The Complexity Landscape of Fixed-Parameter Directed Steiner Network Problems
Given a directed graph \(G\) and a list \((s_1,t_1),\dots,(s_d,t_d)\) of terminal pairs, the Directed Steiner Network problem asks for a minimum-cost subgraph of \(G\) that contains a directed \(s_i\to t_i\) path for every \(1\le i \le k\). The special case Directed Steiner Tree (when we ask for pat...
Gespeichert in:
| Veröffentlicht in: | arXiv.org |
|---|---|
| Hauptverfasser: | , |
| Format: | Paper |
| Sprache: | Englisch |
| Veröffentlicht: |
Ithaca
Cornell University Library, arXiv.org
10.11.2022
|
| Schlagworte: | |
| ISSN: | 2331-8422 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | Given a directed graph \(G\) and a list \((s_1,t_1),\dots,(s_d,t_d)\) of terminal pairs, the Directed Steiner Network problem asks for a minimum-cost subgraph of \(G\) that contains a directed \(s_i\to t_i\) path for every \(1\le i \le k\). The special case Directed Steiner Tree (when we ask for paths from a root \(r\) to terminals \(t_1,\dots,t_d\)) is known to be fixed-parameter tractable parameterized by the number of terminals, while the special case Strongly Connected Steiner Subgraph (when we ask for a path from every \(t_i\) to every other \(t_j\)) is known to be W[1]-hard. We systematically explore the complexity landscape of directed Steiner problems to fully understand which other special cases are FPT or W[1]-hard. Formally, if \(\mathcal{H}\) is a class of directed graphs, then we look at the special case of Directed Steiner Network where the list \((s_1,t_1),\dots,(s_d,t_d)\) of requests form a directed graph that is a member of \(\mathcal{H}\). Our main result is a complete characterization of the classes \(\mathcal{H}\) resulting in fixed-parameter tractable special cases: we show that if every pattern in \(\mathcal{H}\) has the combinatorial property of being "transitively equivalent to a bounded-length caterpillar with a bounded number of extra edges," then the problem is FPT, and it is W[1]-hard for every recursively enumerable \(\mathcal{H}\) not having this property. This complete dichotomy unifies and generalizes the known results showing that Directed Steiner Tree is FPT [Dreyfus and Wagner, Networks 1971], \(q\)-Root Steiner Tree is FPT for constant \(q\) [Suchý, WG 2016], Strongly Connected Steiner Subgraph is W[1]-hard [Guo et al., SIAM J. Discrete Math. 2011], and Directed Steiner Network is solvable in polynomial-time for constant number of terminals [Feldman and Ruhl, SIAM J. Comput. 2006], and moreover reveals a large continent of tractable cases that were not known before. |
|---|---|
| AbstractList | Given a directed graph \(G\) and a list \((s_1,t_1),\dots,(s_d,t_d)\) of terminal pairs, the Directed Steiner Network problem asks for a minimum-cost subgraph of \(G\) that contains a directed \(s_i\to t_i\) path for every \(1\le i \le k\). The special case Directed Steiner Tree (when we ask for paths from a root \(r\) to terminals \(t_1,\dots,t_d\)) is known to be fixed-parameter tractable parameterized by the number of terminals, while the special case Strongly Connected Steiner Subgraph (when we ask for a path from every \(t_i\) to every other \(t_j\)) is known to be W[1]-hard. We systematically explore the complexity landscape of directed Steiner problems to fully understand which other special cases are FPT or W[1]-hard. Formally, if \(\mathcal{H}\) is a class of directed