A (1+ln2)-approximation algorithm for minimum-cost 2-edge-connectivity augmentation of trees with constant radius
We consider the Tree Augmentation problem: given a graph G=(V,E) with edge-costs and a tree T on V disjoint to E, find a minimum-cost edge-subset F⊆E such that T∪F is 2-edge-connected. Tree Augmentation is equivalent to the problem of finding a minimum-cost edge-cover F⊆E of a laminar set-family. Th...
Saved in:
| Published in: | Theoretical computer science Vol. 489-490; pp. 67 - 74 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier B.V
10.06.2013
|
| Subjects: | |
| ISSN: | 0304-3975, 1879-2294 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | We consider the Tree Augmentation problem: given a graph G=(V,E) with edge-costs and a tree T on V disjoint to E, find a minimum-cost edge-subset F⊆E such that T∪F is 2-edge-connected. Tree Augmentation is equivalent to the problem of finding a minimum-cost edge-cover F⊆E of a laminar set-family. The best known approximation ratio for Tree Augmentation is 2, even for trees of radius 2. As laminar families play an important role in network design problems, obtaining a better ratio is a major open problem in connectivity network design. We give a (1+ln2)-approximation algorithm for trees of constant radius. Our algorithm is based on a new decomposition of problem feasible solutions, and on an extension of Steiner Tree technique of Zelikovsky to the Set-Cover problem, which may be of independent interest.
•We consider making a tree 2-edge-connected by adding a minimum cost edge set.•We give a (1+ln2)-approximation algorithm for trees of constant radius.•Our algorithm is based on a new decomposition of problem feasible solutions. |
|---|---|
| AbstractList | We consider the Tree Augmentation problem: given a graph G=(V,E) with edge-costs and a tree T on V disjoint to E, find a minimum-cost edge-subset F⊆E such that T∪F is 2-edge-connected. Tree Augmentation is equivalent to the problem of finding a minimum-cost edge-cover F⊆E of a laminar set-family. The best known approximation ratio for Tree Augmentation is 2, even for trees of radius 2. As laminar families play an important role in network design problems, obtaining a better ratio is a major open problem in connectivity network design. We give a (1+ln2)-approximation algorithm for trees of constant radius. Our algorithm is based on a new decomposition of problem feasible solutions, and on an extension of Steiner Tree technique of Zelikovsky to the Set-Cover problem, which may be of independent interest.
•We consider making a tree 2-edge-connected by adding a minimum cost edge set.•We give a (1+ln2)-approximation algorithm for trees of constant radius.•Our algorithm is based on a new decomposition of problem feasible solutions. |
| Author | Cohen, Nachshon Nutov, Zeev |
| Author_xml | – sequence: 1 givenname: Nachshon surname: Cohen fullname: Cohen, Nachshon email: nachshonc@gmail.com – sequence: 2 givenname: Zeev surname: Nutov fullname: Nutov, Zeev email: nutov@openu.ac.il |
| BookMark | eNp9kM1OAyEURompiW31Adyx1JgZgWGGIa6axr-kiRtdE4aBStOBCrTat5emrlz0bu5d3PMl35mAkfNOA3CNUYkRbu5XZVKxJAhXJaIlQvQMjHHLeEEIpyMwRhWiRcVZfQEmMa5Qnpo1Y_A1gzf4bu3IbSE3m-B_7CCT9Q7K9dIHmz4HaHyAg3V22A6F8jFBUuh-qfPtnFbJ7mzaQ7ldDtqlI-sNTEHrCL9zAMx_MUmXYJC93cZLcG7kOuqrvz0FH0-P7_OXYvH2_DqfLQpFOEsFxVj1TUcM121rmFac0qZqTNWTnrCu5pi0VVd3kuPOUM50b1RlOolargzDqpoCfMxVwccYtBGbkMuFvcBIHJyJlcjOxMGZQFRkZ5lh_xhlj51SkHZ9knw4kjpX2lkdRFRWO6V7G7Ik0Xt7gv4Fn5aLRg |
