A Tight Algorithm for Strongly Connected Steiner Subgraph on Two Terminals with Demands
Given an edge-weighted directed graph G = ( V , E ) on n vertices and a set T = { t 1 , t 2 , … , t p } of p terminals, the objective of the Strongly Connected Steiner Subgraph ( p -SCSS) problem is to find an edge set H ⊆ E of minimum weight such that G [ H ] contains an t i → t j path for each 1 ≤...
Saved in:
| Published in: | Algorithmica Vol. 77; no. 4; pp. 1216 - 1239 |
|---|---|
| Main Authors: | , , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
New York
Springer US
01.04.2017
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 | Given an edge-weighted directed graph
G
=
(
V
,
E
)
on
n
vertices and a set
T
=
{
t
1
,
t
2
,
…
,
t
p
}
of
p
terminals, the objective of the
Strongly Connected Steiner Subgraph
(
p
-SCSS) problem is to find an edge set
H
⊆
E
of minimum weight such that
G
[
H
] contains an
t
i
→
t
j
path for each
1
≤
i
≠
j
≤
p
. The
p
-SCSS problem is NP-hard, but Feldman and Ruhl [FOCS ’99; SICOMP ’06] gave a novel
n
O
(
p
)
time algorithm. In this paper, we investigate the computational complexity of a variant of 2-SCSS where we have demands for the number of paths between each terminal pair. Formally, the
2
-SCSS-
(
k
1
,
k
2
)
problem is defined as follows: given an edge-weighted directed graph
G
=
(
V
,
E
)
with weight function
ω
:
E
→
R
≥
0
, two terminal vertices
s
,
t
, and integers
k
1
,
k
2
; the objective is to find a set of
k
1
paths
F
1
,
F
2
,
…
,
F
k
1
from
s
⇝
t
and
k
2
paths
B
1
,
B
2
,
…
,
B
k
2
from
t
⇝
s
such that
∑
e
∈
E
ω
(
e
)
·
ϕ
(
e
)
is minimized, where
ϕ
(
e
)
=
max
{
|
{
i
∈
[
k
1
]
:
e
∈
F
i
}
|
,
|
{
j
∈
[
k
2
]
:
e
∈
B
j
}
|
}
. For each
k
≥
1
, we show the following:
The
2
-SCSS-
(
k
,
1
)
problem can be solved in time
n
O
(
k
)
.
A matching lower bound for our algorithm: the
2
-SCSS-
(
k
,
1
)
problem does not have an
f
(
k
)
·
n
o
(
k
)
time algorithm for any computable function
f
, unless the Exponential Time Hypothesis fails.
Our algorithm for
2
-SCSS-
(
k
,
1
)
relies on a structural result regarding an optimal solution followed by using the idea of a “token game” similar to that of Feldman and Ruhl. We show with an example that the structural result does not hold for the
2
-SCSS-
(
k
1
,
k
2
)
problem if
min
{
k
1
,
k
2
}
≥
2
. Therefore
2
-SCSS-
(
k
,
1
)
is the most general problem one can attempt to solve with our techniques. To obtain the lower bound matching the algorithm, we reduce from a special variant of the
Grid Tiling
problem introduced by Marx [FOCS ’07; ICALP ’12]. |
|---|---|
| AbstractList | Given an edge-weighted directed graph G = ( V , E ) on n vertices and a set T = { t 1 , t 2 , … , t p } of p terminals, the objective of the Strongly Connected Steiner Subgraph (p-SCSS) problem is to find an edge set H ⊆ E of minimum weight such that G[H] contains an t i → t j path for each 1 ≤ i ≠ j ≤ p . The p-SCSS problem is NP-hard, but Feldman and Ruhl [FOCS ’99; SICOMP ’06] gave a novel n O ( p ) time algorithm. In this paper, we investigate the computational complexity of a variant of 2-SCSS where we have demands for the number of paths between each terminal pair. Formally, the 2 -SCSS- ( k 1 , k 2 ) problem is defined as follows: given an edge-weighted directed graph G = ( V , E ) with weight function ω : E → R ≥ 0 , two terminal vertices s, t, and integers k 1 , k 2 ; the objective is to find a set of k 1 paths F 1 , F 2 , … , F k 1 from s ⇝ t and k 2 paths B 1 , B 2 , … , B k 2 from t ⇝ s such that ∑ e ∈ E ω ( e ) · ϕ ( e ) is minimized, where ϕ ( e ) = max { | { i ∈ [ k 1 ] : e ∈ F i } | , | { j ∈ [ k 2 ] : e ∈ B j } | } . For each k ≥ 1 , we show the following: The 2 -SCSS- ( k , 1 ) problem can be solved in time n O ( k ) . A matching lower bound for our algorithm: the 2 -SCSS- ( k , 1 ) problem does not have an f ( k ) · n o ( k ) time algorithm for any computable function f, unless the Exponential Time Hypothesis fails. Our algorithm for 2 -SCSS- ( k , 1 ) relies on a structural result regarding an optimal solution followed by using the idea of a “token game” similar to that of Feldman and Ruhl. We show with an example that the structural result does not hold for the 2 -SCSS- ( k 1 , k 2 ) problem if min { k 1 , k 2 } ≥ 2 . Therefore 2 -SCSS- ( k , 1 ) is the most general problem one can attempt to solve with our techniques. To obtain the lower bound matching the algorithm, we reduce from a special variant of the Grid Tiling problem introduced by Marx [FOCS ’07; ICALP ’12]. Given an edge-weighted directed graph G = ( V , E ) on n vertices and a set T = { t 1 , t 2 , … , t p } of p terminals, the objective of the Strongly Connected Steiner Subgraph ( p -SCSS) problem is to find an edge set H ⊆ E of minimum weight such that G [ H ] contains an t i → t j path for each 1 ≤ i ≠ j ≤ p . The p -SCSS problem is NP-hard, but Feldman and Ruhl [FOCS ’99; SICOMP ’06] gave a novel n O ( p ) time algorithm. In this paper, we investigate the computational complexity of a variant of 2-SCSS where we have demands for the number of paths between each terminal pair. Formally, the 2 -SCSS- ( k 1 , k 2 ) problem is defined as follows: given an edge-weighted directed graph G = ( V , E ) with weight function ω : E → R ≥ 0 , two terminal vertices s , t , and integers k 1 , k 2 ; the objective is to find a set of k 1 paths F 1 , F 2 , … , F k 1 from s ⇝ t and k 2 paths B 1 , B 2 , … , B k 2 from t ⇝ s such that ∑ e ∈ E ω ( e ) · ϕ ( e ) is minimized, where ϕ ( e ) = max { | { i ∈ [ k 1 ] : e ∈ F i } | , | { j ∈ [ k 2 ] : e ∈ B j } | } . For each k ≥ 1 , we show the following: The 2 -SCSS- ( k , 1 ) problem can be solved in time n O ( k ) . A matching lower bound for our algorithm: the 2 -SCSS- ( k , 1 ) problem does not have an f ( k ) · n o ( k ) time algorithm for any computable function f , unless the Exponential Time Hypothesis fails. Our algorithm for 2 -SCSS- ( k , 1 ) relies on a structural result regarding an optimal solution followed by using the idea of a “token game” similar to that of Feldman and Ruhl. We show with an example that the structural result does not hold for the 2 -SCSS- ( k 1 , k 2 ) problem if min { k 1 , k 2 } ≥ 2 . Therefore 2 -SCSS- ( k , 1 ) is the most general problem one can attempt to solve with our techniques. To obtain the lower bound matching the algorithm, we reduce from a special variant of the Grid Tiling problem introduced by Marx [FOCS ’07; ICALP ’12]. |
| Author | Hajiaghayi, MohammadTaghi Kortsarz, Guy Esfandiari, Hossein Chitnis, Rajesh Seddighin, Saeed Khandekar, Rohit |
