Component Order Connectivity in Directed Graphs
A directed graph D is semicomplete if for every pair x , y of vertices of D , there is at least one arc between x and y . Thus, a tournament is a semicomplete digraph. In the Directed Component Order Connectivity (DCOC) problem, given a digraph D = ( V , A ) and a pair of natural numbers k and ℓ ,...
Uloženo v:
| Vydáno v: | Algorithmica Ročník 84; číslo 9; s. 2767 - 2784 |
|---|---|
| Hlavní autoři: | , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
Springer US
01.09.2022
Springer Nature B.V |
| Témata: | |
| ISSN: | 0178-4617, 1432-0541 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | A directed graph
D
is semicomplete if for every pair
x
,
y
of vertices of
D
, there is at least one arc between
x
and
y
. Thus, a tournament is a semicomplete digraph. In the Directed Component Order Connectivity (DCOC) problem, given a digraph
D
=
(
V
,
A
)
and a pair of natural numbers
k
and
ℓ
, we are to decide whether there is a subset
X
of
V
of size
k
such that the largest strongly connected component in
D
-
X
has at most
ℓ
vertices. Note that DCOC reduces to the Directed Feedback Vertex Set problem for
ℓ
=
1
.
We study the parameterized complexity of DCOC for general and semicomplete digraphs with the following parameters:
k
,
ℓ
,
ℓ
+
k
and
n
-
ℓ
. In particular, we prove that DCOC with parameter
k
on semicomplete digraphs can be solved in time
O
∗
(
2
16
k
)
but not in time
O
∗
(
2
o
(
k
)
)
unless the Exponential Time Hypothesis (ETH) fails. The upper bound
O
∗
(
2
16
k
)
implies the upper bound
O
∗
(
2
16
(
n
-
ℓ
)
)
for the parameter
n
-
ℓ
.
We complement the latter by showing that there is no algorithm of time complexity
O
∗
(
2
o
(
n
-
ℓ
)
)
unless ETH fails. Finally, we improve (in dependency on
ℓ
) the upper bound of Göke, Marx and Mnich (2019) for the time complexity of DCOC with parameter
ℓ
+
k
on general digraphs from
O
∗
(
2
O
(
k
ℓ
log
(
k
ℓ
)
)
)
to
O
∗
(
2
O
(
k
log
(
k
ℓ
)
)
)
.
Note that Drange, Dregi and van ’t Hof (2016) proved that even for the undirected version of DCOC on split graphs there is no algorithm of running time
O
∗
(
2
o
(
k
log
ℓ
)
)
unless ETH fails and it is a long-standing problem to decide whether Directed Feedback Vertex Set admits an algorithm of time complexity
O
∗
(
2
o
(
k
log
k
)
)
. |
|---|---|
| AbstractList | A directed graph
D
is semicomplete if for every pair
x
,
y
of vertices of
D
, there is at least one arc between
x
and
y
. Thus, a tournament is a semicomplete digraph. In the Directed Component Order Connectivity (DCOC) problem, given a digraph
$$D=(V,A)$$
D
=
(
V
,
A
)
and a pair of natural numbers
k
and
$$\ell $$
ℓ
, we are to decide whether there is a subset
X
of
V
of size
k
such that the largest strongly connected component in
$$D-X$$
D
-
X
has at most
$$\ell $$
ℓ
vertices. Note that DCOC reduces to the Directed Feedback Vertex Set problem for
$$\ell =1.$$
ℓ
=
1
.
We study the parameterized complexity of DCOC for general and semicomplete digraphs with the following parameters:
$$k, \ell ,\ell +k$$
k
,
ℓ
,
ℓ
+
k
and
$$n-\ell $$
n
-
ℓ
. In particular, we prove that DCOC with parameter
k
on semicomplete digraphs can be solved in time
$$O^*(2^{16k})$$
O
∗
(
2
16
k
)
but not in time
$$O^*(2^{o(k)})$$
O
∗
(
2
o
(
k
)
)
unless the Exponential Time Hypothesis (ETH) fails. The upper bound
$$O^*(2^{16k})$$
O
∗
(
2
16
k
)
implies the upper bound
$$O^*(2^{16(n-\ell )})$$
O
∗
(
2
16
(
n
-
ℓ
)
)
for the parameter
$$n-\ell .$$
n
-
ℓ
.
