Double interdiction problem on trees on the sum of root-leaf distances by upgrading edges

The double interdiction problem on trees (DIT) for the sum of root-leaf distances (SRD) has significant implications in diverse areas such as transportation networks, military strategies, and counter-terrorism efforts. It aims to maximize the SRD by upgrading edge weights subject to two constraints....

Celý popis

Uloženo v:

Podrobná bibliografie
Vydáno v:	Journal of global optimization Ročník 92; číslo 4; s. 951 - 972
Hlavní autoři:	Li, Xiao, Guan, Xiucui, Jia, Junhua, Pardalos, Panos M.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Springer US 01.08.2025 Springer Nature B.V
Témata:	Algorithms Complexity Computer Science Counterterrorism Dynamic programming Greedy algorithms Hardness Knapsack problem Lower bounds Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Polynomials Real Functions Search algorithms Traffic congestion Transportation networks Trees Upper bounds Shortest path Upgrade critical edges Dynamic programming algorithm Sum of root-leaf distance Network interdiction problem
ISSN:	0925-5001, 1573-2916
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

Abstract	The double interdiction problem on trees (DIT) for the sum of root-leaf distances (SRD) has significant implications in diverse areas such as transportation networks, military strategies, and counter-terrorism efforts. It aims to maximize the SRD by upgrading edge weights subject to two constraints. One gives an upper bound for the cost of upgrades under certain norm and the other specifies a lower bound for the shortest root-leaf distance (StRD). We utilize both weighted l ∞ norm and Hamming distance to measure the upgrade cost and denote the corresponding (DIT) problem by ( DIT H ∞ ) and its minimum cost problem by ( MCDIT H ∞ ). We establish the N P -hardness of problem ( DIT H ∞ ) by building a reduction from the 0–1 knapsack problem. We solve the problem ( DIT H ∞ ) by two scenarios based on the number N of upgrade edges. When N = 1 , a greedy algorithm with O ( n ) complexity is proposed. For the general case, an exact dynamic programming algorithm within a pseudo-polynomial time is proposed, which is established on a structure of left subtrees by maximizing a convex combination of the StRD and SRD. Furthermore, we confirm the N P -hardness of problem ( MCDIT H ∞ ) by reducing from the 0–1 knapsack problem. To tackle problem ( MCDIT H ∞ ), a binary search algorithm with pseudo-polynomial time complexity is outlined, which iteratively solves problem ( DIT H ∞ ). We culminate our study with numerical experiments, showcasing effectiveness of the algorithm.
AbstractList	The double interdiction problem on trees (DIT) for the sum of root-leaf distances (SRD) has significant implications in diverse areas such as transportation networks, military strategies, and counter-terrorism efforts. It aims to maximize the SRD by upgrading edge weights subject to two constraints. One gives an upper bound for the cost of upgrades under certain norm and the other specifies a lower bound for the shortest root-leaf distance (StRD). We utilize both weighted l ∞ norm and Hamming distance to measure the upgrade cost and denote the corresponding (DIT) problem by ( DIT H ∞ ) and its minimum cost problem by ( MCDIT H ∞ ). We establish the N P -hardness of problem ( DIT H ∞ ) by building a reduction from the 0–1 knapsack problem. We solve the problem ( DIT H ∞ ) by two scenarios based on the number N of upgrade edges. When N = 1 , a greedy algorithm with O ( n ) complexity is proposed. For the general case, an exact dynamic programming algorithm within a pseudo-polynomial time is proposed, which is established on a structure of left subtrees by maximizing a convex combination of the StRD and SRD. Furthermore, we confirm the N P -hardness of problem ( MCDIT H ∞ ) by reducing from the 0–1 knapsack problem. To tackle problem ( MCDIT H ∞ ), a binary search algorithm with pseudo-polynomial time complexity is outlined, which iteratively solves problem ( DIT H ∞ ). We culminate our study with numerical experiments, showcasing effectiveness of the algorithm. The double interdiction problem on trees (DIT) for the sum of root-leaf distances (SRD) has significant implications in diverse areas such as transportation networks, military strategies, and counter-terrorism efforts. It aims to maximize the SRD by upgrading edge weights subject to two constraints. One gives an upper bound for the cost of upgrades under certain norm and the other specifies a lower bound for the shortest root-leaf distance (StRD). We utilize both weighted l∞ norm and Hamming distance to measure the upgrade cost and denote the corresponding (DIT) problem by (DITH∞) and its minimum cost problem by (MCDITH∞). We establish the NP-hardness of problem (DITH∞) by building a reduction from the 0–1 knapsack problem. We solve the problem (DITH∞) by two scenarios based on the number N of upgrade edges. When N=1, a greedy algorithm with O(n) complexity is proposed. For the general case, an exact dynamic programming algorithm within a pseudo-polynomial time is proposed, which is established on a structure of left subtrees by maximizing a convex combination of the StRD and SRD. Furthermore, we confirm the NP-hardness of problem (MCDITH∞) by reducing from the 0–1 knapsack problem. To tackle problem (MCDITH∞), a binary search algorithm with pseudo-polynomial time complexity is outlined, which iteratively solves problem (DITH∞). We culminate our study with numerical experiments, showcasing effectiveness of the algorithm.