graphs, then we look at the special case of Directed Steiner Network where the list \((s_1,t_1),\dots,(s_d,t_d)\) of requests form a directed graph that is a member of \(\mathcal{H}\). Our main result is a complete characterization of the classes \(\mathcal{H}\) resulting in fixed-parameter tractable special cases: we show that if every pattern in \(\mathcal{H}\) has the combinatorial property of being "transitively equivalent to a bounded-length caterpillar with a bounded number of extra edges," then the problem is FPT, and it is W[1]-hard for every recursively enumerable \(\mathcal{H}\) not having this property. This complete dichotomy unifies and generalizes the known results showing that Directed Steiner Tree is FPT [Dreyfus and Wagner, Networks 1971], \(q\)-Root Steiner Tree is FPT for constant \(q\) [Suchý, WG 2016], Strongly Connected Steiner Subgraph is W[1]-hard [Guo et al., SIAM J. Discrete Math. 2011], and Directed Steiner Network is solvable in polynomial-time for constant number of terminals [Feldman and Ruhl, SIAM J. Comput. 2006], and moreover reveals a large continent of tractable cases that were not known before. |
| Author | Feldmann, Andreas Emil Marx, Daniel |
| Author_xml | – sequence: 1 givenname: Andreas surname: Feldmann middlename: Emil fullname: Feldmann, Andreas Emil – sequence: 2 givenname: Daniel surname: Marx fullname: Marx, Daniel |
| BookMark | eNotj01LxDAYhIMouK77A7wFPLe-TZqPHqW6KlRdsPclad5i17apaVfrv7egp4FheGbmgpz2vkdCrhKIUy0E3JgwN19xokDFIDXoE7JinCeRThk7J5txPAAAk4oJwVfkuXxHmvtuaHFuph9amN6NlRmQ-ppumxldtDPBdDhhoHdNwGpCR98mbPrFeMHp24cPugvettiNl-SsNu2Im39dk3J7X-aPUfH68JTfFpERjEVMKGellJlTkEKdSssyzY1yHDWXZtmMqq5tra2ALLWVTEwmrBFqeZACd3xNrv-wQ_CfRxyn_cEfQ7807hkomWm5RPkvlmRQig |
| ContentType | Paper |
| Copyright | 2022. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| Copyright_xml | – notice: 2022. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| DBID | 8FE 8FG ABJCF ABUWG AFKRA AZQEC BENPR BGLVJ CCPQU DWQXO HCIFZ L6V M7S PHGZM PHGZT PIMPY PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS |
| DOI | 10.48550/arxiv.1707.06808 |
| DatabaseName | ProQuest SciTech Collection ProQuest Technology Collection Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland ProQuest Central Essentials - QC ProQuest Central Database Suite (ProQuest) ProQuest Technology Collection ProQuest One ProQuest Central Korea SciTech Collection (ProQuest) ProQuest Engineering Collection Engineering Database Proquest Central Premium ProQuest One Academic (New) ProQuest Publicly Available Content Database ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection |
| DatabaseTitle | Publicly Available Content Database Engineering Database Technology Collection ProQuest One Academic Middle East (New) ProQuest Central Essentials ProQuest One Academic Eastern Edition ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Technology Collection ProQuest SciTech Collection ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest One Academic UKI Edition ProQuest Central Korea Materials Science & Engineering Collection ProQuest Central (New) ProQuest One Academic ProQuest One Academic (New) Engineering Collection |
| DatabaseTitleList | Publicly Available Content Database |
| Database_xml | – sequence: 1 dbid: PIMPY name: ProQuest Publicly Available Content Database url: http://search.proquest.com/publiccontent sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Physics |
