Combining Crown Structures for Vulnerability Measures
Over the past decades, various metrics have emerged in graph theory to grasp the complex nature of network vulnerability. In this paper, we study two specific measures: (weighted) vertex integrity (wVI) and (weighted) component order connectivity (wCOC). These measures not only evaluate the number o...
Saved in:
| Published in: | Algorithmica Vol. 88; no. 1 |
|---|---|
| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
New York
Springer US
01.02.2026
Springer Nature B.V |
| Subjects: | |
| ISSN: | 0178-4617, 1432-0541 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | Over the past decades, various metrics have emerged in graph theory to grasp the complex nature of network vulnerability. In this paper, we study two specific measures: (weighted) vertex integrity (wVI) and (weighted) component order connectivity (wCOC). These measures not only evaluate the number of vertices that need to be removed to decompose a graph into fragments, but also take into account the size of the largest remaining component. The main focus of our paper is on kernelization algorithms tailored to both measures. We capitalize on the structural attributes inherent in different crown decompositions, strategically combining them to introduce novel kernelization algorithms that advance the current state of the field. In particular, we extend the scope of the balanced crown decomposition provided by Casel et al. [
1
] and expand the applicability of crown decomposition techniques. In summary, we improve the vertex kernel of VI from
to
, and of wVI from
to
, where
represents the weight of the heaviest component after removing a solution. For wCOC we improve the vertex kernel from
to
, where
. We also give a combinatorial algorithm that provides a 2
kW
vertex kernel in fixed-parameter tractable time when parameterized by
r
, where
is the size of a maximum
-packing. We further show that the algorithm computing the 2
kW
vertex kernel for COC can be transformed into a polynomial algorithm for two special cases, namely when
, which corresponds to the well-known vertex cover problem, and for claw-free graphs. In particular, we show a new way to obtain a 2
k
vertex kernel (or to obtain a 2-approximation) for the vertex cover problem by only using crown structures. |
|---|---|
| AbstractList | Over the past decades, various metrics have emerged in graph theory to grasp the complex nature of network vulnerability. In this paper, we study two specific measures: (weighted) vertex integrity (wVI) and (weighted) component order connectivity (wCOC). These measures not only evaluate the number of vertices that need to be removed to decompose a graph into fragments, but also take into account the size of the largest remaining component. The main focus of our paper is on kernelization algorithms tailored to both measures. We capitalize on the structural attributes inherent in different crown decompositions, strategically combining them to introduce novel kernelization algorithms that advance the current state of the field. In particular, we extend the scope of the balanced crown decomposition provided by Casel et al. [
1
] and expand the applicability of crown decomposition techniques. In summary, we improve the vertex kernel of VI from
to
, and of wVI from