| Author_xml | – sequence: 1 givenname: Rajesh surname: Chitnis fullname: Chitnis, Rajesh email: rajeshchitnis@gmail.com organization: The Weizmann Institute of Science – sequence: 2 givenname: Hossein surname: Esfandiari fullname: Esfandiari, Hossein organization: Department of Computer Science, University of Maryland – sequence: 3 givenname: MohammadTaghi surname: Hajiaghayi fullname: Hajiaghayi, MohammadTaghi organization: Department of Computer Science, University of Maryland – sequence: 4 givenname: Rohit surname: Khandekar fullname: Khandekar, Rohit organization: KCG Holdings Inc – sequence: 5 givenname: Guy surname: Kortsarz fullname: Kortsarz, Guy organization: Department of Computer Science, Rutgers University-Camden – sequence: 6 givenname: Saeed surname: Seddighin fullname: Seddighin, Saeed organization: Department of Computer Science, University of Maryland |
| BookMark | eNp9kEtrwzAQhEVJoUnaH9CboGe3u7Zs2ceQPiHQQ116FH7IjoIjpZJCyL-vgnsohfawLOzMtwwzIxNttCTkGuEWAfidA2BpEgFmYVga5WdkiiyJI0gZTsgUkOcRy5BfkJlzGwCMeZFNyceClqpfe7oYemOVX29pZyx989bofjjSpdFaNl624SSVlkHa172tdmtqNC0PhpbSbpWuBkcPAaf3clvp1l2S8y7c5NX3npP3x4dy-RytXp9elotV1CRp4aMki1nNsC4wh67peJe2kjeIVQ1tIbHIEVnLeZ0Epcp5CzVrujhrsemQZzUmc3Iz_t1Z87mXzouN2dtTHIF5DjxLAYrg4qOrscY5KzvRKF95ZbS3lRoEgji1KMYWRWhRnFoUeSDxF7mzalvZ479MPDIueHUv7Y9Mf0JfaDyF4w |
| CitedBy_id | crossref_primary_10_1007_s00453_019_00580_x crossref_primary_10_1137_18M122371X |
| Cites_doi | 10.1145/948205.948247 10.1007/978-3-319-13524-3_14 10.1006/jcss.2000.1727 10.1145/780542.780628 10.1109/90.532865 10.1007/978-3-642-20807-2_7 10.1137/S0097539704441241 10.1137/1.9781611973402.129 10.1109/FOCS.2007.26 10.1145/781027.781069 10.1007/978-3-642-31594-7_57 10.1007/978-3-662-48350-3_72 10.1006/jagm.1999.1042 10.1016/j.jcss.2006.04.007 |
| ContentType | Journal Article |
| Copyright | Springer Science+Business Media New York 2016 Copyright Springer Science & Business Media 2017 |
| Copyright_xml | – notice: Springer Science+Business Media New York 2016 – notice: Copyright Springer Science & Business Media 2017 |
| DBID | AAYXX CITATION JQ2 |
| DOI | 10.1007/s00453-016-0145-8 |
| DatabaseName | CrossRef ProQuest Computer Science Collection |
| DatabaseTitle | CrossRef ProQuest Computer Science Collection |
| DatabaseTitleList | ProQuest Computer Science Collection |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science |
| EISSN | 1432-0541 |
| EndPage | 1239 |
| ExternalDocumentID | 10_1007_s00453_016_0145_8 |
| GrantInformation_xml | – fundername: National Science Foundation (US) grantid: CAREER 1053605 funderid: http://dx.doi.org/10.13039/100000001 – fundername: National Science Foundation (US) grantid: 1218620 funderid: http://dx.doi.org/10.13039/100000001 – fundername: Office of Naval Research (US) grantid: YIP Award N000141110662 funderid: http://dx.doi.org/10.13039/100000006 – fundername: National Science Foundation (US) grantid: CCF-1161626 funderid: http://dx.doi.org/10.13039/100000001 – fundername: Defense Advanced Research Projects Agency (US) grantid: FA9550-12-1-0423 funderid: http://dx.doi.org/10.13039/100000185 |
| 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 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-c359t-3624b41b9180fcf7f5de7c11ab0d9e198114d77b37f5a87d0b4cf26d1cf176b13 |
| IEDL.DBID | RSV |
| ISICitedReferencesCount | 3 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000395509500011&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 16:27:03 EDT 2025 Tue Nov 18 21:28:19 EST 2025 Sat Nov 29 02:20:27 EST 2025 Fri Feb 21 02:40:20 EST 2025 |