| CitedBy_id | crossref_primary_10_1007_s00453_020_00765_9 crossref_primary_10_1007_s00453_016_0270_4 crossref_primary_10_1007_s10107_023_02018_3 crossref_primary_10_1038_s41598_020_75087_5 crossref_primary_10_1007_s00224_020_10025_6 crossref_primary_10_1145_3722101 crossref_primary_10_1287_ijoc_2022_0295 crossref_primary_10_1007_s10107_022_01854_z crossref_primary_10_1137_21M1430601 crossref_primary_10_1145_3182395 crossref_primary_10_1016_j_orl_2022_10_007 crossref_primary_10_1137_21M1421143 crossref_primary_10_1137_21M1453505 crossref_primary_10_1145_2786981 crossref_primary_10_1016_j_tcs_2023_114367 crossref_primary_10_1007_s00224_024_10175_x crossref_primary_10_1016_j_orl_2022_10_002 crossref_primary_10_1016_j_orl_2023_03_008 crossref_primary_10_1109_TNSM_2023_3237832 |
| Cites_doi | 10.1016/S0166-218X(02)00218-4 10.1016/j.dam.2010.04.002 10.1016/0304-3975(82)90059-7 10.1016/j.ipl.2010.12.010 10.1007/s004930170004 10.1007/3-540-48481-7_44 10.1016/j.orl.2008.01.009 |
| ContentType | Journal Article |
| Copyright | 2013 Elsevier B.V. |
| Copyright_xml | – notice: 2013 Elsevier B.V. |
| DBID | 6I. AAFTH AAYXX CITATION |
| DOI | 10.1016/j.tcs.2013.04.004 |
| DatabaseName | ScienceDirect Open Access Titles Elsevier:ScienceDirect:Open Access CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics Computer Science |
| EISSN | 1879-2294 |
| EndPage | 74 |
| ExternalDocumentID | 10_1016_j_tcs_2013_04_004 S0304397513002661 |
| GroupedDBID | --K --M -~X .DC .~1 0R~ 123 1B1 1RT 1~. 1~5 4.4 457 4G. 5VS 6I. 7-5 71M 8P~ 9JN AABNK AACTN AAEDW AAFTH AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAXUO AAYFN ABAOU ABBOA ABJNI ABMAC ABVKL ABXDB ABYKQ ACAZW ACDAQ ACGFS ACRLP ACZNC ADBBV ADEZE AEBSH AEKER AENEX AEXQZ AFKWA AFTJW AGUBO AGYEJ AHHHB AHZHX AIALX AIEXJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD ARUGR AXJTR BKOJK BLXMC CS3 DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FIRID FNPLU FYGXN G-Q GBLVA GBOLZ HVGLF IHE IXB J1W KOM LG9 M26 M41 MHUIS MO0 N9A NCXOZ O-L O9- OAUVE OK1 OZT P-8 P-9 P2P PC. Q38 RIG ROL RPZ SCC SDF SDG SES SPC SPCBC SSV SSW SSZ T5K TN5 WH7 YNT ZMT ~G- 29Q 9DU AAEDT AAQXK AATTM AAXKI AAYWO AAYXX ABDPE ABEFU ABFNM ABWVN ACLOT ACNNM ACRPL ACVFH ADCNI ADMUD ADNMO ADVLN AEIPS AEUPX AFJKZ AFPUW AGHFR AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP ASPBG AVWKF AZFZN CITATION EFKBS FGOYB G-2 HZ~ R2- SEW TAE WUQ ZY4 ~HD |
| ID | FETCH-LOGICAL-c297t-411cd6b2f9e88f7ec944636f3d2d27b591283b5ba91bf497edfc3fba089cf71c3 |
| ISICitedReferencesCount | 40 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000320973900006&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 | Sat Nov 29 05:15:13 EST 2025 Tue Nov 18 21:31:42 EST 2025 Fri Feb 23 02:30:22 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Edge-connectivity Tree Augmentation Approximation algorithms Laminar family Local replacement |
| Language | English |
| License | http://www.elsevier.com/open-access/userlicense/1.0 |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c297t-411cd6b2f9e88f7ec944636f3d2d27b591283b5ba91bf497edfc3fba089cf71c3 |
| OpenAccessLink | https://dx.doi.org/10.1016/j.tcs.2013.04.004 |
| PageCount | 8 |
| ParticipantIDs | crossref_primary_10_1016_j_tcs_2013_04_004 crossref_citationtrail_10_1016_j_tcs_2013_04_004 elsevier_sciencedirect_doi_10_1016_j_tcs_2013_04_004 |
| PublicationCentury | 2000 |
| PublicationDate | 2013-06-10 |
| PublicationDateYYYYMMDD | 2013-06-10 |
| PublicationDate_xml | – month: 06 year: 2013 text: 2013-06-10 day: 10 |
| PublicationDecade | 2010 |
| PublicationTitle | Theoretical computer science |
| PublicationYear | 2013 |
| Publisher | Elsevier B.V |
| Publisher_xml | – name: Elsevier B.V |