Author	Guan, Xiucui Jia, Junhua Li, Xiao Pardalos, Panos M.
Author_xml	– sequence: 1 givenname: Xiao surname: Li fullname: Li, Xiao organization: School of Mathematics, Southeast University – sequence: 2 givenname: Xiucui orcidid: 0000-0002-2653-1868 surname: Guan fullname: Guan, Xiucui email: xcguan@163.com organization: School of Mathematics, Southeast University – sequence: 3 givenname: Junhua surname: Jia fullname: Jia, Junhua organization: School of Mathematics, Southeast University – sequence: 4 givenname: Panos M. surname: Pardalos fullname: Pardalos, Panos M. organization: Center for Applied Optimization, University of Florida
BookMark	eNp9ULtOAzEQtFCQSAI_QGWJ2rC2zzm7ROEpRaKBgso6P-64KLGDfVfk7zEcEh3VjmZnZlezQLMQg0foksI1BahvMgWpJAEmCNBKAVEnaE5FzQlTdDVDc1BlJQDoGVrkvAUAJQWbo_e7OJqdx30YfHK9HfoY8CHFwu1xgUPyPv-AD4_zWLgWpxgHsvNNi12fhybYojBHPB661Lg-dNi7zudzdNo2u-wvfucSvT3cv66fyObl8Xl9uyGW1WwgknJBTSt9BYIqECvPGgDXUlcJSS11jsvauFoY33LKrZHKWNFUihtbKUf5El1NueXrz9HnQW_jmEI5qTnjNdRScCgqNqlsijkn3-pD6vdNOmoK-rtCPVWoS4X6p0KtiolPplzEofPpL_of1xd8B3Xv
Cites_doi	10.1016/j.orl.2009.09.013 10.1007/s00224-007-9025-6 10.1007/s11590-022-01916-3 10.1016/0167-6377(82)90020-7 10.1016/j.cor.2012.02.023 10.1007/978-3-319-18173-8_3 10.1002/net.21832 10.1016/0020-0190(93)90082-K 10.1007/11602613_96 10.1016/j.dam.2010.06.006 10.1016/j.orl.2013.10.001 10.1007/s10898-020-00958-0 10.1016/j.disc.2009.08.009 10.1038/35019019 10.1007/s10878-012-9469-8 10.1016/j.disc.2009.01.006 10.1016/S0020-0190(00)00175-7 10.1016/S0166-218X(01)00189-5 10.1016/j.dam.2010.04.008 10.1007/s11590-020-01687-9 10.1007/s10878-024-01230-x
ContentType	Journal Article
Copyright	The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025 Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.
Copyright_xml	– notice: The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025 Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. – notice: The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.