| IsDoiOpenAccess | false |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 4 |
| Keywords | Exponential time hypothesis Directed graphs FPT algorithms Strongly connected Steiner subgraph |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c359t-3624b41b9180fcf7f5de7c11ab0d9e198114d77b37f5a87d0b4cf26d1cf176b13 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| OpenAccessLink | https://research.birmingham.ac.uk/en/publications/11e63ff3-1fa8-46fa-9ced-52cf5847001a |
| PQID | 1880765009 |
| PQPubID | 2043795 |
| PageCount | 24 |
| ParticipantIDs | proquest_journals_1880765009 crossref_citationtrail_10_1007_s00453_016_0145_8 crossref_primary_10_1007_s00453_016_0145_8 springer_journals_10_1007_s00453_016_0145_8 |
| PublicationCentury | 2000 |
| PublicationDate | 2017-04-01 |
| PublicationDateYYYYMMDD | 2017-04-01 |
| PublicationDate_xml | – month: 04 year: 2017 text: 2017-04-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | Algorithmica |
| PublicationTitleAbbrev | Algorithmica |
| PublicationYear | 2017 |
| Publisher | Springer US Springer Nature B.V |
| Publisher_xml | – name: Springer US – name: Springer Nature B.V |
| References | Marx, D.: A tight lower bound for planar multiway cut with fixed number of terminals. In: Automata, Languages, and Programming-39th International Colloquium, ICALP 2012, Warwick. Part I, pp. 677–688 (2012) Chitnis, R.H., Esfandiari, H., Hajiaghayi, M., Khandekar, R., Kortsarz, G., Seddighin, S.: A tight algorithm for strongly connected Steiner subgraph on two terminals with demands (extended abstract). In: Parameterized and Exact Computation-9th International Symposium, IPEC 2014, Wroclaw, pp. 159–171 (2014) RamanathanSMulticast tree generation in networks with asymmetric linksIEEE ACM Trans. Netw. (TON)199644558568142561610.1109/90.532865 Ramachandran, K., Kokku, R., Mahindra, R., Rangarajan, S.: Wireless network connectivity in data centers, US Patent App. 12/499,906. http://www.google.com/patents/US20100172292 (2010) FeldmanJRuhlMThe directed Steiner network problem is tractable for a constant number of terminalsSIAM J. Comput.2006362543561224773910.1137/S00975397044412411118.05039 Guo, C., Lu, G., Li, D., Wu, H., Shi, Y., Zhang, D., Zhang, Y., Lu, S.: Hybrid butterfly cube architecture for modular data centers, US Patent 8,065,433. https://www.google.com/patents/US8065433 (2011) ChenJHuangXKanjIAXiaGStrong computational lower bounds via parameterized complexityJ. Comput. Syst. Sci.200672813461367227341210.1016/j.jcss.2006.04.0071119.68092 Chakrabarty, D., Chekuri, C., Khanna, S., Korula, N.: Approximability of capacitated network design. In: Integer Programming and Combinatoral Optimization-15th International Conference, IPCO 2011, New York, pp. 78–91 (2011) Halperin, E., Krauthgamer, R.: Polylogarithmic inapproximability. In: Proceedings of the 35th Annual ACM Symposium on Theory of Computing, STOC 2003, San Diego, pp. 585–594 (2003) Marx, D., Pilipczuk, M.: Optimal parameterized algorithms for planar facility location problems using voronoi diagrams. In: Algorithms-ESA 2015-23rd Annual European Symposium, Patras, pp. 865–877 (2015) Chitnis, R.H., Hajiaghayi, M., Marx, D.: Tight bounds for planar strongly connected Steiner subgraph with fixed number of terminals (and extensions). In: Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014, Portland, pp. 1782–1801 (2014) Marx, D., Pilipczuk, M.: Everything you always wanted to know about the parameterized complexity of Subgraph Isomorphism (but were afraid to ask). In: 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014), Lyon, pp. 542–553 (2014) Teixeira, R., Marzullo, K., Savage, S., Voelker, G.M.: Characterizing and measuring path diversity of internet topologies. In: International Conference on Measurements and Modeling of Computer Systems, SIGMETRICS 2003, San Diego, pp. 304–305 (2003) Goemans, M.X., Goldberg, A.V., Plotkin, S.A., Shmoys, D.B., Tardos, É., Williamson, D.P.: Improved approximation algorithms for network design problems. In: Proceedings of the Fifth Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1994, Arlington, pp. 223–232 (1994) Teixeira, R., Marzullo, K., Savage, S., Voelker, G.M.: In search of path diversity in ISP networks. In: 3rd ACM SIGCOMM Internet Measurement Conference, IMC 2003, Miami Beach, pp. 313–318 (2003) Marx, D.: On the optimality of planar and geometric approximation schemes. In: 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2007), Providence, pp. 338–348 (2007) Charikar, M., Chekuri, C., Cheung, T.Y., Dai, Z., Goel, A., Guha, S., Li, M.: Approximation algorithms for directed Steiner problems. J. Algorithms 33(1), 73–91 (1999) ImpagliazzoRPaturiROn the complexity of k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}-SATJ. Comput. Syst. Sci.2001622367375182059710.1006/jcss.2000.17270990.68079 J Chen (145_CR3) 2006; 72 R Impagliazzo (145_CR10) 2001; 62 145_CR15 145_CR17 145_CR18 145_CR1 145_CR2 S Ramanathan (145_CR16) 1996; 4 J Feldman (145_CR6) 2006; 36 145_CR11 145_CR12 145_CR13 145_CR14 145_CR8 145_CR9 145_CR4 145_CR5 145_CR7 |
| References_xml | – reference: Marx, D., Pilipczuk, M.: Optimal parameterized algorithms for planar facility location problems using voronoi diagrams. In: Algorithms-ESA 2015-23rd Annual European Symposium, Patras, pp. 865–877 (2015) – reference: Chitnis, R.H., Hajiaghayi, M., Marx, D.: Tight bounds for planar strongly connected Steiner subgraph with fixed number of terminals (and extensions). In: Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014, Portland, pp. 1782–1801 (2014) – reference: Marx, D.: A tight lower bound for planar multiway cut with fixed number of terminals. In: Automata, Languages, and Programming-39th International Colloquium, ICALP 2012, Warwick. Part I, pp. 677–688 (2012) – reference: RamanathanSMulticast tree generation in networks with asymmetric linksIEEE ACM Trans. Netw. (TON)199644558568142561610.1109/90.532865 – reference: ChenJHuangXKanjIAXiaGStrong computational lower bounds via parameterized complexityJ. Comput. Syst. Sci.200672813461367227341210.1016/j.jcss.2006.04.0071119.68092 – reference: Ramachandran, K., Kokku, R., Mahindra, R., Rangarajan, S.: Wireless network connectivity in data centers, US Patent App. 12/499,906. http://www.google.com/patents/US20100172292 (2010) – reference: Chakrabarty, D., Chekuri, C., Khanna, S., Korula, N.: Approximability of capacitated network design. In: Integer Programming and Combinatoral Optimization-15th International Conference, IPCO 2011, New York, pp. 78–91 (2011) – reference: Halperin, E., Krauthgamer, R.: Polylogarithmic inapproximability. In: Proceedings of the 35th Annual ACM Symposium on Theory of Computing, STOC 2003, San Diego, pp. 585–594 (2003) – reference: FeldmanJRuhlMThe directed Steiner