Approximation algorithms for maximum cut with limited unbalance

We consider the problem of partitioning the vertices of a weighted graph into two sets of sizes that differ at most by a given threshold B , so as to maximize the weight of the crossing edges. For B equal to 0 this problem is known as Max Bisection, whereas for B equal to the number n of nodes it is...

Celý popis

Uloženo v:

Podrobná bibliografie
Vydáno v:	Theoretical computer science Ročník 385; číslo 1; s. 78 - 87
Hlavní autoři:	Galbiati, Giulia, Maffioli, Francesco
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Amsterdam Elsevier B.V 15.10.2007 Elsevier
Témata:	Algorithmics. Computability. Computer arithmetics Applied sciences Approximations and expansions Computer science; control theory; systems Exact sciences and technology Information retrieval. Graph Limited unbalance cut Mathematical analysis Mathematics Maximum cut Miscellaneous Randomized approximation algorithm Sciences and techniques of general use Semidefinite programming Theoretical computing Randomized approximation algorithm Maximum cut Semidefinite programming Limited unbalance cut Polynomial Computer theory Methodology Polynomial approximation Node Semi definite programming Approximation algorithm Weighted graph Polynomial time Maximum Performance Threshold
ISSN:	0304-3975, 1879-2294
On-line přístup:	Získat plný text
Tagy:	Přidat tag Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!

Abstract	We consider the problem of partitioning the vertices of a weighted graph into two sets of sizes that differ at most by a given threshold B , so as to maximize the weight of the crossing edges. For B equal to 0 this problem is known as Max Bisection, whereas for B equal to the number n of nodes it is the maximum cut problem. We present polynomial time randomized approximation algorithms with non trivial performance guarantees for its solution. The approximation results are obtained by extending the methodology used by Y. Ye for Max Bisection and by combining this technique with another one that uses the algorithm of Goemans and Williamson for the maximum cut problem. When B is equal to zero the approximation ratio achieved coincides with the one obtained by Y. Ye; otherwise it is always above this value and tends to the value obtained by Goemans and Williamson as B approaches the number n of nodes.
AbstractList	We consider the problem of partitioning the vertices of a weighted graph into two sets of sizes that differ at most by a given threshold B , so as to maximize the weight of the crossing edges. For B equal to 0 this problem is known as Max Bisection, whereas for B equal to the number n of nodes it is the maximum cut problem. We present polynomial time randomized approximation algorithms with non trivial performance guarantees for its solution. The approximation results are obtained by extending the methodology used by Y. Ye for Max Bisection and by combining this technique with another one that uses the algorithm of Goemans and Williamson for the maximum cut problem. When B is equal to zero the approximation ratio achieved coincides with the one obtained by Y. Ye; otherwise it is always above this value and tends to the value obtained by Goemans and Williamson as B approaches the number n of nodes.