DBID	AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D
DOI	10.1007/s10898-025-01490-9
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
DeliveryMethod	fulltext_linktorsrc
Discipline	Engineering Mathematics Sciences (General) Computer Science
EISSN	1573-2916
EndPage	972
ExternalDocumentID	10_1007_s10898_025_01490_9
GrantInformation_xml	– fundername: National Natural Science Foundation of China grantid: 11471073 funderid: http://dx.doi.org/10.13039/501100001809
GroupedDBID	-Y2 -~C .4S .86 .DC .VR 06D 0R~ 0VY 199 1N0 1SB 2.D 203 28- 29K 2J2 2JN 2JY 2KG 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 78A 7WY 88I 8AO 8FE 8FG 8FL 8G5 8TC 8UJ 95- 95. 95~ 96X 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 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 AHSBF AHWEU AHYZX AI. AIAKS AIGIU AIIXL AILAN AITGF AIXLP AJBLW AJRNO AJZVZ 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 CAG CCPQU COF CS3 CSCUP D-I DDRTE DL5 DNIVK DPUIP DU5 DWQXO EBLON EBS EDO EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRNLG FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNUQQ GNWQR GQ7 GQ8 GUQSH GXS H13 HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IAO IHE IJ- IKXTQ ITC ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ K60 K6V K6~ K7- KDC KOV KOW L6V LAK LLZTM M0C M2O M2P M4Y M7S MA- N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM OVD P19 P2P P62 P9M PF0 PHGZM PHGZT PQBIZ PQBZA PQGLB PQQKQ PROAC PT4 PT5 PTHSS Q2X QOK QOS R4E R89 R9I RHV RNI RNS ROL RPX RSV RZC RZE RZK S16 S1Z S26 S27 S28 S3B SAP SBE SCLPG SDD SDH SDM SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TEORI TN5 TSG TSK TSV TUC TUS U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW VH1 W23 W48 WK8 YLTOR Z45 ZMTXR ZWQNP ZY4 ~EX AAYXX AFFHD CITATION 7SC 8FD JQ2 L7M L~C L~D
ID	FETCH-LOGICAL-c272t-81351bf8e40519056e2a00df1d4581c1dd387bd75bef313cb89bc5a493bc49d13
IEDL.DBID	RSV
ISICitedReferencesCount	1
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001471159100001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0925-5001
IngestDate	Wed Nov 05 06:29:12 EST 2025 Sat Nov 29 07:32:58 EST 2025 Thu Aug 07 06:03:49 EDT 2025
IsPeerReviewed	true
IsScholarly	true
Issue	4
Keywords	Shortest path Upgrade critical edges Dynamic programming algorithm Sum of root-leaf distance Network interdiction problem
Language	English
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c272t-81351bf8e40519056e2a00df1d4581c1dd387bd75bef313cb89bc5a493bc49d13
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ORCID	0000-0002-2653-1868
PQID	3237078530
PQPubID	29930
PageCount	22
ParticipantIDs	proquest_journals_3237078530 crossref_primary_10_1007_s10898_025_01490_9 springer_journals_10_1007_s10898_025_01490_9
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 – name: Dordrecht
PublicationSubtitle	An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering
PublicationTitle	Journal of global optimization
PublicationTitleAbbrev	J Glob Optim
PublicationYear	2025
Publisher	Springer US Springer Nature B.V
Publisher_xml	– name: Springer US – name: Springer Nature B.V
References	Y Lei (1490_CR16) 2023; 17 R Zenklusen (1490_CR23) 2009; 309 C Bazgan (1490_CR9) 2013; 41 1490_CR20 C Bazgan (1490_CR8) 2013; 25 BH Korte (1490_CR15) 2011 1490_CR4 R Albert (1490_CR2) 2000; 406 Q Zhang (1490_CR27) 2021; 15 HW Corley (1490_CR10) 1982; 1 TH Cormen (1490_CR11) 2022 R Ramaswami (1490_CR21) 2009 Q Zhang (1490_CR26) 2021; 79 R Zenklusen (1490_CR24) 2010; 158 C Bazgan (1490_CR5) 2019; 73 1490_CR12 C Bazgan (1490_CR6) 2015; 9079 K Iwano (1490_CR13) 1993; 48 W Liang (1490_CR18) 2001; 113 DS Altner (1490_CR3) 2010; 38 X Li (1490_CR17) 2023; 48 R Zenklusen (1490_CR25) 2010; 158 RK Ahuja (1490_CR1) 1995 C Bazgan (1490_CR7) 2012; 39 E Nardelli (1490_CR19) 2001; 79 L Khachiyan (1490_CR14) 2008; 43 B Ries (1490_CR22) 2010; 310