network problem is tractable for a constant number of terminalsSIAM J. Comput.2006362543561224773910.1137/S00975397044412411118.05039 – reference: Marx, D., Pilipczuk, M.: Everything you always wanted to know about the parameterized complexity of Subgraph Isomorphism (but were afraid to ask). In: 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014), Lyon, pp. 542–553 (2014) – reference: Marx, D.: On the optimality of planar and geometric approximation schemes. In: 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2007), Providence, pp. 338–348 (2007) – reference: Teixeira, R., Marzullo, K., Savage, S., Voelker, G.M.: In search of path diversity in ISP networks. In: 3rd ACM SIGCOMM Internet Measurement Conference, IMC 2003, Miami Beach, pp. 313–318 (2003) – reference: Guo, C., Lu, G., Li, D., Wu, H., Shi, Y., Zhang, D., Zhang, Y., Lu, S.: Hybrid butterfly cube architecture for modular data centers, US Patent 8,065,433. https://www.google.com/patents/US8065433 (2011) – reference: Teixeira, R., Marzullo, K., Savage, S., Voelker, G.M.: Characterizing and measuring path diversity of internet topologies. In: International Conference on Measurements and Modeling of Computer Systems, SIGMETRICS 2003, San Diego, pp. 304–305 (2003) – reference: Charikar, M., Chekuri, C., Cheung, T.Y., Dai, Z., Goel, A., Guha, S., Li, M.: Approximation algorithms for directed Steiner problems. J. Algorithms 33(1), 73–91 (1999) – reference: ImpagliazzoRPaturiROn the complexity of k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k$$\end{document}-SATJ. Comput. Syst. Sci.2001622367375182059710.1006/jcss.2000.17270990.68079 – reference: Goemans, M.X., Goldberg, A.V., Plotkin, S.A., Shmoys, D.B., Tardos, É., Williamson, D.P.: Improved approximation algorithms for network design problems. In: Proceedings of the Fifth Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1994, Arlington, pp. 223–232 (1994) – reference: Chitnis, R.H., Esfandiari, H., Hajiaghayi, M., Khandekar, R., Kortsarz, G., Seddighin, S.: A tight algorithm for strongly connected Steiner subgraph on two terminals with demands (extended abstract). In: Parameterized and Exact Computation-9th International Symposium, IPEC 2014, Wroclaw, pp. 159–171 (2014) – ident: 145_CR7 – ident: 145_CR8 – ident: 145_CR18 doi: 10.1145/948205.948247 – ident: 145_CR4 doi: 10.1007/978-3-319-13524-3_14 – volume: 62 start-page: 367 issue: 2 year: 2001 ident: 145_CR10 publication-title: J. Comput. Syst. Sci. doi: 10.1006/jcss.2000.1727 – ident: 145_CR9 doi: 10.1145/780542.780628 – volume: 4 start-page: 558 issue: 4 year: 1996 ident: 145_CR16 publication-title: IEEE ACM Trans. Netw. (TON) doi: 10.1109/90.532865 – ident: 145_CR1 doi: 10.1007/978-3-642-20807-2_7 – volume: 36 start-page: 543 issue: 2 year: 2006 ident: 145_CR6 publication-title: SIAM J. Comput. doi: 10.1137/S0097539704441241 – ident: 145_CR5 doi: 10.1137/1.9781611973402.129 – ident: 145_CR14 doi: 10.1109/FOCS.2007.26 – ident: 145_CR17 doi: 10.1145/781027.781069 – ident: 145_CR13 doi: 10.1007/978-3-642-31594-7_57 – ident: 145_CR12 doi: 10.1007/978-3-662-48350-3_72 – ident: 145_CR15 – ident: 145_CR2 doi: 10.1006/jagm.1999.1042 – volume: 72 start-page: 1346 issue: 8 year: 2006 ident: 145_CR3 publication-title: J. Comput. Syst. Sci. doi: 10.1016/j.jcss.2006.04.007 – ident: 145_CR11 |
| SSID | ssj0012796 |
| Score | 2.1694224 |
