time min)-Convolution max Single machine scheduling Pseudo-polynomial time algorithm Fast polynomial multiplication
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c363t-bb0847ec7b8f76dd7154ffe844db436d64ad50ebd126ff4a8b84fcefe534e7963
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
OpenAccessLink	http://hdl.handle.net/21.11116/0000-0007-287E-0
PQID	2656829422
PQPubID	2043795
PageCount	16
ParticipantIDs	proquest_journals_2656829422 crossref_citationtrail_10_1007_s00453_022_00928_w crossref_primary_10_1007_s00453_022_00928_w springer_journals_10_1007_s00453_022_00928_w
PublicationCentury	2000
PublicationDate	2022-05-01
PublicationDateYYYYMMDD	2022-05-01
PublicationDate_xml	– month: 05 year: 2022 text: 2022-05-01 day: 01
PublicationDecade	2020
PublicationPlace	New York
PublicationPlace_xml	– name: New York
PublicationTitle	Algorithmica
PublicationTitleAbbrev	Algorithmica
PublicationYear	2022
Publisher	Springer US Springer Nature B.V
Publisher_xml	– name: Springer US – name: Springer Nature B.V
References	Karp, R.M.: Reducibility among combinatorial problems. In: Complexity of Computer Computations, pp. 85–103. Springer, Berlin (1972) Bringmann, K.: A near-linear pseudopolynomial time algorithm for subset sum. In: Proceedings of the 28th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1073–1084 (2017) Abboud, A., Bringmann, K., Hermelin, D., Shabtay, D.: SETH-based lower bounds for subset sum and bicriteria path. In: Proceedings of of the 30th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 41–57 (2019) Künnemann, M., Paturi, R., Schneider, S.: On the fine-grained complexity of one-dimensional dynamic programming. In: Proceedings of the 44th International Colloquium on Automata, Languages, and Programming (ICALP), pp. 21:1–21:15 (2017) PanVictor YSimple multivariate polynomial multiplicationJ. Symb. Comput.1994183183186131813310.1006/jsco.1994.1042 CyganMarekMuchaMarcinWegrzyckiKarolWlodarczykMichalOn problems equivalent to (min, +)-convolutionACM Trans. Algorithms201915114:114:2510.1145/3293465 CormenThomas HLeisersonCharles ERivestRonald LSteinCliffordIntroduction to Algorithms20093CambridgeThe MIT Press1187.68679 GrahamRonald LBounds on multiprocessing timing anomaliesSIAM J. Appl. Math.196917241642924921410.1137/0117039 Kosaraju, S.R.: Efficient tree pattern matching. In: Proceedings of the 30th annual symposium on Foundations Of Computer Science (FOCS), pp. 178–183 (1989) Koiliaris, K., Xu, C.: A faster pseudopolynomial time algorithm for subset sum. In: Proceedings of the 28th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1062–1072 (2017) LawlerEugene LMooreJames MA functional equation and its application to resource allocation and sequencing problemsManage. Sci.1969161778410.1287/mnsc.16.1.77 928_CR6 928_CR1 928_CR2 Ronald L Graham (928_CR5) 1969; 17 Thomas H Cormen (928_CR3) 2009 Victor Y Pan (928_CR11) 1994; 18 Marek Cygan (928_CR4) 2019; 15 Eugene L Lawler (928_CR10) 1969; 16 928_CR9 928_CR7 928_CR8