| EISSN | 2331-8422 |
| Genre | Working Paper/Pre-Print |
| GroupedDBID | 8FE 8FG ABJCF ABUWG AFKRA ALMA_UNASSIGNED_HOLDINGS AZQEC BENPR BGLVJ CCPQU DWQXO FRJ HCIFZ L6V M7S M~E PHGZM PHGZT PIMPY PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS |
| ID | FETCH-LOGICAL-a522-257db6669d7040f46b2983a7d3e836a808e7ffbf8b5094bc61a95ba57422403d3 |
| IEDL.DBID | BENPR |
| IngestDate | Mon Jun 30 09:44:24 EDT 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | false |
| IsScholarly | false |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-a522-257db6669d7040f46b2983a7d3e836a808e7ffbf8b5094bc61a95ba57422403d3 |
| Notes | SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50 |
| OpenAccessLink | https://www.proquest.com/docview/2076986742?pq-origsite=%requestingapplication% |
| PQID | 2076986742 |
| PQPubID | 2050157 |
| ParticipantIDs | proquest_journals_2076986742 |
| PublicationCentury | 2000 |
| PublicationDate | 20221110 |
| PublicationDateYYYYMMDD | 2022-11-10 |
| PublicationDate_xml | – month: 11 year: 2022 text: 20221110 day: 10 |
| PublicationDecade | 2020 |
| PublicationPlace | Ithaca |
| PublicationPlace_xml | – name: Ithaca |
| PublicationTitle | arXiv.org |
| PublicationYear | 2022 |
| Publisher | Cornell University Library, arXiv.org |
| Publisher_xml | – name: Cornell University Library, arXiv.org |
| SSID | ssj0002672553 |
| Score | 1.8126727 |
| SecondaryResourceType | preprint |
| Snippet | Given a directed graph \(G\) and a list \((s_1,t_1),\dots,(s_d,t_d)\) of terminal pairs, the Directed Steiner Network problem asks for a minimum-cost subgraph... |
| SourceID | proquest |
| SourceType | Aggregation Database |
| SubjectTerms | Combinatorial analysis Complexity Decision trees Graph theory Graphs Parameters Polynomials Terminals |
| Title | The Complexity Landscape of Fixed-Parameter Directed Steiner Network Problems |
| URI | https://www.proquest.com/docview/2076986742 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8NAEB60VfDkGx-17MFr1DbJPk6C0qJgQ7A91FPZV6CXtia11H_vTJLqQfDiMRsI2dmd2Z3Zb78P4PrOSAyIWRx4GSlMUO7QpXSkA2FjabzQmEG7UmxCJIkcj1VaF9yKGla5iYlloHZzSzVyqoRwJTlmcveL94BUo-h0tZbQ2IYmMZVFDWg-9JL09bvK0uUC98xhdZxZknfd6nw9Xd10BHEXku7EryBcriz9_f_-0wE0U73w-SFs-dkR7JaITlscwwAnACNvJ8bL5Sd7oTu9hHZi84z1p2vvglQTMgsNy6rA5x0bkvglNiQVOpylld5McQKjfm_0-BTU2gmBxh1VgI7oDGYmygn00izipqtkqIULvQy5xm57kWUmk4YI9IzlHa1io2PsChH0ufAUGrP5zJ8Bww8oGWVeWtuJrDXKRtzHwnDNJY-NPYfWxjiTev4Xkx_LXPz9-hL2unShoATWtaCxzD_8FezY1XJa5O16ONuEyBziU_o8SN--AINorRo |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V07T8MwED6VFgQTb_Eo4AHGQJuH7QyIAahatY0i0aFMke04Upe2JKW0P4r_yDlpYEBi68CaSLac-3y5s7-7D-C6ITk6xMSzNHd9TFAauKWEKyymPC41E5hBx7nYBAsCPhz6YQU-y1oYQ6ssfWLuqOOJMmfk5iSE-pxiJvcwfbOMapS5XS0lNApYdPXyA1O27L7zhPa9se3W8-Cxba1UBSyBsYaFEI0lxux-zBC_iUul7XNHsNjR3KGCN7hmSSITLk1rOaloU_ieFB5ObFrXxQ4OuwE1F7HOq1ALO_3w9ftQx6YMQ3SnuD3Ne4XdiXQxmt82mWmVaGQufvn8_EfW2v1nn2APly6mOt2Hih4fwFbOV1XZIfQR3sT4MtPPc7YkPVOxbLhcZJKQ1mihYysUhneGsCGFW9cxeTHSnvggKLjvJCzUdLIjGKxjAcdQHU_G-gQIDuBzN9FcqaarlPSVS7XHJBWUU0-qU6iXtohWuzuLfgxx9vfrK9huD_q9qNcJuuewY5vSiZxCWIfqLH3XF7Cp5rNRll6ukEQgWrPhvgBcegRg |
| 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=The+Complexity+Landscape+of+Fixed-Parameter+Directed+Steiner+Network+Problems&rft.jtitle=arXiv.org&rft.au=Feldmann%2C+Andreas+Emil&rft.au=Marx%2C+Daniel&rft.date=2022-11-10&rft.pub=Cornell+University+Library%2C+arXiv.org&rft.eissn=2331-8422&rft_id=info:doi/10.48550%2Farxiv.1707.06808 |