We complement the latter by showing that there is no algorithm of time complexity
$$O^*(2^{o({n-\ell })})$$
O
∗
(
2
o
(
n
-
ℓ
)
)
unless ETH fails. Finally, we improve (in dependency on
$$\ell $$
ℓ
) the upper bound of Göke, Marx and Mnich (2019) for the time complexity of DCOC with parameter
$$\ell +k$$
ℓ
+
k
on general digraphs from
$$O^*(2^{O(k\ell \log (k\ell ))})$$
O
∗
(
2
O
(
k
ℓ
log
(
k
ℓ
)
)
)
to
$$O^*(2^{O(k\log (k\ell ))}).$$
O
∗
(
2
O
(
k
log
(
k
ℓ
)
)
)
.
Note that Drange, Dregi and van ’t Hof (2016) proved that even for the undirected version of DCOC on split graphs there is no algorithm of running time
$$O^*(2^{o(k\log \ell )})$$
O
∗
(
2
o
(
k
log
ℓ
)
)
unless ETH fails and it is a long-standing problem to decide whether Directed Feedback Vertex Set admits an algorithm of time complexity
$$O^*(2^{o(k\log k)}).$$
O
∗
(
2
o
(
k
log
k
)
)
. A directed graph D is semicomplete if for every pair x , y of vertices of D , there is at least one arc between x and y . Thus, a tournament is a semicomplete digraph. In the Directed Component Order Connectivity (DCOC) problem, given a digraph D = ( V , A ) and a pair of natural numbers k and ℓ , we are to decide whether there is a subset X of V of size k such that the largest strongly connected component in D - X has at most ℓ vertices. Note that DCOC reduces to the Directed Feedback Vertex Set problem for ℓ = 1 . We study the parameterized complexity of DCOC for general and semicomplete digraphs with the following parameters: k , ℓ , ℓ + k and n - ℓ . In particular, we prove that DCOC with parameter k on semicomplete digraphs can be solved in time O ∗ ( 2 16 k ) but not in time O ∗ ( 2 o ( k ) ) unless the Exponential Time Hypothesis (ETH) fails. The upper bound O ∗ ( 2 16 k ) implies the upper bound O ∗ ( 2 16 ( n - ℓ ) ) for the parameter n - ℓ . We complement the latter by showing that there is no algorithm of time complexity O ∗ ( 2 o ( n - ℓ ) ) unless ETH fails. Finally, we improve (in dependency on ℓ ) the upper bound of Göke, Marx and Mnich (2019) for the time complexity of DCOC with parameter ℓ + k on general digraphs from O ∗ ( 2 O ( k ℓ log ( k ℓ ) ) ) to O ∗ ( 2 O ( k log ( k ℓ ) ) ) . Note that Drange, Dregi and van ’t Hof (2016) proved that even for the undirected version of DCOC on split graphs there is no algorithm of running time O ∗ ( 2 o ( k log ℓ ) ) unless ETH fails and it is a long-standing problem to decide whether Directed Feedback Vertex Set admits an algorithm of time complexity O ∗ ( 2 o ( k log k ) ) . A directed graph D is semicomplete if for every pair x, y of vertices of D, there is at least one arc between x and y. Thus, a tournament is a semicomplete digraph. In the Directed Component Order Connectivity (DCOC) problem, given a digraph D=(V,A) and a pair of natural numbers k and ℓ, we are to decide whether there is a subset X of V of size k such that the largest strongly connected component in D-X has at most ℓ vertices. Note that DCOC reduces to the Directed Feedback Vertex Set problem for ℓ=1. We study the parameterized complexity of DCOC for general and semicomplete digraphs with the following parameters: k,ℓ,ℓ+k and n-ℓ. In particular, we