to
, where
represents the weight of the heaviest component after removing a solution. For wCOC we improve the vertex kernel from
to
, where
. We also give a combinatorial algorithm that provides a 2
kW
vertex kernel in fixed-parameter tractable time when parameterized by
r
, where
is the size of a maximum
-packing. We further show that the algorithm computing the 2
kW
vertex kernel for COC can be transformed into a polynomial algorithm for two special cases, namely when
, which corresponds to the well-known vertex cover problem, and for claw-free graphs. In particular, we show a new way to obtain a 2
k
vertex kernel (or to obtain a 2-approximation) for the vertex cover problem by only using crown structures. Over the past decades, various metrics have emerged in graph theory to grasp the complex nature of network vulnerability. In this paper, we study two specific measures: (weighted) vertex integrity (wVI) and (weighted) component order connectivity (wCOC). These measures not only evaluate the number of vertices that need to be removed to decompose a graph into fragments, but also take into account the size of the largest remaining component. The main focus of our paper is on kernelization algorithms tailored to both measures. We capitalize on the structural attributes inherent in different crown decompositions, strategically combining them to introduce novel kernelization algorithms that advance the current state of the field. In particular, we extend the scope of the balanced crown decomposition provided by Casel et al. [1] and expand the applicability of crown decomposition techniques. In summary, we improve the vertex kernel of VI from $$p^3$$ to $$3p^2$$ , and of wVI from $$p^3$$ to $$3(p^2 + p^{1.5} p_\ell )$$ , where $$p_\ell < p$$ represents the weight of the heaviest component after removing a solution. For wCOC we improve the vertex kernel from $$\mathcal {O}(k^2W + kW^2)$$ to $$3\mu (k + \sqrt{\mu }W)$$ , where $$\mu = \max (k,W)$$ . We also give a combinatorial algorithm that provides a 2 kW vertex kernel in fixed-parameter tractable time when parameterized by r , where $$r \le k$$ is the size of a maximum $$(W+1)$$ -packing. We further show that the algorithm computing the 2 kW vertex kernel for COC can be transformed into a polynomial algorithm for two special cases, namely when $$W=1$$ , which corresponds to the well-known vertex cover problem, and for claw-free graphs. In particular, we show a new way to obtain a 2 k vertex kernel (or to obtain a 2-approximation) for the vertex cover problem by only using crown structures. Over the past decades, various metrics have emerged in graph theory to grasp the complex nature of network vulnerability. In this paper, we study two specific measures: (weighted) vertex integrity (wVI) and (weighted) component order connectivity (wCOC). These measures not only evaluate the number of vertices that need to be removed to decompose a graph into fragments, but also take into account the size of the largest remaining component. The main focus of our paper is on kernelization algorithms tailored to both measures. We capitalize on the structural attributes inherent in different crown decompositions, strategically combining them to introduce novel kernelization algorithms that advance the current state of the field. In