Exact and approximation algorithms for covering timeline in temporal graphs

We consider a variant of vertex cover on temporal graphs that has been recently defined for summarization of timeline activities in temporal graphs. The problem has been proved to be NP-hard, even for several restrictions of the time domain and vertex degree. We present novel algorithmic contributio...

Celý popis

Uloženo v:

Podrobná bibliografie
Vydáno v:	Annals of operations research Ročník 351; číslo 1; s. 609 - 628
Hlavní autoři:	Dondi, Riccardo, Popa, Alexandru
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.08.2025 Springer Nature B.V
Témata:	Algorithms Apexes Approximation Business and Management Combinatorics Graph theory Graphs Linear programming Operations Research/Decision Theory Original Research Theory of Computation Timeline cover Temporal graph FPT algorithm NP-hard problem Approximation algorithm
ISSN:	0254-5330, 1572-9338
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

Abstract	We consider a variant of vertex cover on temporal graphs that has been recently defined for summarization of timeline activities in temporal graphs. The problem has been proved to be NP-hard, even for several restrictions of the time domain and vertex degree. We present novel algorithmic contributions for the problem and we give an approximation algorithm of factor O ( T log n ) , on a temporal graph of T timestamps and n vertices. We focus then on the NP-hard restriction of the problem, where at most one temporal edge is defined in each timestamp. For this restriction we present a 4 ( T - 1 ) approximation algorithm and a parameterized algorithm (a reduction to kernel) for parameter the cost, called span, of the solution.
AbstractList	We consider a variant of vertex cover on temporal graphs that has been recently defined for summarization of timeline activities in temporal graphs. The problem has been proved to be NP-hard, even for several restrictions of the time domain and vertex degree. We present novel algorithmic contributions for the problem and we give an approximation algorithm of factor O(Tlogn), on a temporal graph of T timestamps and n vertices. We focus then on the NP-hard restriction of the problem, where at most one temporal edge is defined in each timestamp. For this restriction we present a 4(T-1) approximation algorithm and a parameterized algorithm (a reduction to kernel) for parameter the cost, called span, of the solution. We consider a variant of vertex cover on temporal graphs that has been recently defined for summarization of timeline activities in temporal graphs. The problem has been proved to be NP-hard, even for several restrictions of the time domain and vertex degree. We present novel algorithmic contributions for the problem and we give an approximation algorithm of factor O ( T log n ) , on a temporal graph of T timestamps and n vertices. We focus then on the NP-hard restriction of the problem, where at most one temporal edge is defined in each timestamp. For this restriction we present a 4 ( T - 1 ) approximation algorithm and a parameterized algorithm (a reduction to kernel) for parameter the cost, called span, of the solution. We consider a variant of vertex cover on temporal graphs that has been recently defined for summarization of timeline activities in temporal graphs. The problem has been proved to be NP-hard, even for several restrictions of the time domain and vertex degree. We present novel algorithmic contributions for the problem and we give an approximation algorithm of factor $$O(T \log {n})$$ O ( T log n ) , on a temporal graph of T timestamps and n vertices. We focus then on the NP-hard restriction of the problem, where at most one temporal edge is defined in each timestamp. For this restriction we present a $$4(T-1)$$ 4 ( T - 1 ) approximation algorithm and a parameterized algorithm (a reduction to kernel) for parameter the cost, called span, of the solution.