References_xml	– reference: Karp, R.M.: Reducibility among combinatorial problems. In: Complexity of Computer Computations, pp. 85–103. Springer, Berlin (1972) – reference: CyganMarekMuchaMarcinWegrzyckiKarolWlodarczykMichalOn problems equivalent to (min, +)-convolutionACM Trans. Algorithms201915114:114:2510.1145/3293465 – reference: Künnemann, M., Paturi, R., Schneider, S.: On the fine-grained complexity of one-dimensional dynamic programming. In: Proceedings of the 44th International Colloquium on Automata, Languages, and Programming (ICALP), pp. 21:1–21:15 (2017) – reference: GrahamRonald LBounds on multiprocessing timing anomaliesSIAM J. Appl. Math.196917241642924921410.1137/0117039 – reference: CormenThomas HLeisersonCharles ERivestRonald LSteinCliffordIntroduction to Algorithms20093CambridgeThe MIT Press1187.68679 – reference: Koiliaris, K., Xu, C.: A faster pseudopolynomial time algorithm for subset sum. In: Proceedings of the 28th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1062–1072 (2017) – reference: LawlerEugene LMooreJames MA functional equation and its application to resource allocation and sequencing problemsManage. Sci.1969161778410.1287/mnsc.16.1.77 – reference: Abboud, A., Bringmann, K., Hermelin, D., Shabtay, D.: SETH-based lower bounds for subset sum and bicriteria path. In: Proceedings of of the 30th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 41–57 (2019) – reference: Kosaraju, S.R.: Efficient tree pattern matching. In: Proceedings of the 30th annual symposium on Foundations Of Computer Science (FOCS), pp. 178–183 (1989) – reference: PanVictor YSimple multivariate polynomial multiplicationJ. Symb. Comput.1994183183186131813310.1006/jsco.1994.1042 – reference: Bringmann, K.: A near-linear pseudopolynomial time algorithm for subset sum. In: Proceedings of the 28th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1073–1084 (2017) – volume-title: Introduction to Algorithms year: 2009 ident: 928_CR3 – ident: 928_CR6 doi: 10.1007/978-1-4684-2001-2_9 – ident: 928_CR1 doi: 10.1137/1.9781611975482.3 – ident: 928_CR8 doi: 10.1109/SFCS.1989.63475 – volume: 17 start-page: 416 issue: 2 year: 1969 ident: 928_CR5 publication-title: SIAM J. Appl. Math. doi: 10.1137/0117039 – volume: 18 start-page: 183 issue: 3 year: 1994 ident: 928_CR11 publication-title: J. Symb. Comput. doi: 10.1006/jsco.1994.1042 – ident: 928_CR9 – volume: 15 start-page: 14:1 issue: 1 year: 2019 ident: 928_CR4 publication-title: ACM Trans. Algorithms doi: 10.1145/3293465 – ident: 928_CR2 doi: 10.1137/1.9781611974782.69 – volume: 16 start-page: 77 issue: 1 year: 1969 ident: 928_CR10 publication-title: Manage. Sci. doi: 10.1287/mnsc.16.1.77 – ident: 928_CR7 doi: 10.1137/1.9781611974782.68
SSID	ssj0012796
Score	2.4154758
Snippet	This paper is concerned with the 1 \| \| ∑ p j U j problem, the problem of minimizing the total processing time of tardy jobs on a single machine. This is not... This paper is concerned with the 1\|\|∑pjUj problem, the problem of minimizing the total processing time of tardy jobs on a single machine. This is not only a...
SourceID	proquest crossref springer
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	1341