prove that DCOC with parameter k on semicomplete digraphs can be solved in time O∗(216k) but not in time O∗(2o(k)) unless the Exponential Time Hypothesis (ETH) fails. The upper bound O∗(216k) implies the upper bound O∗(216(n-ℓ)) for the parameter n-ℓ. We complement the latter by showing that there is no algorithm of time complexity O∗(2o(n-ℓ)) unless ETH fails. Finally, we improve (in dependency on ℓ) the upper bound of Göke, Marx and Mnich (2019) for the time complexity of DCOC with parameter ℓ+k on general digraphs from O∗(2O(kℓlog(kℓ))) to O∗(2O(klog(kℓ))). Note that Drange, Dregi and van ’t Hof (2016) proved that even for the undirected version of DCOC on split graphs there is no algorithm of running time O∗(2o(klogℓ)) unless ETH fails and it is a long-standing problem to decide whether Directed Feedback Vertex Set admits an algorithm of time complexity O∗(2o(klogk)). |
| Author | Gutin, Gregory Eiben, Eduard Wahlström, Magnus Yeo, Anders Bang-Jensen, Jørgen |
| Author_xml | – sequence: 1 givenname: Jørgen surname: Bang-Jensen fullname: Bang-Jensen, Jørgen organization: University of Southern Denmark – sequence: 2 givenname: Eduard surname: Eiben fullname: Eiben, Eduard organization: Royal Holloway, University of London – sequence: 3 givenname: Gregory orcidid: 0000-0002-2377-0417 surname: Gutin fullname: Gutin, Gregory email: g.gutin@rhul.ac.uk organization: Royal Holloway, University of London – sequence: 4 givenname: Magnus surname: Wahlström fullname: Wahlström, Magnus organization: Royal Holloway, University of London – sequence: 5 givenname: Anders surname: Yeo fullname: Yeo, Anders organization: University of Southern Denmark |
| BookMark | eNp9kM1KAzEUhYNUsK2-gKsB12PzN0lmKaNWodCNrkNmJtGUNhmTVGif3ugIgouuLudyvnMvZwYmzjsNwDWCtwhCvogQ0oqUEOMS5gUtj2dgiijJsqJoAqYQcVFShvgFmMW4gRBhXrMpWDR-N-Qsl4p16HUoGu-c7pL9tOlQWFfc25Cl7otlUMN7vATnRm2jvvqdc_D6-PDSPJWr9fK5uVuVHWEklca0rRIVMoxrXbdMKMFwrVSvldKa1rWixvSE0xYJSBGsudKCGsJEpxjpWjIHN2PuEPzHXsckN34fXD4pMYeoqjBFPLvE6OqCjzFoIzubVLLepaDsViIov-uRYz0y1yN_6pHHjOJ_6BDsToXDaYiMUMxm96bD31cnqC9ovnoY |
| CitedBy_id | crossref_primary_10_1002_net_22284 crossref_primary_10_1016_j_cosrev_2023_100556 |
| Cites_doi | 10.1007/978-1-4471-5559-1 10.1137/0405027 10.1007/978-3-319-57586-5_13 10.1145/1411509.1411511 10.1006/jcss.2001.1774 10.1007/978-1-84800-998-1 10.1016/S0022-0000(03)00074-6 10.1007/978-1-4612-0515-9 10.1007/3-540-52292-1_16 10.1137/0222038 10.1007/978-3-319-71840-8 10.1007/s10107-018-1255-7 10.1007/s00453-016-0127-x 10.1007/978-3-030-17402-6_21 10.1007/978-3-319-21275-3 |
| ContentType | Journal Article |
| Copyright | The Author(s) 2022 The Author(s) 2022. 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) 2022 – notice: The Author(s) 2022. 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/s00453-022-01004-z |
| 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 |
| EndPage | 2784 |
| ExternalDocumentID | 10_1007_s00453_022_01004_z |
| GrantInformation_xml | – fundername: Leverhulme Trust grantid: RPG-2018-161 funderid: http://dx.doi.org/10.13039/501100000275 – fundername: Danmarks Frie Forskningsfond grantid: DFF 7014-00037B funderid: http://dx.doi.org/10.13039/501100011958 |