Author	Dondi, Riccardo Popa, Alexandru
Author_xml	– sequence: 1 givenname: Riccardo orcidid: 0000-0002-6124-2965 surname: Dondi fullname: Dondi, Riccardo email: riccardo.dondi@unibg.it organization: Dipartimento di Lettere, Filosofia, Comunicazione, Università degli Studi di Bergamo – sequence: 2 givenname: Alexandru surname: Popa fullname: Popa, Alexandru email: alexandru.popa@fmi.unibuc.ro organization: Department of Computer Science, University of Bucharest
BookMark	eNp9kF1LwzAUhoNMcJv-Aa8CXldPkqZtLmXMDxS80euQZsmW0TY1yWT-e7tVELwYHDg373M-nhmadL4zCF0TuCUA5V0kkJciA5pnwIVgWXWGpoSXNBOMVRM0BcrzjDMGF2gW4xYACKn4FL0s90onrLoVVn0f_N61KjnfYdWsfXBp00ZsfcDaf5ngujVOrjWN6wx2HU6m7X1QDV4H1W_iJTq3qonm6rfP0cfD8n3xlL2-PT4v7l8zzQqWsgKgsloxbVe5NtbQoaiwPDdQGsprBkqxulbEELKqgCpTFFYZkWvBal4JNkc349zh3s-diUlu_S50w0rJKOOEFiIvh1Q1pnTwMQZjpXbp-FsKyjWSgDyok6M6OaiTR3WyGlD6D-3D4CV8n4bYCMX-IMqEv6tOUD-c5YSn
CitedBy_id	crossref_primary_10_3390_a18020113
Cites_doi	10.1016/J.TCS.2023.114040 10.14778/2732939.2732945 10.1007/s00453-022-01018-7 10.1007/s10115-019-01403-9 10.1007/978-3-031-34347-6_15 10.1007/s42979-021-00593-w 10.1137/S0895480196305124 10.1007/s00224-023-10150-y 10.1007/978-3-030-79987-8_34 10.1016/j.tcs.2019.03.031 10.1007/s10618-020-00717-5 10.1137/0211045 10.1016/0004-3702(95)00004-6 10.1609/aaai.v36i9.21259 10.1109/TKDE.2016.2594065 10.1007/978-3-030-23495-9_1 10.1006/jcss.2002.1829 10.1016/j.jcss.2021.04.001 10.1137/1.9781611974331.CH80 10.1016/j.jcss.2019.07.006 10.4230/LIPICS.IPEC.2023.12 10.1140/epjb/e2015-60657-4 10.1145/1597036.1597045 10.1016/j.jcss.2021.01.005 10.1080/15427951.2016.1177801 10.1145/1060590.1060675 10.1016/j.jcss.2019.08.002
ContentType	Journal Article
Copyright	The Author(s) 2024 The Author(s) 2024. This work 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: The Author(s) 2024 – notice: The Author(s) 2024. This work 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	C6C AAYXX CITATION 7TA 7TB 8FD FR3 JG9 JQ2 KR7
DOI	10.1007/s10479-024-05993-8
DatabaseName	Springer Nature OA Free Journals CrossRef Materials Business File Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database Materials Research Database ProQuest Computer Science Collection Civil Engineering Abstracts
DatabaseTitle	CrossRef Materials Research Database Civil Engineering Abstracts Technology Research Database Mechanical & Transportation Engineering Abstracts ProQuest Computer Science Collection Engineering Research Database Materials Business File
DatabaseTitleList	Materials Research Database CrossRef
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering Computer Science Business
EISSN	1572-9338
EndPage	628
ExternalDocumentID	10_1007_s10479_024_05993_8
GrantInformation_xml	– fundername: Ministerul Cercetǎrii, Inovarii çi Digitalizǎrii grantid: PN-III-P1-1.1-TE-2021-0253 funderid: http://dx.doi.org/10.13039/100018987
GroupedDBID	-Y2 -~C -~X .4S .86 .DC .VR 06D 0R~ 0VY 1N0 1SB 2.D 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 7WY 88I 8AO 8FE 8FG 8FL 8TC 8VB 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AAPKM AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBRH ABBXA ABDBE ABDZT ABECU ABFSG ABFTV ABHLI ABHQN ABJCF ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABRTQ ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABUWG ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACGOD ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSTC ACZOJ ADHHG ADHIR ADHKG ADIMF ADKFA ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AEZWR