| References | Fredrickson, Jájá (br000020) 1982; 19 Nagamochi (br000050) 2003; 126 Schrijver (br000055) 2004 J. Cheriyan, T. Jordán, R. Ravi, On 2-coverings and 2-packing of laminar families, in: ESA, 1999, pp. 510–520. Cheriyan, Karloff, Khandekar, Könemann (br000010) 2008; 36 Maduel, Nutov (br000045) 2010; 158 Goemans, Williamson (br000025) 1995 Zelikovsky (br000060) 1995 Jain (br000030) 2001; 21 Even, Kortsarz, Nutov (br000015) 2011; 111 Kortsarz, Nutov (br000040) 2007 Khuller (br000035) 1995 Even (10.1016/j.tcs.2013.04.004_br000015) 2011; 111 Schrijver (10.1016/j.tcs.2013.04.004_br000055) 2004 10.1016/j.tcs.2013.04.004_br000005 Kortsarz (10.1016/j.tcs.2013.04.004_br000040) 2007 Fredrickson (10.1016/j.tcs.2013.04.004_br000020) 1982; 19 Nagamochi (10.1016/j.tcs.2013.04.004_br000050) 2003; 126 Khuller (10.1016/j.tcs.2013.04.004_br000035) 1995 Cheriyan (10.1016/j.tcs.2013.04.004_br000010) 2008; 36 Zelikovsky (10.1016/j.tcs.2013.04.004_br000060) 1995 Jain (10.1016/j.tcs.2013.04.004_br000030) 2001; 21 Maduel (10.1016/j.tcs.2013.04.004_br000045) 2010; 158 Goemans (10.1016/j.tcs.2013.04.004_br000025) 1995 |
| References_xml | – volume: 21 start-page: 39 year: 2001 end-page: 60 ident: br000030 article-title: A factor 2 approximation algorithm for the generalized Steiner network problem publication-title: Combinatorica – volume: 36 start-page: 399 year: 2008 end-page: 401 ident: br000010 article-title: On the integrality ratio for tree augmentation publication-title: Operations Research Letters – volume: 19 start-page: 189 year: 1982 end-page: 201 ident: br000020 article-title: On the relationship between the biconnectivity augmentation and traveling salesman problem publication-title: Theorethical Computer Science – year: 2007 ident: br000040 article-title: Approximating minimum cost connectivity problems publication-title: Approximation Algorithms and Metahueristics – start-page: 144 year: 1995 end-page: 191 ident: br000025 article-title: The primal dual method for approximation algorithms and its applications to network design problems publication-title: Approximation Algorithms for NP-hard Problems – start-page: 236 year: 1995 end-page: 265 ident: br000035 article-title: Approximation algorithms for for finding highly connected subgraphs publication-title: Approximation Algorithms for NP-hard Problems – reference: J. Cheriyan, T. Jordán, R. Ravi, On 2-coverings and 2-packing of laminar families, in: ESA, 1999, pp. 510–520. – volume: 111 start-page: 296 year: 2011 end-page: 300 ident: br000015 article-title: A 1.5 approximation algorithm for augmenting edge-connectivity of a graph from 1 to 2 publication-title: Information Processing Letters – year: 2004 ident: br000055 article-title: Combinatorial Optimization, Polyhedra and Efficiency – year: 1995 ident: br000060 article-title: Better approximation bounds for the network and euclidean steiner tree problems. Technical report – volume: 126 start-page: 83 year: 2003 end-page: 113 ident: br000050 article-title: An approximation for finding a smallest 2-edge connected subgraph containing a specified spanning tree publication-title: Discrete Applied Mathematics – volume: 158 start-page: 1424 year: 2010 end-page: 1432 ident: br000045 article-title: Covering a laminar family by leaf to leaf links publication-title: Discrete Applied Mathematics – start-page: 236 year: 1995 ident: 10.1016/j.tcs.2013.04.004_br000035 article-title: Approximation algorithms for for finding highly connected subgraphs – volume: 126 start-page: 83 year: 2003 ident: 10.1016/j.tcs.2013.04.004_br000050 article-title: An approximation for finding a smallest 2-edge connected subgraph containing a specified spanning tree publication-title: Discrete Applied Mathematics doi: 10.1016/S0166-218X(02)00218-4 – year: 2007 ident: 10.1016/j.tcs.2013.04.004_br000040 article-title: Approximating minimum