References_xml	– volume: 38 start-page: 33 issue: 1 year: 2010 ident: 1490_CR3 publication-title: Oper. Res. Lett. doi: 10.1016/j.orl.2009.09.013 – volume: 43 start-page: 204 issue: 2 year: 2008 ident: 1490_CR14 publication-title: Theory Comput. Syst. doi: 10.1007/s00224-007-9025-6 – volume: 17 start-page: 453 issue: 2 year: 2023 ident: 1490_CR16 publication-title: Optim. Lett. doi: 10.1007/s11590-022-01916-3 – volume-title: Combinatorial Optimization year: 2011 ident: 1490_CR15 – volume-title: Optical Networks: A Practical Perspective year: 2009 ident: 1490_CR21 – volume: 1 start-page: 157 year: 1982 ident: 1490_CR10 publication-title: Oper. Res. Lett. doi: 10.1016/0167-6377(82)90020-7 – volume: 39 start-page: 2888 issue: 11 year: 2012 ident: 1490_CR7 publication-title: Comput. Oper. Res. doi: 10.1016/j.cor.2012.02.023 – volume: 9079 start-page: 47 year: 2015 ident: 1490_CR6 publication-title: Lect. Notes Comput. Sci. doi: 10.1007/978-3-319-18173-8_3 – volume: 73 start-page: 23 issue: 1 year: 2019 ident: 1490_CR5 publication-title: Networks doi: 10.1002/net.21832 – ident: 1490_CR12 – volume: 48 start-page: 211 issue: 5 year: 1993 ident: 1490_CR13 publication-title: Inf. Process. Lett. doi: 10.1016/0020-0190(93)90082-K – ident: 1490_CR20 doi: 10.1007/11602613_96 – volume: 158 start-page: 1676 issue: 15 year: 2010 ident: 1490_CR24 publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2010.06.006 – ident: 1490_CR4 – volume: 41 start-page: 685 year: 2013 ident: 1490_CR9 publication-title: Oper. Res. Lett. doi: 10.1016/j.orl.2013.10.001 – volume: 79 start-page: 959 issue: 4 year: 2021 ident: 1490_CR26 publication-title: J. Global Optim. doi: 10.1007/s10898-020-00958-0 – volume-title: Network Flows: Theory, Algorithms and Applications year: 1995 ident: 1490_CR1 – volume: 310 start-page: 132 issue: 1 year: 2010 ident: 1490_CR22 publication-title: Discrete Math. doi: 10.1016/j.disc.2009.08.009 – volume: 406 start-page: 378 issue: 6794 year: 2000 ident: 1490_CR2 publication-title: Nature doi: 10.1038/35019019 – volume: 25 start-page: 191 issue: 2 year: 2013 ident: 1490_CR8 publication-title: J. Comb. Optim. doi: 10.1007/s10878-012-9469-8 – volume: 309 start-page: 4306 issue: 13 year: 2009 ident: 1490_CR23 publication-title: Discrete Math. doi: 10.1016/j.disc.2009.01.006 – volume: 79 start-page: 81 issue: 2 year: 2001 ident: 1490_CR19 publication-title: Inf. Process. Lett. doi: 10.1016/S0020-0190(00)00175-7 – volume: 113 start-page: 319 issue: 2–3 year: 2001 ident: 1490_CR18 publication-title: Discrete Appl. Math. doi: 10.1016/S0166-218X(01)00189-5 – volume: 158 start-page: 1441 issue: 13 year: 2010 ident: 1490_CR25 publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2010.04.008 – volume: 15 start-page: 2661 issue: 8 year: 2021 ident: 1490_CR27 publication-title: Optim. Lett. doi: 10.1007/s11590-020-01687-9 – volume: 48 start-page: 39 issue: 5 year: 2023 ident: 1490_CR17 publication-title: J. Comb. Optim. doi: 10.1007/s10878-024-01230-x – volume-title: Introduction to Algorithms year: 2022 ident: 1490_CR11
SSID	ssj0009852
Score	2.428203
Snippet	The double interdiction problem on trees (DIT) for the sum of root-leaf distances (SRD) has significant implications in diverse areas such as transportation...