AFBBN AFDZB AFEXP AFGCZ AFHIU AFKRA AFLOW AFOHR AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGQPQ AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHPBZ AHQJS AHSBF AHWEU AHYZX AIAKS AIGIU AIIXL AILAN AITGF AIXLP AJBLW AJRNO AJZVZ AKVCP ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMVHM AMXSW AMYLF AMYQR AOCGG ARAPS ARCSS ARMRJ ASPBG ATHPR AVWKF AXYYD AYFIA AYQZM AZFZN AZQEC B-. BA0 BAPOH BBWZM BDATZ BENPR BEZIV BGLVJ BGNMA BPHCQ BSONS C6C CAG CCPQU COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DWQXO EBLON EBO EBS EBU EDO EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRNLG FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNUQQ GNWQR GQ7 GQ8 GROUPED_ABI_INFORM_RESEARCH GXS H13 HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I-F I09 IAO ICD IEA IHE IJ- IKXTQ ITC ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ K1G K60 K6V K6~ K7- KDC KOV KOW L6V LAK LLZTM M0C M2P M4Y M7S MA- N2Q N95 N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I OAM OVD P19 P2P P62 P9M PF0 PHGZM PHGZT PQBIZ PQBZA PQGLB PQQKQ PROAC PT4 PT5 PTHSS Q2X QOK QOS QWB R4E R89 R9I RHV RNI RNS ROL RPX RSV RZC RZD RZK S16 S1Z S26 S27 S28 S3B SAP SBE SCF SCLPG SDH SDM SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TEORI TH9 TSG TSK TSV TUC TUS U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 ZL0 ZMTXR ZYFGU ~8M ~A9 ~EX AAYXX AFFHD CITATION 7TA 7TB 8FD FR3 JG9 JQ2 KR7
ID	FETCH-LOGICAL-c363t-6008fca3cfd4cefe2fe229f54e07e25b30aa3bba1e11d802ae66fae94c93b5893
IEDL.DBID	RSV
ISICitedReferencesCount	1
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001208653700002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0254-5330
IngestDate	Wed Nov 05 14:51:28 EST 2025 Sat Nov 29 07:40:12 EST 2025 Tue Nov 18 21:40:21 EST 2025 Fri Aug 01 03:41:21 EDT 2025
IsDoiOpenAccess	true
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Issue	1
Keywords	Timeline cover Temporal graph FPT algorithm NP-hard problem Approximation algorithm
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c363t-6008fca3cfd4cefe2fe229f54e07e25b30aa3bba1e11d802ae66fae94c93b5893
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ORCID	0000-0002-6124-2965
OpenAccessLink	https://link.springer.com/10.1007/s10479-024-05993-8
PQID	3235126947
PQPubID	25585
PageCount	20
ParticipantIDs	proquest_journals_3235126947 crossref_citationtrail_10_1007_s10479_024_05993_8 crossref_primary_10_1007_s10479_024_05993_8 springer_journals_10_1007_s10479_024_05993_8
PublicationCentury	2000
PublicationDate	20250800 2025-08-00 20250801
PublicationDateYYYYMMDD	2025-08-01
PublicationDate_xml	– month: 8 year: 2025 text: 20250800
PublicationDecade	2020
PublicationPlace	New York
PublicationPlace_xml	– name: New York
PublicationTitle	Annals of operations research
PublicationTitleAbbrev	Ann Oper Res
PublicationYear	2025
Publisher	Springer US Springer Nature B.V
Publisher_xml	– name: Springer US – name: Springer Nature B.V
References	P Rozenshtein (5993_CR24) 2021; 35 5993_CR1 5993_CR14 5993_CR15 5993_CR7 BM Bumpus (5993_CR6) 2023; 85 5993_CR8 T Fluschnik (5993_CR12) 2020; 806 P Rozenshtein (5993_CR23) 2020; 62 V Bafna (5993_CR4) 1999; 12 R Dondi (5993_CR10) 2021; 2 DS Hochbaum (5993_CR16) 1982; 11 P Holme (5993_CR17) 2015; 88 D Kempe (5993_CR20) 2002; 64 O Michail (5993_CR22) 2016; 12 V Froese (5993_CR13) 2023 5993_CR25 T Erlebach (5993_CR11) 2021; 119 P Zschoche (5993_CR27) 2020; 107 EC Akrida (5993_CR2) 2021; 120 H Wu (5993_CR26) 2016; 28 A Becker (5993_CR5) 1996; 83 P Holme (5993_CR18) 2019 G Karakostas (5993_CR19) 2009; 5 R Dondi (5993_CR9) 2023; 969 EC Akrida (5993_CR3) 2020; 107 5993_CR21