Author	Maffioli, Francesco Galbiati, Giulia
Author_xml	– sequence: 1 givenname: Giulia surname: Galbiati fullname: Galbiati, Giulia email: giulia.galbiati@unipv.it organization: Dipartimento di Informatica e Sistemistica, Università degli Studi di Pavia, 27100 Pavia, Italy – sequence: 2 givenname: Francesco surname: Maffioli fullname: Maffioli, Francesco email: maffioli@elet.polimi.it organization: Dipartimento di Elettronica e Informazione, Politecnico di Milano, 20133 Milano, Italy
BackLink	http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=19121733$$DView record in Pascal Francis
BookMark	eNp9kD1PwzAQhi0EEm3hB7BlYUw420mciAFVFV9SJRaYLce5gKskjmyXj3-PSxEDQ71Ysu-5u_eZk-PRjkjIBYWMAi2vNlnQPmMAIoMiA14ekRmtRJ0yVufHZAYc8pTXojglc-83EE8hyhm5WU6Ts59mUMHYMVH9q3UmvA0-6axLBhV_tkOityH5iM9JbwYTsE22Y6N6NWo8Iyed6j2e_94L8nJ3-7x6SNdP94-r5TrVnImQ5sAqgQpK2oimLnlT6bzURZtj2-R5KxTTKIoGaQ28YlXFODCBRSO06jgK4Atyue87Ka9V37k43Hg5ubi5-5K0powKzmOd2NdpZ7132Eltwk-24JTpJQW58yU3MvqSO18SChl9RZL-I_-aH2Cu9wzG6O8GnfTaYNTSGoc6yNaaA_Q3CU-FeA
CODEN	TCSCDI
CitedBy_id	crossref_primary_10_1007_s10878_022_00978_4 crossref_primary_10_1016_j_dam_2025_05_033 crossref_primary_10_1007_s11425_014_4900_5 crossref_primary_10_1007_s10898_022_01183_7 crossref_primary_10_1007_s12190_009_0290_1 crossref_primary_10_26599_TST_2024_9010214 crossref_primary_10_1016_j_aml_2012_04_015 crossref_primary_10_1002_net_20369 crossref_primary_10_1111_itor_12009
Cites_doi	10.1109/SFCS.1992.267823 10.1145/227683.227684 10.1007/PL00011415 10.1007/BF02523688 10.1006/jagm.2001.1183 10.1137/0805002 10.1016/0166-218X(81)90001-9
ContentType	Journal Article
Copyright	2007 Elsevier Ltd 2008 INIST-CNRS
Copyright_xml	– notice: 2007 Elsevier Ltd – notice: 2008 INIST-CNRS
DBID	6I. AAFTH AAYXX CITATION IQODW
DOI	10.1016/j.tcs.2007.05.036
DatabaseName	ScienceDirect Open Access Titles Elsevier:ScienceDirect:Open Access CrossRef Pascal-Francis
DatabaseTitle	CrossRef
DatabaseTitleList
DeliveryMethod	fulltext_linktorsrc
Discipline	Mathematics Computer Science Applied Sciences
EISSN	1879-2294
EndPage	87
ExternalDocumentID	19121733 10_1016_j_tcs_2007_05_036 S0304397507004732
GroupedDBID	--K --M -~X .DC .~1 0R~ 123 1B1 1RT 1~. 1~5 29Q 4.4 457 4G. 5VS 6I. 7-5 71M 8P~ 9JN AABNK AACTN AAEDT AAEDW AAFTH AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO AAYFN ABAOU ABBOA ABEFU ABFNM ABJNI ABMAC ABTAH ABVKL ABXDB ABYKQ ACAZW ACDAQ ACGFS ACNNM ACRLP ACZNC ADBBV ADEZE ADMUD AEBSH AEKER AENEX AEXQZ AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHZHX AIALX AIEXJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD ARUGR ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CS3 DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q G8K GBLVA GBOLZ HVGLF HZ~ IHE IXB J1W KOM LG9 M26 M41 MHUIS MO0 N9A NCXOZ O-L O9- OAUVE OK1 OZT P-8 P-9 P2P PC. Q38 R2- RIG ROL RPZ SCC SDF SDG SES SEW SPC SPCBC SSV SSW SSZ T5K TAE TN5 WH7 WUQ XJT YNT ZMT ZY4 ~G- 9DU AATTM AAXKI AAYWO AAYXX ABDPE ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO ADVLN AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD AFXIZ AGCQF AGRNS BNPGV IQODW SSH
ID	FETCH-LOGICAL-c327t-40287ea061b7b963b8c46c5d4edb44d7a2ce75be1903828823027e5b7caf3e703
ISICitedReferencesCount	13
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000250417300007&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0304-3975