| GroupedDBID | -4Z -59 -5G -BR -EM -Y2 -~C -~X .86 .DC .VR 06D 0R~ 0VY 199 1N0 1SB 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 78A 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AAOBN AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDPE ABDZT ABECU ABFSI ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABLJU ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTAH ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFGCZ AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AI. AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BBWZM BDATZ BGNMA BSONS C6C CAG COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP E.L EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ H~9 I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV KOW LAS LLZTM M4Y MA- N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM P19 P9O PF- PT4 PT5 QOK QOS R4E R89 R9I RHV RIG RNI RNS ROL RPX RSV RZK S16 S1Z S26 S27 S28 S3B SAP SCJ SCLPG SCO SDH SDM SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TN5 TSG TSK TSV TUC U2A UG4 UOJIU UQL UTJUX UZXMN VC2 VFIZW VH1 VXZ W23 W48 WK8 YLTOR Z45 Z7X Z83 Z88 Z8R Z8W Z92 ZMTXR ZY4 ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC ADHKG AEZWR AFDZB AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP ATHPR AYFIA CITATION JQ2 |
| ID | FETCH-LOGICAL-c363t-ffbba851f67ee9b68a8629aadeaaee499a4ffd374b18041097ae84f368ca63cb3 |
| IEDL.DBID | RSV |
| ISICitedReferencesCount | 2 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000829125600002&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 | Thu Oct 02 16:28:48 EDT 2025 Sat Nov 29 02:20:33 EST 2025 Tue Nov 18 22:08:46 EST 2025 Fri Feb 21 02:45:58 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 9 |
| Keywords | Parameterized Complexity Order connectivity Strong connectivity Directed graph |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c363t-ffbba851f67ee9b68a8629aadeaaee499a4ffd374b18041097ae84f368ca63cb3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0002-2377-0417 |
| OpenAccessLink | https://link.springer.com/10.1007/s00453-022-01004-z |
| PQID | 2701552417 |
| PQPubID | 2043795 |
| PageCount | 18 |
| ParticipantIDs | proquest_journals_2701552417 crossref_citationtrail_10_1007_s00453_022_01004_z crossref_primary_10_1007_s00453_022_01004_z springer_journals_10_1007_s00453_022_01004_z |
| PublicationCentury | 2000 |
| PublicationDate | 2022-09-01 |
| PublicationDateYYYYMMDD | 2022-09-01 |
| PublicationDate_xml | – month: 09 year: 2022 text: 2022-09-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | Algorithmica |
| PublicationTitleAbbrev | Algorithmica |
| PublicationYear | 2022 |
| Publisher | Springer US Springer Nature B.V |
| Publisher_xml | – name: Springer US – name: Springer Nature B.V |