particular, we extend the scope of the balanced crown decomposition provided by Casel et al. [1] and expand the applicability of crown decomposition techniques. In summary, we improve the vertex kernel of VI from to , and of wVI from to , where represents the weight of the heaviest component after removing a solution. For wCOC we improve the vertex kernel from to , where . We also give a combinatorial algorithm that provides a 2kW vertex kernel in fixed-parameter tractable time when parameterized by r, where is the size of a maximum -packing. We further show that the algorithm computing the 2kW vertex kernel for COC can be transformed into a polynomial algorithm for two special cases, namely when , which corresponds to the well-known vertex cover problem, and for claw-free graphs. In particular, we show a new way to obtain a 2k vertex kernel (or to obtain a 2-approximation) for the vertex cover problem by only using crown structures. |
| ArticleNumber | 9 |
| Author | Niklanovits, Aikaterini Simonov, Kirill Zeif, Ziena Casel, Katrin Friedrich, Tobias |
| Author_xml | – sequence: 1 givenname: Katrin surname: Casel fullname: Casel, Katrin organization: Humboldt-Universität zu Berlin – sequence: 2 givenname: Tobias surname: Friedrich fullname: Friedrich, Tobias organization: Hasso Plattner Institute, University of Potsdam – sequence: 3 givenname: Aikaterini surname: Niklanovits fullname: Niklanovits, Aikaterini organization: Hasso Plattner Institute, University of Potsdam – sequence: 4 givenname: Kirill surname: Simonov fullname: Simonov, Kirill organization: Hasso Plattner Institute, University of Potsdam – sequence: 5 givenname: Ziena surname: Zeif fullname: Zeif, Ziena email: Ziena.Zeif@hpi.de organization: Hasso Plattner Institute, University of Potsdam |
| BookMark | eNp9kMtOwzAQRS1UJNrCD7CKxNowYzu2s0QRL6mIBY-tldhOlap1ip0I9e9pCBI7VrO499yRzoLMQhc8IZcI1wigbhKAyDkFllNALjRlJ2SOgjMKucAZmQMqTYVEdUYWKW0AkKlCzkledru6DW1YZ2XsvkL22sfB9kP0KWu6mH0M2-BjVbfbtj9kz75KY3ROTptqm_zF712S9_u7t_KRrl4ensrbFbUcZU-tQ2ed0Aq5tBqttOBkZWXDRSFrrT0XPleuqQXnTmADjhXSo9BQOK8E40tyNe3uY_c5-NSbTTfEcHxpOFMCpUYYW2xq2dilFH1j9rHdVfFgEMyox0x6zFGP-dFjRohPUDqWw9rHv-l_qG9VR2jy |
| Cites_doi | 10.4230/LIPIcs.ESA.2021.26 10.4230/LIPIcs.IPEC.2016.20 10.1016/J.TCS.2019.04.018 10.3390/A16030144 10.1016/J.TCS.2024.114954 10.1016/J.JCSS.2017.04.004 10.46298/lmcs-20(4:18)2024 10.1007/978-1-4612-0515-9 10.1080/00207160701365721 10.1016/0166-218X(92)90122-Q 10.1016/J.TCS.2023.113872 10.1017/9781107415157 10.48550/arXiv.2011.04528 10.1007/s00453-016-0127-x 10.1016/J.TCS.2018.05.004 10.1016/S0166-218X(96)00133-3 10.1007/S00453-023-01161-9 10.1016/J.TCS.2022.03.021 10.1016/0095-8956(80)90074-X 10.4230/LIPICS.APPROX/RANDOM.2021.27 10.1007/S00453-020-00795-3 10.1007/s10107-018-1255-7 10.1007/S00453-024-01290-9 10.4230/LIPICS.ESA.2023.16 10.4230/LIPICS.MFCS.2024.58 |
| ContentType | Journal Article |
| Copyright | The Author(s) 2025 The Author(s) 2025. 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) 2025 – notice: The Author(s) 2025. 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 JQ2 |
| DOI | 10.1007/s00453-025-01348-2 |
| DatabaseName | Springer Nature OA Free Journals CrossRef ProQuest Computer Science Collection |
| DatabaseTitle | CrossRef ProQuest Computer Science Collection |