IngestDate	Mon Jul 21 09:15:31 EDT 2025 Tue Nov 18 20:00:22 EST 2025 Sat Nov 29 05:14:53 EST 2025 Fri Feb 23 02:16:38 EST 2024
IsDoiOpenAccess	true
IsOpenAccess	true
IsPeerReviewed	true
IsScholarly	true
Issue	1
Keywords	Randomized approximation algorithm Maximum cut Semidefinite programming Limited unbalance cut Polynomial Computer theory Methodology Polynomial approximation Node Semi definite programming Approximation algorithm Weighted graph Polynomial time Maximum Performance Threshold
Language	English
License	http://www.elsevier.com/open-access/userlicense/1.0 https://www.elsevier.com/tdm/userlicense/1.0 https://www.elsevier.com/open-access/userlicense/1.0 CC BY 4.0
LinkModel	OpenURL
MergedId	FETCHMERGED-LOGICAL-c327t-40287ea061b7b963b8c46c5d4edb44d7a2ce75be1903828823027e5b7caf3e703
OpenAccessLink	https://dx.doi.org/10.1016/j.tcs.2007.05.036
PageCount	10
ParticipantIDs	pascalfrancis_primary_19121733 crossref_citationtrail_10_1016_j_tcs_2007_05_036 crossref_primary_10_1016_j_tcs_2007_05_036 elsevier_sciencedirect_doi_10_1016_j_tcs_2007_05_036
PublicationCentury	2000
PublicationDate	2007-10-15
PublicationDateYYYYMMDD	2007-10-15
PublicationDate_xml	– month: 10 year: 2007 text: 2007-10-15 day: 15
PublicationDecade	2000
PublicationPlace	Amsterdam
PublicationPlace_xml	– name: Amsterdam
PublicationTitle	Theoretical computer science
PublicationYear	2007
Publisher	Elsevier B.V Elsevier
Publisher_xml	– name: Elsevier B.V – name: Elsevier
References	Ye (b12) 2001; 90 Frieze, Jerrum (b6) 1997; 18 G. Galbiati, S. Gualandi, F. Maffioli, Computational experince with a SDP-based algorithm for maximum cut with limited unbalance, in: Proc. of the 3rd International Network Optimization Conference, INOC 2007, 2007. File n. 24 Hayrapetyan, Kempe, Pal, Svitkina (b9) 2005; vol. 3669 Goemans, Williamson (b8) 1995; 42 S. Arora, C. Lund, R. Motwani, M. Sudan, M. Szegedy, Proof verification and hardness of approximation problems, in: Proc. of the 33rd FOCS, 1992, pp. 14–23 Vazirani (b11) 2001 Ageev, Sviridenko (b1) 1999; vol. 1610 Akiyama, Avis, Chvatal, Era (b2) 1981; 3 Alizadeh (b3) 1995; 5 Feige, Langberg (b5) 2001; 41 Poljak, Tuza (b10) 1995; vol. 20 10.1016/j.tcs.2007.05.036_b4 10.1016/j.tcs.2007.05.036_b7 Alizadeh (10.1016/j.tcs.2007.05.036_b3) 1995; 5 Frieze (10.1016/j.tcs.2007.05.036_b6) 1997; 18 Hayrapetyan (10.1016/j.tcs.2007.05.036_b9) 2005; vol. 3669 Poljak (10.1016/j.tcs.2007.05.036_b10) 1995; vol. 20 Ye (10.1016/j.tcs.2007.05.036_b12) 2001; 90 Goemans (10.1016/j.tcs.2007.05.036_b8) 1995; 42 Vazirani (10.1016/j.tcs.2007.05.036_b11) 2001 Feige (10.1016/j.tcs.2007.05.036_b5) 2001; 41 Ageev (10.1016/j.tcs.2007.05.036_b1) 1999; vol. 1610 Akiyama (10.1016/j.tcs.2007.05.036_b2) 1981; 3
References_xml	– volume: 18 start-page: 67 year: 1997 end-page: 81 ident: b6 article-title: Improved approximation algorithms for MAX publication-title: Algorithmica – reference: S. Arora, C. Lund, R. Motwani, M. Sudan, M. Szegedy, Proof verification and hardness of approximation problems, in: Proc. of the 33rd FOCS, 1992, pp. 14–23 – volume: vol. 3669 start-page: 191 year: 2005 end-page: 202 ident: b9 article-title: Unbalanced graph cuts publication-title: ESA 2005 – volume: vol. 1610 start-page: 17 year: 1999 end-page: 30 ident: b1 article-title: Approximation algorithms for maximum coverage and max cut with given sizes of parts publication-title: IPCO 1999 – reference: G. Galbiati, S. Gualandi, F. Maffioli, Computational experince with a SDP-based algorithm for maximum cut with limited unbalance, in: Proc. of the 3rd International Network Optimization Conference, INOC 2007, 2007. File n. 24 – volume: 42 start-page: 1115 year: 1995 end-page: 1145 ident: b8 article-title: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming publication-title: J. ACM – volume: 3 start-page: 227 year: 1981 end-page: 233 ident: b2 article-title: Balancing signed graphs publication-title: Discrete Appl. Math. – year: 2001 ident: b11 article-title: Approximation Algorithms – volume: 90 start-page: 101 year: 2001 end-page: 111 ident: b12 article-title: A. 699-approximation algorithm for max-bisection publication-title: Math. Program. Ser. A – volume: 5 start-page: 13 year: 1995 end-page: 51 ident: b3 article-title: Interior point methods in semidefinite programming with applications to combinatorial optimization publication-title: SIAM J. Optim. – volume: 41 start-page: 174 year: 2001 end-page: 211 ident: b5 article-title: Approximation algorithms for maximization problems in graph partitioning publication-title: J. Algorithms – volume: vol. 20 start-page: 181 year: 1995 end-page: 244 ident: b10 article-title: Maximum cuts and large bipartite subgraphs publication-title: Combinatorial Optimization – ident: 10.1016/j.tcs.2007.05.036_b4 doi: 10.1109/SFCS.1992.267823 – volume: 42 start-page: 1115 year: 1995 ident: 10.1016/j.tcs.2007.05.036_b8 article-title: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming publication-title: J. ACM doi: 10.1145/227683.227684 – volume: vol. 20 start-page: 181 year: 1995 ident: 10.1016/j.tcs.2007.05.036_b10 article-title: Maximum cuts and large bipartite subgraphs – ident: 10.1016/j.tcs.2007.05.036_b7 – volume: 90 start-page: 101 year: 2001 ident: 10.1016/j.tcs.2007.05.036_b12 article-title: A. 699-approximation algorithm for max-bisection publication-title: Math. Program. Ser. A doi: 10.1007/PL00011415 – volume: 18 start-page: 67 year: 1997 ident: 10.1016/j.tcs.2007.05.036_b6 article-title: Improved approximation algorithms for MAX k-CUT and MAX BISECTION publication-title: Algorithmica doi: 10.1007/BF02523688 – volume: vol. 3669 start-page: 191 year: 2005 ident: 10.1016/j.tcs.2007.05.036_b9 article-title: Unbalanced graph cuts – volume: 41 start-page: 174 year: 2001 ident: 10.1016/j.tcs.2007.05.036_b5 article-title: Approximation algorithms for maximization problems in graph partitioning publication-title: J. Algorithms doi: 10.1006/jagm.2001.1183 – year: 2001 ident: 10.1016/j.tcs.2007.05.036_b11 – volume: 5 start-page: 13 year: 1995 ident: 10.1016/j.tcs.2007.05.036_b3 article-title: Interior point methods in semidefinite programming with applications to combinatorial optimization publication-title: SIAM J. Optim. doi: 10.1137/0805002 – volume: vol. 1610 start-page: 17 year: 1999 ident: 10.1016/j.tcs.2007.05.036_b1 article-title: Approximation algorithms for maximum coverage and max cut with given sizes of parts – volume: 3 start-page: 227 year: 1981 ident: 10.1016/j.tcs.2007.05.036_b2 article-title: Balancing signed graphs publication-title: Discrete Appl. Math. doi: 10.1016/0166-218X(81)90001-9
SSID	ssj0000576
Score	1.8915278
Snippet	We consider the problem of partitioning the vertices of a weighted graph into two sets of sizes that differ at most by a given threshold B , so as to maximize...