cost connectivity problems – volume: 158 start-page: 1424 issue: 13 year: 2010 ident: 10.1016/j.tcs.2013.04.004_br000045 article-title: Covering a laminar family by leaf to leaf links publication-title: Discrete Applied Mathematics doi: 10.1016/j.dam.2010.04.002 – year: 2004 ident: 10.1016/j.tcs.2013.04.004_br000055 – volume: 19 start-page: 189 issue: 2 year: 1982 ident: 10.1016/j.tcs.2013.04.004_br000020 article-title: On the relationship between the biconnectivity augmentation and traveling salesman problem publication-title: Theorethical Computer Science doi: 10.1016/0304-3975(82)90059-7 – start-page: 144 year: 1995 ident: 10.1016/j.tcs.2013.04.004_br000025 article-title: The primal dual method for approximation algorithms and its applications to network design problems – volume: 111 start-page: 296 issue: 6 year: 2011 ident: 10.1016/j.tcs.2013.04.004_br000015 article-title: A 1.5 approximation algorithm for augmenting edge-connectivity of a graph from 1 to 2 publication-title: Information Processing Letters doi: 10.1016/j.ipl.2010.12.010 – volume: 21 start-page: 39 issue: 1 year: 2001 ident: 10.1016/j.tcs.2013.04.004_br000030 article-title: A factor 2 approximation algorithm for the generalized Steiner network problem publication-title: Combinatorica doi: 10.1007/s004930170004 – ident: 10.1016/j.tcs.2013.04.004_br000005 doi: 10.1007/3-540-48481-7_44 – volume: 36 start-page: 399 issue: 4 year: 2008 ident: 10.1016/j.tcs.2013.04.004_br000010 article-title: On the integrality ratio for tree augmentation publication-title: Operations Research Letters doi: 10.1016/j.orl.2008.01.009 – year: 1995 ident: 10.1016/j.tcs.2013.04.004_br000060 |
| SSID | ssj0000576 |
| Score | 2.3241987 |
| Snippet | We consider the Tree Augmentation problem: given a graph G=(V,E) with edge-costs and a tree T on V disjoint to E, find a minimum-cost edge-subset F⊆E such that... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 67 |
| SubjectTerms | Approximation algorithms Edge-connectivity Laminar family Local replacement Tree Augmentation |
| Title | A (1+ln2)-approximation algorithm for minimum-cost 2-edge-connectivity augmentation of trees with constant radius |
| URI | https://dx.doi.org/10.1016/j.tcs.2013.04.004 |
| Volume | 489-490 |
| WOSCitedRecordID | wos000320973900006&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/eLvHCXMwtV1Lj9MwELaqLgc48FhAu7w0Bw5AZFQnTm0fC1oESFQcFqm3KHGc3VZpsmrTUvHr8StpdtlF7IGLFUWN-5ivnrFn5vsQep2aGF5SjlMhKaYqkpgTSXBqOgZYnBmvY8Um2HTKZzPxfTD41fbCbEtWVXy3Exf_1dT6nja2aZ29hbm7SfUNfa2Nrkdtdj3-k-EnJmgMiB4_BGUVhIHZ-GPLHb6bu0bFIC3P6tW8OV_aKkNDL7LcLLGs100QYnPCpq_1Aiy9tES6OVv6HiUbXZpM9rqrWjfxZROs0nzuDxEWHQK7HknpxSMC73G71EfbHTI1vObn-5qA6aaptzZzotS2fzRhZSKwL1L1LVkm7SKcNEq73FJuZO1GvUXT6XF49-s0e_5Y2N0Zw-J9Iw3HOoksP60TLr5Mon3FuXUlh2012yLRUyRmimREE0slexCyWPAhOph8OZl93fvxmLlMt_8SbU7cVgde-RzXRzW9SOX0IbrvtxgwcdB4hAaqOkQPWvkO8Kv5Ibr3raPsXT9GPyfwBggEUFYQwlu4jBjoEAMaMdBHDFyDGOgjBuoCLGLAIAZaxIBDzBP049PJ6cfP2KtyYBkK1mBKiMzHWVgIxXnBlBTUkM4VUR7mIctioSOeKIuzVJCsoIKpvJBRkaUjLmTBiIyeomFVV-oIgRiTQiqRaceiaBYrocPVPJJ6Bz7W0_P4GI3aXzWRnrLeKKeUyY3WPEbvukcuHF_L315MW1MlHv4ukEw07G5-7Nlt3uM5urv_a7xAw2a1US_RHblt5uvVK4-536RgoLA |
| 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=A+%28+1+%2B+ln+2+%29+-approximation+algorithm+for+minimum-cost+2-edge-connectivity+augmentation+of+trees+with+constant+radius&rft.jtitle=Theoretical+computer+science&rft.au=Cohen%2C+Nachshon&rft.au=Nutov%2C+Zeev&rft.date=2013-06-10&rft.issn=0304-3975&rft.volume=489-490&rft.spage=67&rft.epage=74&rft_id=info:doi/10.1016%2Fj.tcs.2013.04.004&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_tcs_2013_04_004 |
| 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 |