SourceID	proquest crossref springer
SourceType	Aggregation Database Index Database Publisher
StartPage	951
SubjectTerms	Algorithms Complexity Computer Science Counterterrorism Dynamic programming Greedy algorithms Hardness Knapsack problem Lower bounds Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Polynomials Real Functions Search algorithms Traffic congestion Transportation networks Trees Upper bounds
Title	Double interdiction problem on trees on the sum of root-leaf distances by upgrading edges
URI	https://link.springer.com/article/10.1007/s10898-025-01490-9 https://www.proquest.com/docview/3237078530
Volume	92
WOSCitedRecordID	wos001471159100001&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: 1573-2916 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0009852 issn: 0925-5001 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/eLvHCXMwnV3NS8MwFH_o9KAH56bidEoOHhQNtE27JEcRxYMO8Yt5Ks1HVRjbWDvB_94kS90UPegtoeG15L2X_Jq893sAB2GsNFOSYE5JB8eyo3GmMoq5MH2ea0JClyh8Rbtd1uvxG58UVlTR7tWVpFup55LdmE0Hi2ywWcwDzBdhyWx3zLrj7d3jjGqXuTo7ATcjE7MK-1SZn2V83Y5mGPPbtajbbS7q__vOdVjz6BKdTs2hAQt60IR6VbkBeUduwuocDaHpXX9ytxZNaPhRBTr0nNRHG_BkgLboa2TZJYxJuWQI5IvRINO0d9uFa7xoZIwbDXNkMHmJ-zrLkbIg1YkU72gyeh67wH1kj_KKTXi4OL8_u8S-KgOWEY1KzGxNP5EzHVv0Z_CTjrIgUHmo4oSFMlSKMCoUTYTOSUikYFzIJIs5ETLmKiRbUBsMB3obzGtUQGVAdZKzWCsiQp5IQhVV7kc0acFxpZx0NCXfSGc0y3aaUzPNqZvmlLegXekv9Y5YpCQils8oIUELTip9zR7_Lm3nb8N3YSVyKrehgW2oleOJ3oNl-Va-FuN9Z6AfK5PfEw
linkProvider	Springer Nature
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LS8QwEB50FdSDj1VxfebgQdFA26QmOYooiusivtBTaR5VYdldtqvgvzfJpq6KHvSW0DAtmUnmazLzDcB2TLXhWhEsGDnAVB0YnOucYSFtXxSGkNgnCjdZq8Xv78VlSAorq2j36krS79Sfkt24SwdLXLAZFREW4zBBrcdygXxX13cjql3u6-xEwo5M7S4cUmV-lvHVHY0w5rdrUe9tTub-953zMBvQJTocmsMCjJlOHeaqyg0oLOQ6zHyiIbS9iw_u1rIOC2FUiXYCJ_XuIjxYoC3bBjl2CWtSPhkChWI0yDbd3XbpG08GWeNG3QJZTD7AbZMXSDuQ6kXKN_TSe-z7wH3kjvLKJbg9Ob45OsWhKgNWCUsGmLuafrLghjr0Z_GTSfIo0kWsacpjFWtNOJOapdIUJCZKciFVmlNBpKJCx2QZap1ux6yAfY2OmIqYSQtOjSYyFqkiTDPtf0TTBuxVysl6Q_KNbESz7KY5s9Oc-WnORAPWK_1lYSGWGUmI4zNKSdSA_Upfo8e_S1v92_AtmDq9uWhmzbPW-RpMJ179LkxwHWqD_ovZgEn1Ongu-5veWN8BqOTh9w
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1bS8MwFD7oFNEHL1NxXvPgg6JhbZOa5FHUoahD8II-leZSFWSOtRP89yZZ66bog_iW0JCWnJPmS3K-7wBsh1QbrhXBgpEDTNWBwalOGRbS1kVmCAk9UfiCtdv8_l5cjbD4fbR7dSU54DQ4laZO0ezqrDlCfOOOGha5wDMqAizGYYK6pEFuv359N5Td5T7nTiBsy9j-kUvazM99fF2ahnjz2xWpX3lac___5nmYLVEnOhy4yQKMmU4d5qqMDqic4HWYGZEntLXLT03XvA4LZasc7ZRa1buL8GABuHwxyKlOWFfzJAlUJqlBtujuvHNfeDLIOj16zZDF6gV-MWmGtAOvvkv5jvrdx54P6EfuiC9fgtvWyc3RKS6zNWAVsajA3OX6kxk31KFCi6tMlAaBzkJNYx6qUGvCmdQsliYjIVGSC6nilAoiFRU6JMtQ67x2zArY1-iAqYCZOOPUaCJDESvCNNN-gxo3YK8yVNIdiHIkQ_llN8yJHebED3MiGrBe2TIpJ2iekIg4naOYBA3Yr2w3fPx7b6t_a74FU1fHreTirH2-BtORt76LHlyHWtHrmw2YVG_Fc97b9H77AU_N6ts
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=Double+interdiction+problem+on+trees+on+the+sum+of+root-leaf+distances+by+upgrading+edges&rft.jtitle=Journal+of+global+optimization&rft.au=Li%2C+Xiao&rft.au=Guan%2C+Xiucui&rft.au=Jia%2C+Junhua&rft.au=Pardalos%2C+Panos+M.&rft.date=2025-08-01&rft.issn=0925-5001&rft.eissn=1573-2916&rft.volume=92&rft.issue=4&rft.spage=951&rft.epage=972&rft_id=info:doi/10.1007%2Fs10898-025-01490-9&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s10898_025_01490_9
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0925-5001&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0925-5001&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0925-5001&client=summon