References_xml	– volume: 969 year: 2023 ident: 5993_CR9 publication-title: Theoretical Computer Science doi: 10.1016/J.TCS.2023.114040 – ident: 5993_CR25 doi: 10.14778/2732939.2732945 – volume: 85 start-page: 688 issue: 3 year: 2023 ident: 5993_CR6 publication-title: Algorithmica doi: 10.1007/s00453-022-01018-7 – volume: 62 start-page: 1611 issue: 4 year: 2020 ident: 5993_CR23 publication-title: Knowledge and Information Systems doi: 10.1007/s10115-019-01403-9 – ident: 5993_CR8 doi: 10.1007/978-3-031-34347-6_15 – volume: 2 start-page: 158 issue: 3 year: 2021 ident: 5993_CR10 publication-title: SN Computer Science doi: 10.1007/s42979-021-00593-w – volume: 12 start-page: 289 issue: 3 year: 1999 ident: 5993_CR4 publication-title: SIAM Journal on Discrete Mathematics doi: 10.1137/S0895480196305124 – year: 2023 ident: 5993_CR13 publication-title: Theory of Computing Systems doi: 10.1007/s00224-023-10150-y – ident: 5993_CR21 doi: 10.1007/978-3-030-79987-8_34 – volume: 806 start-page: 197 year: 2020 ident: 5993_CR12 publication-title: Theoretical Computer Science doi: 10.1016/j.tcs.2019.03.031 – volume: 35 start-page: 213 issue: 1 year: 2021 ident: 5993_CR24 publication-title: Data Mining and Knowledge Discovery doi: 10.1007/s10618-020-00717-5 – volume: 11 start-page: 555 issue: 3 year: 1982 ident: 5993_CR16 publication-title: SIAM Journal on Computing doi: 10.1137/0211045 – volume: 83 start-page: 167 issue: 1 year: 1996 ident: 5993_CR5 publication-title: Artificial Intelligence doi: 10.1016/0004-3702(95)00004-6 – ident: 5993_CR15 doi: 10.1609/aaai.v36i9.21259 – volume: 28 start-page: 2927 issue: 11 year: 2016 ident: 5993_CR26 publication-title: IEEE Transactions on Knowledge and Data Engineering doi: 10.1109/TKDE.2016.2594065 – year: 2019 ident: 5993_CR18 publication-title: Temporal Network Theory doi: 10.1007/978-3-030-23495-9_1 – volume: 64 start-page: 820 issue: 4 year: 2002 ident: 5993_CR20 publication-title: Journal of Computer and System Sciences doi: 10.1006/jcss.2002.1829 – volume: 120 start-page: 179 year: 2021 ident: 5993_CR2 publication-title: Journal of Computer and System Sciences doi: 10.1016/j.jcss.2021.04.001 – ident: 5993_CR14 doi: 10.1137/1.9781611974331.CH80 – volume: 107 start-page: 72 year: 2020 ident: 5993_CR27 publication-title: Journal of Computer and System Sciences doi: 10.1016/j.jcss.2019.07.006 – ident: 5993_CR7 doi: 10.4230/LIPICS.IPEC.2023.12 – volume: 88 start-page: 234 issue: 9 year: 2015 ident: 5993_CR17 publication-title: The European Physical Journal B doi: 10.1140/epjb/e2015-60657-4 – volume: 5 start-page: 41 issue: 4 year: 2009 ident: 5993_CR19 publication-title: ACM Transactions on Algorithms doi: 10.1145/1597036.1597045 – volume: 119 start-page: 1 year: 2021 ident: 5993_CR11 publication-title: Journal of Computer and System Sciences doi: 10.1016/j.jcss.2021.01.005 – volume: 12 start-page: 239 issue: 4 year: 2016 ident: 5993_CR22 publication-title: Internet Mathematics doi: 10.1080/15427951.2016.1177801 – ident: 5993_CR1 doi: 10.1145/1060590.1060675 – volume: 107 start-page: 108 year: 2020 ident: 5993_CR3 publication-title: Journal of Computer and System Sciences doi: 10.1016/j.jcss.2019.08.002
SSID	ssj0001185
Score	2.4524825
Snippet	We consider a variant of vertex cover on temporal graphs that has been recently defined for summarization of timeline activities in temporal graphs. The...