| DatabaseTitleList | CrossRef ProQuest Computer Science Collection |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science |
| EISSN | 1432-0541 |
| ExternalDocumentID | 10_1007_s00453_025_01348_2 |
| GrantInformation_xml | – fundername: Hasso-Plattner-Institut für Digital Engineering gGmbH (4420) |
| GroupedDBID | -~C -~X .86 .DC .VR 06D 0R~ 0VY 199 1N0 203 23M 2J2 2JN 2JY 2KG 2KM 2LR 2~H 30V 4.4 406 408 409 40D 40E 5GY 5VS 67Z 6NX 78A 8TC 8UJ 95- 95. 95~ 96X AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AAPKM AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN ABAKF ABBBX ABBRH ABBXA ABDBE ABDZT ABECU ABFSG ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABLJU ABMNI ABMQK ABNWP ABQBU ABRTQ ABSXP ABTEG ABTHY ABTKH ABTMW ABWNU ABXPI ACAOD ACDTI ACGFS ACHSB ACHXU ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSTC ACZOJ ADHHG ADHIR ADIMF ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEFQL AEGAL AEGNC AEJHL AEJRE AEMSY AENEX AEOHA AEPYU AETLH AEVLU AEXYK AEZWR AFBBN AFDZB AFHIU AFLOW AFOHR AFQWF AFWTZ AFZKB AGAYW AGDGC AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHPBZ AHSBF AHWEU AHYZX AIAKS AIGIU AIIXL AILAN AITGF AIXLP AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG ATHPR AVWKF AXYYD AYFIA AYJHY AZFZN B-. BA0 BGNMA BSONS C6C CS3 CSCUP DDRTE DL5 DNIVK DPUIP EBLON EBS EIOEI ESBYG FEDTE FERAY FFXSO FIGPU FNLPD FRRFC FWDCC GGCAI GGRSB GJIRD GNWQR GQ7 GQ8 GXS HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV LAS LLZTM M4Y MA- N9A NB0 NPVJJ NQJWS NU0 O93 O9G O9I O9J OAM P19 P9O PF- PT4 PT5 QOK QOS R89 R9I RHV RNS ROL RPX RSV S16 S1Z S27 S3B SAP SCO SDH SDM SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 TN5 TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 ZMTXR ~EX -Y2 1SB 28- 2P1 2VQ 5QI AAAVM AAOBN AARHV AAYTO AAYXX ABDPE ABFSI ABQSL ABULA ACBXY ADHKG AEBTG AEFIE AEKMD AFEXP AFGCZ AGGDS AGQPQ AI. AJBLW BBWZM BDATZ CAG CITATION COF E.L EJD FINBP FSGXE H13 H~9 KOW N2Q NDZJH O9- R4E RNI RZK S26 S28 SCJ SCLPG T16 UQL VH1 ZY4 JQ2 |
| ID | FETCH-LOGICAL-c316t-cd1dcd487136c81c6c0d6ac6f3496b88e34e57dfb433d41f0d296e14809de7423 |
| IEDL.DBID | RSV |
| ISICitedReferencesCount | 0 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001621069800001&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 | Sat Nov 22 20:41:15 EST 2025 Thu Nov 27 01:04:04 EST 2025 Sat Nov 22 01:13:26 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Keywords | Crown decomposition Component order connectivity Kernelization Vertex Integrity |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c316t-cd1dcd487136c81c6c0d6ac6f3496b88e34e57dfb433d41f0d296e14809de7423 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| OpenAccessLink | https://link.springer.com/10.1007/s00453-025-01348-2 |
| PQID | 3274168102 |
| PQPubID | 2043795 |
| ParticipantIDs | proquest_journals_3274168102 crossref_primary_10_1007_s00453_025_01348_2 springer_journals_10_1007_s00453_025_01348_2 |
| PublicationCentury | 2000 |
| PublicationDate | 2026-02-01 |
| PublicationDateYYYYMMDD | 2026-02-01 |
| PublicationDate_xml | – month: 02 year: 2026 text: 2026-02-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | Algorithmica |
| PublicationTitleAbbrev | Algorithmica |
| PublicationYear | 2026 |
| Publisher | Springer US Springer Nature B.V |
| Publisher_xml | – name: Springer US – name: Springer Nature B.V |
