Parameterized Complexity of Geodetic Set
A vertex set $S$ of a graph $G$ is geodetic if every vertex of $G$ lies on a shortest path between two vertices in $S$. Given a graph $G$ and $k \in \mathbb{N}$, the NP-hard ${\rm G{\small EODETIC}~S{ \small ET}}$ problem asks whether there is a geodetic set of size at most $k$. Complementing variou...
Uloženo v:
| Vydáno v: | Journal of graph algorithms and applications Ročník 26; číslo 4; s. 401 - 419 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
01.07.2022
|
| ISSN: | 1526-1719, 1526-1719 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | A vertex set $S$ of a graph $G$ is geodetic if every vertex of $G$ lies on a shortest path between two vertices in $S$. Given a graph $G$ and $k \in \mathbb{N}$, the NP-hard ${\rm G{\small EODETIC}~S{ \small ET}}$ problem asks whether there is a geodetic set of size at most $k$.
Complementing various works on ${\rm G{\small EODETIC}~S{ \small ET}}$ restricted to special graph classes, we initiate a parameterized complexity study of ${\rm G{\small EODETIC}~S{ \small ET}}$ and show, on the one side, that ${\rm G{\small EODETIC}~S{ \small ET}}$ is $W[1]$-hard when parameterized by feedback vertex number, path-width, and solution size, combined.
On the other side, we develop fixed-parameter algorithms with respect to the feedback edge number, the tree-depth, and the modular-width of the input graph. |
|---|---|
| AbstractList | A vertex set $S$ of a graph $G$ is geodetic if every vertex of $G$ lies on a shortest path between two vertices in $S$. Given a graph $G$ and $k \in \mathbb{N}$, the NP-hard ${\rm G{\small EODETIC}~S{ \small ET}}$ problem asks whether there is a geodetic set of size at most $k$.
Complementing various works on ${\rm G{\small EODETIC}~S{ \small ET}}$ restricted to special graph classes, we initiate a parameterized complexity study of ${\rm G{\small EODETIC}~S{ \small ET}}$ and show, on the one side, that ${\rm G{\small EODETIC}~S{ \small ET}}$ is $W[1]$-hard when parameterized by feedback vertex number, path-width, and solution size, combined.
On the other side, we develop fixed-parameter algorithms with respect to the feedback edge number, the tree-depth, and the modular-width of the input graph. |
| Author | Kellerhals, Leon Koana, Tomohiro |
| Author_xml | – sequence: 1 givenname: Leon surname: Kellerhals fullname: Kellerhals, Leon – sequence: 2 givenname: Tomohiro surname: Koana fullname: Koana, Tomohiro |
| BookMark | eNptj8FKxDAURYOM4Mzoxi_oUoSOeUmTtEspOgoDCuq6vKYvkqFthjQLx6_XURciru5dnHvhLNhsDCMxdg58ZUCpq-0r4opzzeGIzUEJnYOBavarn7DFNG05F1KYcs4uHjHiQImif6cuq8Ow6-nNp30WXLam0FHyNnuidMqOHfYTnf3kkr3c3jzXd_nmYX1fX29yC6WAHBwCVtpx1G1VFVISWdvqwigkIZ3tdEtQduhMV2hlpVSlKFTLoeC2rEwrl-zy-9fGME2RXLOLfsC4b4A3B8fm4Nh8OX7C_A9sfcLkw5gi-v6_yQeY31Ys |
| CitedBy_id | crossref_primary_10_1016_j_disc_2025_114595 crossref_primary_10_1016_j_dam_2024_12_032 |
| ContentType | Journal Article |
| DBID | AAYXX CITATION |
| DOI | 10.7155/jgaa.00601 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | CrossRef |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1526-1719 |
| EndPage | 419 |
| ExternalDocumentID | 10_7155_jgaa_00601 |
| GroupedDBID | -~9 29K 2WC 5GY AAFWJ AAKPC AAYXX ACGFO ACIPV AFPKN ALMA_UNASSIGNED_HOLDINGS CITATION D-I E3Z EBS EJD F5P GROUPED_DOAJ M~E OK1 OVT P2P REM RNS TR2 XSB |