| References | DowneyRFellowsMFundamentals of Parameterized Complexity2013LondonSpringer10.1007/978-1-4471-5559-1 Neogi, R., Ramanujan, M.S., Saurabh, S., Sharma, R.: On the parameterized complexity of deletion to H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\cal{H}$$\end{document}-free strong components. In: Esparza, J., Král’, D. (eds.) 45th International Symposium on Mathematical Foundations of Computer Science, MFCS 2020, August 24-28, 2020, Prague, Czech Republic, volume 170 of LIPIcs, pp. 75:1–75:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020) ImpagliazzoRPaturiRZaneFWhich problems have strongly exponential complexity?J. Comput. System Sci.2001634512530189451910.1006/jcss.2001.1774 BussJFGoldsmithJNondeterminism within PSIAM J. Comput.1993223560572121904110.1137/0222038 CaiLJuedesDOn the existence of subexponential parameterized algorithmsJ. Comput. System Sci.2003674789807203651410.1016/S0022-0000(03)00074-6 DrangePDregiMvan’t HofPOn the computational complexity of vertex integrity and component order connectivityAlgorithmica201676411811202356763210.1007/s00453-016-0127-x Bang-JensenJGutinGDigraphs: Theory, Algorithms and Applications20092LondonSpringer-Verlag10.1007/978-1-84800-998-1 Göke, A., Marx, D., Mnich, M.: Parameterized algorithms for generalizations of directed feedback vertex set. In: Heggernes, P. (ed.) Algorithms and Complexity - 11th International Conference, CIAC 2019, Rome, Italy, May 27-29, 2019, Proceedings, volume 11485 of Lecture Notes in Computer Science, pp. 249–261. Springer (2019) FlumJGroheMParameterized Complexity Theory2006BerlinSpringer1143.68016 LeeEPartitioning a graph into small pieces with applications to path transversalMath. Program.20191771–2119398719210.1007/s10107-018-1255-7 GrossDHeinigMIswaraLKazmierczakLWLuttrellKSaccomanJTSuffelCA survey of component order connectivity models of graph theoretic networksWSEAS Trans. on Math.201312895910 Bshouty, N., Gabizon, A.: Almost optimal cover-free families. In: Fotakis, D., Pagourtzis, A., Paschos, V.T. (eds.) Algorithms and Complexity - 10th International Conference, CIAC 2017, Athens, Greece, May 24-26, 2017, Proceedings, volume 10236 of Lecture Notes in Computer Science, pp. 140–151 (2017) DowneyRFellowsMParameterized Complexity1999New YorkMonographs in Computer Science. Springer10.1007/978-1-4612-0515-9 Speckenmeyer, E.: On feedback problems in digraphs. In: Nagl, M. (ed.) Graph-Theoretic Concepts in Computer Science, 15th International Workshop, WG ’89, 1989, Proceedings, volume 411 of Lecture Notes in Computer Science, pp. 218–231. Springer (1989) Bang-JensenJThomassenCA polynomial algorithm for the 2-path problem for semicomplete digraphsSIAM J. Discrete Math.199253366376117274410.1137/0405027 Kumar, M., Lokshtanov, D..: A 2lk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2lk$$\end{document} kernel for l\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l$$\end{document}-component order connectivity. In: Guo, J., Hermelin, D. (eds.) 11th International Symposium on Parameterized and Exact Computation, IPEC 2016, August 24-26, 2016, Aarhus, Denmark, volume 63 of LIPIcs, pp. 20:1–20:14. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2016) Bang-Jensen, J., Gutin, G. (eds.) Classes of Directed Graphs. Springer Monographs in Mathematics. Springer (2018) ChenJLiuYLuSO’SullivanBRazgonIA fixed-parameter algorithm for the directed feedback vertex set problemJ. Assoc. Comput. Mach.200855521:121:19245654610.1145/1411509.1411511 CyganMFominFKowalikLLokshtanovDMarxDPilipczukMPilipczukMSaurabhSParameterized Algorithms2015ChamSpringer10.1007/978-3-319-21275-3 1004_CR19 J Flum (1004_CR12) 2006 1004_CR18 J Bang-Jensen (1004_CR3) 1992; 5 1004_CR16 M Cygan (1004_CR8) 2015 R Downey (1004_CR9) 1999 P Drange (1004_CR11) 2016; 76 R Downey (1004_CR10) 2013 D Gross (1004_CR14) 2013; 12 R Impagliazzo (1004_CR15) 2001; 63 1004_CR2 L Cai (1004_CR6) 2003; 67 JF Buss (1004_CR5) 1993; 22 E Lee (1004_CR17) 2019; 177 J Chen (1004_CR7) 2008; 55 1004_CR13 J Bang-Jensen (1004_CR1) 2009 1004_CR4 |
| References_xml | – reference: Bshouty, N., Gabizon, A.: Almost optimal cover-free families. In: Fotakis, D., Pagourtzis, A., Paschos, V.T. (eds.) Algorithms and Complexity - 10th International Conference, CIAC 2017, Athens, Greece, May 24-26, 2017, Proceedings, volume 10236 of Lecture Notes in Computer Science, pp. 140–151 (2017) – reference: FlumJGroheMParameterized Complexity Theory2006BerlinSpringer1143.68016 – reference: DrangePDregiMvan’t HofPOn the computational complexity of vertex integrity and component order connectivityAlgorithmica201676411811202356763210.1007/s00453-016-0127-x – reference: LeeEPartitioning a graph into small pieces with applications to path transversalMath. Program.20191771–2119398719210.1007/s10107-018-1255-7 – reference: Neogi, R., Ramanujan, M.S., Saurabh, S., Sharma, R.: On the parameterized complexity of deletion to H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\cal{H}$$\end{document}-free strong components. In: Esparza, J., Král’, D. (eds.) 45th International Symposium on Mathematical Foundations of Computer Science, MFCS 2020, August 24-28, 2020, Prague, Czech Republic, volume 170 of LIPIcs, pp. 75:1–75:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020) – reference: Bang-Jensen, J., Gutin, G. (eds.) Classes of Directed Graphs. Springer Monographs in Mathematics. Springer (2018) – reference: DowneyRFellowsMParameterized Complexity1999New YorkMonographs in Computer Science. Springer10.1007/978-1-4612-0515-9 – reference: ChenJLiuYLuSO’SullivanBRazgonIA fixed-parameter algorithm for the directed feedback vertex set problemJ. Assoc. Comput. Mach.200855521:121:19245654610.1145/1411509.1411511 – reference: GrossDHeinigMIswaraLKazmierczakLWLuttrellKSaccomanJTSuffelCA survey of component order connectivity models of graph theoretic networksWSEAS Trans. on Math.201312895910 – reference: Bang-JensenJGutinGDigraphs: Theory, Algorithms and Applications20092LondonSpringer-Verlag10.1007/978-1-84800-998-1 – reference: CaiLJuedesDOn the existence of subexponential parameterized algorithmsJ. Comput. System Sci.2003674789807203651410.1016/S0022-0000(03)00074-6 – reference: Speckenmeyer, E.: On feedback problems in digraphs. In: Nagl, M. (ed.) Graph-Theoretic Concepts in Computer Science, 15th International Workshop, WG ’89, 1989, Proceedings, volume 411 of Lecture Notes in Computer Science, pp. 218–231. Springer (1989) – reference: ImpagliazzoRPaturiRZaneFWhich problems have strongly exponential complexity?J. Comput. System Sci.2001634512530189451910.1006/jcss.2001.1774 – reference: Göke, A., Marx, D., Mnich, M.: Parameterized algorithms for generalizations of directed feedback vertex set. In: Heggernes, P. (ed.) Algorithms