| References | T Gima (1348_CR4) 2025; 1024 1348_CR21 1348_CR20 J Chen (1348_CR18) 2019; 790 1348_CR25 1348_CR28 1348_CR27 T Gima (1348_CR6) 2024; 86 T Gima (1348_CR3) 2022; 918 A Jacob (1348_CR9) 2023; 16 D Kratsch (1348_CR14) 1997; 77 CA Barefoot (1348_CR8) 1987; 1 KS Bagga (1348_CR11) 1992; 37 MR Fellows (1348_CR16) 1989; 6 E Lee (1348_CR17) 2019; 177 W Li (1348_CR23) 2018; 739 S Baguley (1348_CR26) 2025; 87 LH Clark (1348_CR12) 1987; 2 M Xiao (1348_CR22) 2023; 959 M Xiao (1348_CR19) 2017; 88 Y Li (1348_CR15) 2008; 85 1348_CR5 R Ganian (1348_CR10) 2021; 83 GJ Minty (1348_CR24) 1980; 28 1348_CR7 PG Drange (1348_CR13) 2016; 76 1348_CR1 1348_CR2 |
| References_xml | – ident: 1348_CR1 doi: 10.4230/LIPIcs.ESA.2021.26 – ident: 1348_CR20 doi: 10.4230/LIPIcs.IPEC.2016.20 – volume: 790 start-page: 152 year: 2019 ident: 1348_CR18 publication-title: Theor. Comput. Sci. doi: 10.1016/J.TCS.2019.04.018 – volume: 16 start-page: 144 issue: 3 year: 2023 ident: 1348_CR9 publication-title: Algorithms doi: 10.3390/A16030144 – volume: 1024 year: 2025 ident: 1348_CR4 publication-title: Theor. Comput. Sci. doi: 10.1016/J.TCS.2024.114954 – volume: 1 start-page: 13 issue: 38 year: 1987 ident: 1348_CR8 publication-title: J. Combin. Math. Combin. Comput – volume: 2 start-page: 179 year: 1987 ident: 1348_CR12 publication-title: J. Combin. Math. Combin. Comput – volume: 88 start-page: 260 year: 2017 ident: 1348_CR19 publication-title: J. Comput. Syst. Sci. doi: 10.1016/J.JCSS.2017.04.004 – ident: 1348_CR7 doi: 10.46298/lmcs-20(4:18)2024 – ident: 1348_CR25 doi: 10.1007/978-1-4612-0515-9 – volume: 85 start-page: 19 issue: 1 year: 2008 ident: 1348_CR15 publication-title: Int. J. Comput. Math. doi: 10.1080/00207160701365721 – volume: 37 start-page: 13 issue: 38 year: 1992 ident: 1348_CR11 publication-title: Discret. Appl. Math. doi: 10.1016/0166-218X(92)90122-Q – volume: 959 year: 2023 ident: 1348_CR22 publication-title: Theor. Comput. Sci. doi: 10.1016/J.TCS.2023.113872 – ident: 1348_CR21 doi: 10.1017/9781107415157 – ident: 1348_CR28 doi: 10.48550/arXiv.2011.04528 – volume: 76 start-page: 1181 issue: 4 year: 2016 ident: 1348_CR13 publication-title: Algorithmica doi: 10.1007/s00453-016-0127-x – volume: 739 start-page: 80 year: 2018 ident: 1348_CR23 publication-title: Theor. Comput. Sci. doi: 10.1016/J.TCS.2018.05.004 – volume: 77 start-page: 259 issue: 3 year: 1997 ident: 1348_CR14 publication-title: Discret. Appl. Math. doi: 10.1016/S0166-218X(96)00133-3 – volume: 6 start-page: 23 issue: 1 year: 1989 ident: 1348_CR16 publication-title: J. Combin. Math. Combin. Comput – volume: 86 start-page: 147 issue: 1 year: 2024 ident: 1348_CR6 publication-title: Algorithmica doi: 10.1007/S00453-023-01161-9 – volume: 918 start-page: 60 year: 2022 ident: 1348_CR3 publication-title: Theor. Comput. Sci. doi: 10.1016/J.TCS.2022.03.021 – volume: 28 start-page: 284 issue: 3 year: 1980 ident: 1348_CR24 publication-title: J. Comb. Theory B doi: 10.1016/0095-8956(80)90074-X – ident: 1348_CR27 doi: 10.4230/LIPICS.APPROX/RANDOM.2021.27 – volume: 83 start-page: 1605 issue: 6 year: 2021 ident: 1348_CR10 publication-title: Algorithmica doi: 10.1007/S00453-020-00795-3 – volume: 177 start-page: 1 issue: 1–2 year: 2019 ident: 1348_CR17 publication-title: Math. Program. doi: 10.1007/s10107-018-1255-7 – volume: 87 start-page: 537 issue: 4 year: 2025 ident: 1348_CR26 publication-title: Algorithmica doi: 10.1007/S00453-024-01290-9 – ident: 1348_CR2 doi: 10.4230/LIPICS.ESA.2023.16 – ident: 1348_CR5 doi: 10.4230/LIPICS.MFCS.2024.58 |