| ID | FETCH-LOGICAL-c1821-1fa1a96f0a6b99433eeccb6475ae23fcd6be18daf7d465c3358245b0140c897b3 |
| ISSN | 1526-1719 |
| IngestDate | Tue Nov 18 01:55:57 EST 2025 Tue Nov 18 22:41:43 EST 2025 |
| IsDoiOpenAccess | false |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 4 |
| Language | English |
| License | https://creativecommons.org/licenses/by/4.0 |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c1821-1fa1a96f0a6b99433eeccb6475ae23fcd6be18daf7d465c3358245b0140c897b3 |
| OpenAccessLink | https://doi.org/10.7155/jgaa.00601 |
| PageCount | 19 |
| ParticipantIDs | crossref_primary_10_7155_jgaa_00601 crossref_citationtrail_10_7155_jgaa_00601 |
| PublicationCentury | 2000 |
| PublicationDate | 2022-07-01 |
| PublicationDateYYYYMMDD | 2022-07-01 |
| PublicationDate_xml | – month: 07 year: 2022 text: 2022-07-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationTitle | Journal of graph algorithms and applications |
| PublicationYear | 2022 |
| SSID | ssj0023278 |
| Score | 2.3789227 |
| Snippet | A vertex set $S$ of a graph $G$ is geodetic if every vertex of $G$ lies on a shortest path between two vertices in $S$. Given a graph $G$ and $k \in... |
| SourceID | crossref |
| SourceType | Enrichment Source Index Database |
| StartPage | 401 |
| Title | Parameterized Complexity of Geodetic Set |
| Volume | 26 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAON databaseName: DOAJ Directory of Open Access Journals customDbUrl: eissn: 1526-1719 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0023278 issn: 1526-1719 databaseCode: DOA dateStart: 20030101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals – providerCode: PRVHPJ databaseName: ROAD: Directory of Open Access Scholarly Resources customDbUrl: eissn: 1526-1719 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0023278 issn: 1526-1719 databaseCode: M~E dateStart: 19970101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV07T8MwELZKYYAB8RTPKhIMIBSoEyeOR4TKYwAxFKlb5VdopTZBpaCKgd_O2UmTUDrAwGJFji-J89n3sO_OCB1j7glKIwVTPBQuYUK5gsK84ooIzbnUIub2sAn68BB1OuyxVrubxsK8D2iSRJMJe_lXqKEOwDahs3-Au3goVMA1gA4lwA7lr4B_5MbfyqRg_jCrt8ZlXE9yx4sbnSoTtQgs4tuafEUttRmsz_jgOR31x71hlsK5us1dsmgTRdiD_ljbXlf281OeRZq102Ha64_S6tKCV7qhFtzQC11Mc56m59TlLDQLes-HCqnwQ5I_LhOtJKOa5doUdBrDtZ85P7f5YUrZNN2PnxFZhSMhmDCGumtou5Z2AS16NGDGu-_-s1XY3r5nhXLx9VmmWkN7Ub63optUlIz2GlrNYXAuM1TXUU0nG2jlvkit-7qJTr7h65T4OmnsTPF1AN8t9HTdal_duvlxF64EIw-7OOaYszBu8lAwRnxfw_QSIaEB154fSxUKjSPFY6pIGEjfxDiTQBgTWUaMCn8b1ZM00TvIwZFsgnai7F2pBIsExtJvShl4Ig7FLjqddrQr81zw5kiSQffnD91FR0XblywDypxWe79qtY-Wy3F2gOrj0Zs-REvyfdx_HTXsekjD4vYFnCZTVA |
| linkProvider | ISSN International Centre |
| 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=Parameterized+Complexity+of+Geodetic+Set&rft.jtitle=Journal+of+graph+algorithms+and+applications&rft.au=Kellerhals%2C+Leon&rft.au=Koana%2C+Tomohiro&rft.date=2022-07-01&rft.issn=1526-1719&rft.eissn=1526-1719&rft.volume=26&rft.issue=4&rft.spage=401&rft.epage=419&rft_id=info:doi/10.7155%2Fjgaa.00601&rft.externalDBID=n%2Fa&rft.externalDocID=10_7155_jgaa_00601 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1526-1719&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1526-1719&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1526-1719&client=summon |