SubjectTerms	Algorithm Analysis and Problem Complexity Algorithms Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Integers Knapsack problem Mathematics of Computing Multiplication Polynomials Run time (computers) Theory of Computation
Title	Faster Minimization of Tardy Processing Time on a Single Machine
URI	https://link.springer.com/article/10.1007/s00453-022-00928-w https://www.proquest.com/docview/2656829422
Volume	84
WOSCitedRecordID	wos000749006400001&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: PRVAVX databaseName: Springer LINK customDbUrl: eissn: 1432-0541 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0012796 issn: 0178-4617 databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LSwMxEA5aPXixPrFaJQdvGthm02xyU8TiwRaxVXpb8oRC3Upb7d83SbNbFBX0uOS1zGR2vmXmmwHgnKUplypTyHKSICKUQkJwgXDGqUPAlFgZirjeZ70eGw75QySFzcps9zIkGb7UFdnNow8fc8TIFwpiaLEONpy7Y94cH_vPVezAHxMSF93_EXEOOlJlvt_jsztaYcwvYdHgbTr1_73nDtiO6BJeL6_DLlgzxR6ol50bYDTkfXDVEb5AAuyOitFLZGLCiYUDH8eHkTzgDoWeIQLdmIB99zg2sBuSL80BeOrcDm7uUOylgFRK0zmSMnF-yKhMMptRrTMHnaw1jBAtSUo1JUK3EyN1C1NriWCSEauMNe2UGCfQ9BDUiklhjgBUCuOW0ZprpklKFFesbVoOKVqKE250A7RKkeYqFhr3_S7GeVUiOYgodyLKg4jyRQNcVGtel2U2fp3dLDWVR5Ob5dghU4Y5wbgBLkvNrIZ_3u34b9NPwBYOyvVJj01Qm0_fzCnYVO_z0Wx6Fq7iB1Kp2Eg
linkProvider	Springer Nature
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1bS8MwFD7oFPTFecXp1Dz4poEtzdrkTRHHxG2Im7K30uYCg9nJNt3fN8nSDkUFfSy5lXOSnq-c830BOGdBwFMRCaw5rWGaCIGThCeYRDw0CDikOnUiru2o22WDAX_wpLBpXu2epyTdl7ogu1n0YXOOBFuhIIbnq7BGTcSyhXyPvecid2CXcYWL5v-ImgDtqTLfz_E5HC0x5pe0qIs2zfL_3nMbtjy6RNeL7bADKyrbhXJ-cwPyB3kPrpqJFUhAnWE2fPFMTDTWqG_z-MiTB8yiyDJEkGlLUM88jhTquOJLtQ9Pzdv-TQv7uxSwCMJghtO0ZuKQElHKdBRKGRnopLVilMqUBqEMaSIbNZXKOgm1pglLGdVCadUIqDIGDQ6glI0zdQhICELqSkoumaQBFVywhqobpKhDUuNKVqCemzQWXmjc3ncxiguJZGei2JgodiaK5xW4KMa8LmQ2fu1dzT0V-yM3jYlBpoxwSkgFLnPPLJt_nu3ob93PYKPV77Tj9l33_hg2iXO0LYCsQmk2eVMnsC7eZ8Pp5NRtyw9_Qtss
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LTwIxEJ4oGuNFfEYUtQdv2sB2y25706hEIxAS0HDb7PaRkOBCAOXv25ZdUKMmxuOmj22mbeZrZr5vAM6Z7_NEhAJrTquYxkLgOOYxJiEPDAIOqE6ciGsjbLVYr8fbH1j8Lts9D0nOOQ1WpSmdVkZSVxbEN4tEbPyRYCsaxPBsFdaoLRpk3-ud50Ucwf7SJTGatxI1zjqjzXw_x2fXtMSbX0KkzvPUi_9f8zZsZagTXc-PyQ6sqHQXinlFB5Rd8D24qsdWOAE1-2n_JWNooqFGXRvfRxmpwCwAWeYIMm0x6pjPgUJNl5Sp9uGpfte9ucdZjQUs_MCf4iSpGv-kRJgwHQZShgZSaa0YpTKhfiADGstaVSXSI4HWNGYJo1oorWo-Vca4_gEU0mGqDgEJQYinpOSSSepTwQWrKc8gSB2QKleyBF5u3khkAuS2DsYgWkgnOxNFxkSRM1E0K8HFYsxoLr_xa-9yvmtRdhUnETGIlRFOCSnBZb5Ly-afZzv6W_cz2Gjf1qPGQ-vxGDaJ22ebF1mGwnT8qk5gXbxN-5PxqTuh72D15BA
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=Faster+Minimization+of+Tardy+Processing+Time+on+a+Single+Machine&rft.jtitle=Algorithmica&rft.au=Bringmann%2C+Karl&rft.au=Fischer%2C+Nick&rft.au=Hermelin%2C+Danny&rft.au=Shabtay%2C+Dvir&rft.date=2022-05-01&rft.pub=Springer+US&rft.issn=0178-4617&rft.eissn=1432-0541&rft.volume=84&rft.issue=5&rft.spage=1341&rft.epage=1356&rft_id=info:doi/10.1007%2Fs00453-022-00928-w&rft.externalDocID=10_1007_s00453_022_00928_w
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0178-4617&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0178-4617&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0178-4617&client=summon