SourceID	proquest crossref springer
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	609
SubjectTerms	Algorithms Apexes Approximation Business and Management Combinatorics Graph theory Graphs Linear programming Operations Research/Decision Theory Original Research Theory of Computation
Title	Exact and approximation algorithms for covering timeline in temporal graphs
URI	https://link.springer.com/article/10.1007/s10479-024-05993-8 https://www.proquest.com/docview/3235126947
Volume	351
WOSCitedRecordID	wos001208653700002&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: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1572-9338 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001185 issn: 0254-5330 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/eLvHCXMwnV1bS8MwFD7oFNEHL1NxOiUPvmmgbXrLo8iGoAzxMvZWkjTRwuxkrbKfb5K12xQVFPqWC-WcJOcLOef7AE65hsRBoLiRSfWxr89GTEPBsRszKhRPlWMLafs3Ua8XDwb0tioKK-ps9_pJ0p7UC8VufkSxjinYcIoQHC_Dig53sRFsuLvvz85fDZlt4qK--mCTO1mVynw_x-dwNMeYX55FbbTpbv3vP7dhs0KX6GK6HHZgSeZNWKuT25uwVYs4oGpPN2FjgZFwF647EyZKxPIUWbbxSTYtbURs-DQaZ-XzS4E0zEXCZH7qEcho0xukirIcVTRXQ2RZsIs9eOx2Hi6vcKW3gAUJSYk19omVYESo1BdSSU9_HlWBL51IegEnDmOEc-ZK101jx2MyDBWT1BeU8EADn31o5KNcHgByoih2I1cqc2FLtUeYq5ECT1nkM0EFbYFbmz0RFRm50cQYJnMaZWPGRJsxsWZM4haczca8Tqk4fu3drr2ZVNuySIhHNMAJqR-14Lz23rz559kO_9b9CNY9oxNsEwXb0CjHb_IYVsV7mRXjE7tcPwDkbOOX
linkProvider	Springer Nature
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1JS8QwFH644XJwGRXHNQdvGmibdMlRZERxHMQNbyVJEx0YOzKt4s83ybTOKCoo9JaF8l6S94W8930A-8JA4jDUwsqkUkzN2YhZJAX2E86kFpn2XCHtXTvudJL7e3ZZFYUVdbZ7_STpTuqxYjcaM2xiCracIgQnkzBNTcSyjPlX13cf56-BzC5x0Vx9sM2drEplvp_jczgaYcwvz6Iu2pws_e8_l2GxQpfoaLgcVmBC5Q2YrZPbG7BUizigak83YGGMkXAVzltvXJaI5xlybONv3WFpI-K9h_6gWz4-FcjAXCRt5qcZgaw2vUWqqJujiuaqhxwLdrEGtyetm-NTXOktYEkiUmKDfRItOZE6o1JpFZgvYDqkyotVEAricU6E4L7y_SzxAq6iSHPFqGREhAb4rMNU3s_VBiAvjhM_9pW2F7bMeIT7BimIjMeUSyZZE_za7KmsyMitJkYvHdEoWzOmxoypM2OaNOHgY8zzkIrj197btTfTalsWKQmIATgRo3ETDmvvjZp_nm3zb933YO705qKdts8651swH1jNYJc0uA1T5eBF7cCMfC27xWDXLd13l6jmew
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1bS8MwFD54Y-iDl6k4r3nwTcPaJr3kUdShKEPwgm8lSRMdzE7WKv58k6x1U1QQoW-5UHKSnO-Q73wHYF8YSByGWtgyqRRTczdiFkmB_YQzqUWmPZdIe3cZd7vJ_T27msjid2z3-klylNNgVZrysv2c6fZE4huNGTb-BVt9EYKTaZillkhv4_Xru4-72MBnR2I0YRC2PMoqbeb7OT67pjHe_PJE6jxPZ-n__7wMixXqREejbbICUypvQqMmvTdhqS7ugKqz3oSFCaXCVbg4feOyRDzPkFMhf-uNUh4R7z8Mhr3y8alABv4iaRmhZgSyNestgkW9HFXyV33k1LGLNbjtnN4cn-GqDgOWJCIlNpgo0ZITqTMqlVaB-QKmQ6q8WAWhIB7nRAjuK9_PEi_gKoo0V4xKRkRoANE6zOSDXG0A8uI48WNfaRvIZcY63DcIQmQ8plwyyVrg1yZIZSVSbmtl9NOxvLJdxtQsY-qWMU1acPAx5nkk0fFr7-3asml1XIuUBMQAn4jRuAWHtSXHzT_Ptvm37nvQuDrppJfn3YstmA9sKWHHJdyGmXL4onZgTr6WvWK463bxO7Ft718
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=Exact+and+approximation+algorithms+for+covering+timeline+in+temporal+graphs&rft.jtitle=Annals+of+operations+research&rft.au=Dondi%2C+Riccardo&rft.au=Popa%2C+Alexandru&rft.date=2025-08-01&rft.issn=0254-5330&rft.eissn=1572-9338&rft.volume=351&rft.issue=1&rft.spage=609&rft.epage=628&rft_id=info:doi/10.1007%2Fs10479-024-05993-8&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s10479_024_05993_8
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0254-5330&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0254-5330&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0254-5330&client=summon