| SSID | ssj0012796 |
| Score | 2.4285665 |
| Snippet | Over the past decades, various metrics have emerged in graph theory to grasp the complex nature of network vulnerability. In this paper, we study two specific... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Index Database Publisher |
| SubjectTerms | Algorithm Analysis and Problem Complexity Algorithms Apexes Combinatorial analysis Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Decomposition Fields (mathematics) Graph theory Mathematics of Computing Polynomials Theory of Computation |
| Title | Combining Crown Structures for Vulnerability Measures |
| URI | https://link.springer.com/article/10.1007/s00453-025-01348-2 https://www.proquest.com/docview/3274168102 |
| Volume | 88 |
| WOSCitedRecordID | wos001621069800001&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 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/eLvHCXMwnV3PS8MwFH7I9ODF-ROnU3LwpoGmSZv2KMPhxSFOx26h-VEQZIrdBv73vqTthqIHvTYlhK9J3nt9730fwIXXbnDCcmqyvKBCCjxSRaKpiwx6E9Z3i5ZBbEKORtl0mt83TWFVW-3epiTDTb1qdvPeh885-mIzjnPixbuJ5i7zgg0P48kqdxDLoMrldeepQAPdtMr8PMdXc7T2Mb-lRYO1GXb_t85d2Gm8S3Jdb4c92HCzfei2yg2kOcgHkOAjHaQhyMDH4WQcaGQXGHsT9GLJZPHi2ahD4ewHuav_I1aH8DS8eRzc0kZAgRrO0jk1llljMSRhPDUZM6mJbFqYtPQs8TrLHH6nRNpSC86tYGVk4zx1GCBFuXU-hXsEndnrzB0DKfKCc2mliYpIlMxobRIXozPIrMidlj24bHFUbzVPhloxIgdEFCKiAiIq7kG_hVo1Z6ZS3DPpeHo0HL5qoV0P_z7byd9eP4XtGCPPuvS6Dx0E2J3BllnOn6v387CXPgHRMsIJ |
| linkProvider | Springer Nature |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LSwMxEB6kCnqxPrFaNQdvurDZZF9HKZaKbRFbS29h81gQpIrbCv57J9ndFkUPet0sIXybZGZ2Zr4P4MJqNxiumaeSNPN4zPFIZaH0jK_Qm9C2WzR3YhPxcJhMp-l91RRW1NXudUrS3dTLZjfrfdicoy02YzgnXrzrHC2WZcx_GE2WuYMgdqpcVnfe42igq1aZn-f4ao5WPua3tKizNt3m_9a5A9uVd0muy-2wC2tmtgfNWrmBVAd5H0J8JJ00BOnYOJyMHI3sAmNvgl4smSyeLRu1K5z9IIPyP2JxAI_dm3Gn51UCCp5iNJp7SlOtNIYklEUqoSpSvo4yFeWWJV4micHvFMY6l5wxzWnu6yCNDAZIfqqNTeEeQmP2MjNHQLI0YyzWsfIzn-dUSalCE6AzSDVPjYxbcFnjKF5LngyxZER2iAhERDhERNCCdg21qM5MIZhl0rH0aDh8VUO7Gv59tuO_vX4Om73xoC_6t8O7E9gKMAoty7Db0ECwzSlsqPf5U_F25vbVJ_Q2xO0 |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1NS8NAEB1ERbxYP7FadQ_eNDTJbr6OUi2KWgrV0tuS7G5AkFhsK_jvndkkrYoexGs2DOFlJzuTmXkP4JS0G4zQ3FFxkjoiEuhSaZA5xlUYTWiaFs2t2ETU68WjUdL_NMVvu93rkmQ500AsTcW0PdZ5ez74RpEI1R-p8YyjffwIrwhqpKd8fTCc1xH8yCp0kQa9I_CwrsZmfrbx9WhaxJvfSqT25Ok2_v_Mm7BRRZ3sotwmW7Bkim1o1IoOrHLwHQjwUmYlI1iH8nM2sPSyM8zJGUa3bDh7JpZq21D7zu7L_4uTXXjsXj10rp1KWMFR3AunjtKeVhpTFY-HKvZUqFwdpirMiT0-i2OD7y-IdJ4JzrXwclf7SWgwcXITbai0uwfLxUth9oGlScp5pCPlpq7IPZVlKjA-BomeFonJoiac1ZjKccmfIedMyRYRiYhIi4j0m9CqYZeVL00kJ4Ydok3D5fMa5sXy79YO_nb7Caz1L7vy7qZ3ewjrPianZXd2C5YRa3MEq-pt-jR5PbZb7AOVr83R |
| 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=Combining+Crown+Structures+for+Vulnerability+Measures&rft.jtitle=Algorithmica&rft.au=Casel+Katrin&rft.au=Friedrich%2C+Tobias&rft.au=Niklanovits+Aikaterini&rft.au=Simonov+Kirill&rft.date=2026-02-01&rft.pub=Springer+Nature+B.V&rft.issn=0178-4617&rft.eissn=1432-0541&rft.volume=88&rft.issue=1&rft_id=info:doi/10.1007%2Fs00453-025-01348-2&rft.externalDBID=NO_FULL_TEXT |
| 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 |