| Snippet | Given an edge-weighted directed graph
G
=
(
V
,
E
)
on
n
vertices and a set
T
=
{
t
1
,
t
2
,
…
,
t
p
}
of
p
terminals, the objective of the
Strongly Connected... Given an edge-weighted directed graph G = ( V , E ) on n vertices and a set T = { t 1 , t 2 , … , t p } of p terminals, the objective of the Strongly Connected... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 1216 |
| SubjectTerms | Algorithm Analysis and Problem Complexity Algorithms Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Graph theory Graphs Integers Matching Mathematics of Computing Minimum weight Terminals Theory of Computation Tiling Weighting functions |
| Title | A Tight Algorithm for Strongly Connected Steiner Subgraph on Two Terminals with Demands |
| URI | https://link.springer.com/article/10.1007/s00453-016-0145-8 https://www.proquest.com/docview/1880765009 |
| Volume | 77 |
| WOSCitedRecordID | wos000395509500011&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/eLvHCXMwnV05T8MwFLagMLBQTlEoyAMTyFKco47HCqgYUIVogG6Rr5RKaYKaAOLfY7tJOARIsMb2U-Trfc_v-AA4FgwHRPgMCYEDQ2HGEQ19F1GiNL5wHEGlLZl_RYbDcDym11Ued1FHu9cuSXtTN8luBn2Y2B9jAfsBCpfBitZ2oeFruBndNa4Dl1hSLkM7j3ytn2tX5nciPiujd4T5xSlqdc2g_a-_3ADrFbSE_cVe2ARLKtsC7Zq2AVaneBvc92FkTHLYTyf5fFo-zKBGrnBkHsUn6Su0sS9CI1H9SZncQKhvF1vYGuYZjF5yGC0iaNICmmdceK5mJmF4B9wOLqKzS1TxKyDhBbREWnf53Mec4tBJREKSQCoiMGbckVRhGmpbSRLCPd3CQiId7ovE7UksEkx6HHu7oJXlmdoDUCZKCsZcT2qZCeW8JznxNHpnjPkBDzrAqSc6FlXxccOBkcZN2WQ7cbEJODMTF4cdcNIMeVxU3vitc7devbg6hEVsSs0RjUAd2gGn9Wp9aP5J2P6feh-ANdeoehvN0wWtcv6kDsGqeC6nxfzI7s03DnXdNQ |
| linkProvider | Springer Nature |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3JTsMwEB1BQYILZRVl9YETKFKcOHV8rFhURKkQDcst8paCFFrUFhB_j-0mZREgwTW2R5G3eeOZeQOwJzmOqCTckxJHtoSZ8FhMAo9RbfCF70umHGV-i7bb8e0tuyjyuIdltHvpknQ39STZzaIPG_tjLWASefE0zBCjsCxh_mXneuI6CKgrymXLznvE6OfSlfmdiM_K6B1hfnGKOl1zUv3XXy7CQgEtUWO8F5ZgSveWoVqWbUDFKV6BmwZKrEmOGnm3P7gf3T0gg1xRxz6Kd_NX5GJfpEGi5pO2uYHI3C6O2Br1eyh56aNkHEGTD5F9xkVH-sEmDK_C1clxctj0ivoKngwjNvKM7iKCYMFw7Gcyo1mkNJUYc-ErpjGLja2kKBWhaeExVb4gMgvqCssM07rA4RpUev2eXgekMq0k50GojMyMCVFXgoYGvXPOSSSiGvjlRKeyIB-3NTDydEKb7CYutQFnduLSuAb7kyGPY-aN3zpvlauXFodwmFqqOWoQqM9qcFCu1ofmn4Rt_Kn3Lsw1k_NW2jptn23CfGDVvovs2YLKaPCkt2FWPo_uh4Mdt0_fAHWg4Bk |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LS8NAEB60injxLVar7sGTEswmm272WNSiKEWwPm5hX1GhptJGxX_vTprUByqI1-xmCfvIfLPzzXwAO1rSiGsmPa1phBJmyhMxCzzBrcMXvq-FKUrmn_FOJ765EeelzumwYrtXIclRTgNWacry_UeT7o8T3xCJIA8IvWEWefEkTDHk0aO7fnE1DiMEvBDoQgl6jzlbXYU1vxvis2F6R5tfAqSF3WnP__uLF2CuhJykNdojizBhsyWYr-QcSHm6l-G6RbroqpNW77Y_uM_vHohDtOQCL8tve6-k4MRoh1DdI4s5g8T9dYqC16Sfke5Ln3RHzJrekOD1Ljm0D5hIvAKX7aPuwbFX6i54OoxE7jmbxhSjStDYT3XK08hYrimVyjfCUhE7H8pwrkLXImNufMV0GjQN1SnlTUXDVahl_cyuATGpNVrKIDRuzFQo1TSKhw7VSylZpKI6-NWkJ7osSo7aGL1kXE65mLgEiWg4cUlch93xK4-jihy_dW5UK5mUh3OYYAk67pCpL-qwV63ch-afBlv_U-9tmDk_bCdnJ53TDZgNEA0UhJ8G1PLBk92Eaf2c3w8HW8WWfQPbFej9 |
| 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=A+Tight+Algorithm+for+Strongly+Connected+Steiner+Subgraph+on+Two+Terminals+with+Demands&rft.jtitle=Algorithmica&rft.au=Chitnis%2C+Rajesh&rft.au=Esfandiari%2C+Hossein&rft.au=Hajiaghayi%2C+MohammadTaghi&rft.au=Khandekar%2C+Rohit&rft.date=2017-04-01&rft.pub=Springer+Nature+B.V&rft.issn=0178-4617&rft.eissn=1432-0541&rft.volume=77&rft.issue=4&rft.spage=1216&rft.epage=1239&rft_id=info:doi/10.1007%2Fs00453-016-0145-8&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 |