and Complexity - 11th International Conference, CIAC 2019, Rome, Italy, May 27-29, 2019, Proceedings, volume 11485 of Lecture Notes in Computer Science, pp. 249–261. Springer (2019) – reference: Kumar, M., Lokshtanov, D..: A 2lk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2lk$$\end{document} kernel for l\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l$$\end{document}-component order connectivity. In: Guo, J., Hermelin, D. (eds.) 11th International Symposium on Parameterized and Exact Computation, IPEC 2016, August 24-26, 2016, Aarhus, Denmark, volume 63 of LIPIcs, pp. 20:1–20:14. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2016) – reference: Bang-JensenJThomassenCA polynomial algorithm for the 2-path problem for semicomplete digraphsSIAM J. Discrete Math.199253366376117274410.1137/0405027 – reference: CyganMFominFKowalikLLokshtanovDMarxDPilipczukMPilipczukMSaurabhSParameterized Algorithms2015ChamSpringer10.1007/978-3-319-21275-3 – reference: DowneyRFellowsMFundamentals of Parameterized Complexity2013LondonSpringer10.1007/978-1-4471-5559-1 – reference: BussJFGoldsmithJNondeterminism within PSIAM J. Comput.1993223560572121904110.1137/0222038 – volume-title: Fundamentals of Parameterized Complexity year: 2013 ident: 1004_CR10 doi: 10.1007/978-1-4471-5559-1 – volume: 5 start-page: 366 issue: 3 year: 1992 ident: 1004_CR3 publication-title: SIAM J. Discrete Math. doi: 10.1137/0405027 – ident: 1004_CR4 doi: 10.1007/978-3-319-57586-5_13 – volume: 55 start-page: 21:1 issue: 5 year: 2008 ident: 1004_CR7 publication-title: J. Assoc. Comput. Mach. doi: 10.1145/1411509.1411511 – volume: 63 start-page: 512 issue: 4 year: 2001 ident: 1004_CR15 publication-title: J. Comput. System Sci. doi: 10.1006/jcss.2001.1774 – volume-title: Digraphs: Theory, Algorithms and Applications year: 2009 ident: 1004_CR1 doi: 10.1007/978-1-84800-998-1 – volume: 67 start-page: 789 issue: 4 year: 2003 ident: 1004_CR6 publication-title: J. Comput. System Sci. doi: 10.1016/S0022-0000(03)00074-6 – volume-title: Parameterized Complexity year: 1999 ident: 1004_CR9 doi: 10.1007/978-1-4612-0515-9 – ident: 1004_CR19 doi: 10.1007/3-540-52292-1_16 – volume: 12 start-page: 895 year: 2013 ident: 1004_CR14 publication-title: WSEAS Trans. on Math. – volume: 22 start-page: 560 issue: 3 year: 1993 ident: 1004_CR5 publication-title: SIAM J. Comput. doi: 10.1137/0222038 – ident: 1004_CR2 doi: 10.1007/978-3-319-71840-8 – volume-title: Parameterized Complexity Theory year: 2006 ident: 1004_CR12 – ident: 1004_CR16 – volume: 177 start-page: 1 issue: 1–2 year: 2019 ident: 1004_CR17 publication-title: Math. Program. doi: 10.1007/s10107-018-1255-7 – volume: 76 start-page: 1181 issue: 4 year: 2016 ident: 1004_CR11 publication-title: Algorithmica doi: 10.1007/s00453-016-0127-x – ident: 1004_CR13 doi: 10.1007/978-3-030-17402-6_21 – ident: 1004_CR18 – volume-title: Parameterized Algorithms year: 2015 ident: 1004_CR8 doi: 10.1007/978-3-319-21275-3 |
| SSID | ssj0012796 |
| Score | 2.3502285 |
| Snippet | A directed graph
D
is semicomplete if for every pair
x
,
y
of vertices of
D
, there is at least one arc between
x
and
y