SourceID	pascalfrancis crossref elsevier
SourceType	Index Database Enrichment Source Publisher
StartPage	78
SubjectTerms	Algorithmics. Computability. Computer arithmetics Applied sciences Approximations and expansions Computer science; control theory; systems Exact sciences and technology Information retrieval. Graph Limited unbalance cut Mathematical analysis Mathematics Maximum cut Miscellaneous Randomized approximation algorithm Sciences and techniques of general use Semidefinite programming Theoretical computing
Title	Approximation algorithms for maximum cut with limited unbalance
URI	https://dx.doi.org/10.1016/j.tcs.2007.05.036
Volume	385
WOSCitedRecordID	wos000250417300007&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: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1879-2294 dateEnd: 20180131 omitProxy: false ssIdentifier: ssj0000576 issn: 0304-3975 databaseCode: AIEXJ dateStart: 19950109 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1bi9QwFA6y64MiXlbF9bLkwSdLh9o0k-ZJBllRYRfBEeatJGmqXbqdYdvK_HxPetLOdhcXFXwpQ2Z6mZyv55ac8xHyOufzNJ-bKIx0IsMEAo5QKc5Cy4rIgnlJjMp7sglxepquVvKLb0_Q9HQCoq7T7VZu_quoYQyE7Upn_0Lc40VhAD6D0OEIYofjHwl-4bqEb0ssSQxU9X0N8f8P7LsQnCv4pjsPTNdiCrbCAqegq7Xb5GgmO4OWl6ocjad_CLzNHDfuqEo78fYJ9rKrylHPn6iiKNdYft3zd9jGrCdZBuHUM9ZZYurrWvkLlly5ZRWJ1Cczixo0FTKMY2QuHlQsQ1qeCZZQYSJ_z8T0XlPqmF84m7Wm8T0n-SxiVxpo9yb5q3si90CR69ovGNjm_VhwCRp7f_HpePV5Z6S5wGVs_w-GBe9-69-VG_3OZbm3UQ0IoEAGlEtuyfIhue_jCbpAHDwit2x9QB4MXB3Uq-4Dcvdk7M_bPCbvJiChO5BQAAn1IKEAEupAQj1I6AiSJ-Tbh-Pl-4-hp9IIDYtF67IEqbAKnDctNOhcnZpkbnie2FwnSS5UbKzg2oJ7yCAGd6uvsbBcC6MKZsEqPCV79bq2zwiFMZlaw-CVThPFjbQ5S5WII5mrHALQQxINs5UZ32fe0Z1U2bCh8CyDCXb8pyKLeAYTfEjejKdssMnKTT9OBhFkHvHo_WWAl5tOO5qIa3cj-RbCcsae_9t1X5A7u_flJdlrLzr7itw2P9uyuTjysPsFVc6Xug
linkProvider	Elsevier
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=Approximation+algorithms+for+maximum+cut+with+limited+unbalance&rft.jtitle=Theoretical+computer+science&rft.au=Galbiati%2C+Giulia&rft.au=Maffioli%2C+Francesco&rft.date=2007-10-15&rft.pub=Elsevier+B.V&rft.issn=0304-3975&rft.eissn=1879-2294&rft.volume=385&rft.issue=1&rft.spage=78&rft.epage=87&rft_id=info:doi/10.1016%2Fj.tcs.2007.05.036&rft.externalDocID=S0304397507004732
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0304-3975&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0304-3975&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0304-3975&client=summon