. Thus, a tournament is a... A directed graph D is semicomplete if for every pair x, y of vertices of D, there is at least one arc between x and y. Thus, a tournament is a semicomplete... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 2767 |
| SubjectTerms | Algorithm Analysis and Problem Complexity Algorithms Apexes Complexity Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Feedback Graph theory Graphs Mathematics of Computing Number theory Parameters Special Issue: Parameterized and Exact Computation (IPEC 2020) Theory of Computation Upper bounds Vertex sets |
| Title | Component Order Connectivity in Directed Graphs |
| URI | https://link.springer.com/article/10.1007/s00453-022-01004-z https://www.proquest.com/docview/2701552417 |
| Volume | 84 |
| WOSCitedRecordID | wos000829125600002&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: 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/eLvHCXMwnV1LSwMxEA5aPXixPrFaJQdvGtxs0k1yFPFxkCq-6G3JEwqySrd66K83yT6KooJed5MQZpLMDDPzfQAcOpMoO2AMaakGiIpEIaEzjCTGDEvrBNGxUfiaDYd8NBK3dVNY2VS7NynJ-FK3zW7B-wg5x1BKEMonZotgyZs7Hggb7u6f2txByiIrV-CdR9Qb6LpV5vs1PpujuY_5JS0arc1F93_7XAOrtXcJT6vjsA4WbLEBug1zA6wv8iY4CZ9eCm9w4E3A3oSx3kVXTBJwXMDqJbQGXgZA63ILPF6cP5xdoZo6AWmSkSlyTinpnSmXMWuFyrj0kYuQ0lgprfVRjqTOGcKowgGAKBFMWk4dybiWGdGKbINO4bexA2BiJOFU80EmfCiHLWepptgIYXwkYonpAdxIMNc1rnigt3jOW0TkKJHcSySPEslnPXDUznmtUDV-Hd1vFJPXN6zMUxbR4yhmPXDcKGL---fVdv82fA-spFGXoaysDzrTyZvdB8v6fTouJwfx5H0Ah6LSNQ |
| linkProvider | Springer Nature |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3dS8MwED90Cvri_MTp1D74psGmyZrmUUSdOKfolL2FNE1hIFXW6cP-epP0Yygq6GubhHCX5O64u98P4DBN_Fh3GENKxh1EuR8jrkKMJMYMS51yolyjcI_1-9FwyO_KprC8qnavUpLupa6b3az3YXOOtpTAlk9M52GBGotlEfPvH57q3EHAHCuX5Z1H1BjoslXm-zU-m6OZj_klLeqszUXzf_tchZXSu_ROi-OwBnM6W4dmxdzglRd5A07sp5fMGBzv1mJveq7eRRVMEt4o84qXUCfepQW0zjfh8eJ8cNZFJXUCUiQkE5SmcSyNM5WGTGseh5E0kQuXMtFSam2iHEnTNCGMxtgCEPmcSR3RlISRkiFRMdmCRma2sQ2en0gSURV1Qm5COawjFiiKE84TE4lokrQAVxIUqsQVt_QWz6JGRHYSEUYiwklETFtwVM95LVA1fh3drhQjyhuWi4A59DiKWQuOK0XMfv-82s7fhh_AUndw0xO9q_71LiwHTq-2xKwNjcn4Te_BonqfjPLxvjuFH2uN1Rk |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LSwMxEB60inixPrFadQ_edGmzSTebo6hVsdSCD3pbsnlAQdbSrh76602yj6qoIF53s0OYSXZmmG--ATjWsp2oDqW-4EnHJ6yd-EyEyOcIUcSVZli4RuEe7fej4ZANPnTxO7R7WZLMexosS1OatcZSt6rGNxuJ2PqjhRVYKMVsEZaIBdLbfP3-qaojBNRN6LIz6H1inHXRNvO9jM-uaR5vfimROs_Trf9_z-uwVkSd3ll-TDZgQaWbUC8nOnjFBd-Cln30khqh3p3l5PQcDkbkEya8Uerlf0glvStLdD3dhsfu5cP5tV-MVPAFDnHma50k3ARZOqRKsSSMuMloGOdSca6UyX440VpiShJkiYnajHIVEY3DSPAQiwTvQC0129gFry05joiIOiEzKR5SEQ0EQZIxaTIUhWUDUKnNWBR843bsxXNcMSU7jcRGI7HTSDxrwEn1zThn2_h1dbM0UlzcvGkcUMcqRxBtwGlplPnrn6Xt_W35EawMLrpx76Z_uw-rgTOrRZ41oZZNXtUBLIu3bDSdHLoD-Q7BhN39 |
| 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=Component+Order+Connectivity+in+Directed+Graphs&rft.jtitle=Algorithmica&rft.au=Bang-Jensen%2C+J%C3%B8rgen&rft.au=Eiben%2C+Eduard&rft.au=Gutin%2C+Gregory&rft.au=Wahlstr%C3%B6m%2C+Magnus&rft.date=2022-09-01&rft.issn=0178-4617&rft.eissn=1432-0541&rft.volume=84&rft.issue=9&rft.spage=2767&rft.epage=2784&rft_id=info:doi/10.1007%2Fs00453-022-01004-z&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s00453_022_01004_z |
| 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 |