On the hardness of approximating label-cover
The Label-Cover problem, defined by S. Arora, L. Babai, J. Stern, Z. Sweedyk [Proceedings of 34th IEEE Symposium on Foundations of Computer Science, 1993, pp. 724–733], serves as a starting point for numerous hardness of approximation reductions. It is one of six ‘canonical’ approximation problems i...
Gespeichert in:
| Veröffentlicht in: | Information processing letters Jg. 89; H. 5; S. 247 - 254 |
|---|---|
| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Amsterdam
Elsevier B.V
16.03.2004
Elsevier Science Elsevier Sequoia S.A |
| Schlagworte: | |
| ISSN: | 0020-0190, 1872-6119 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | The
Label-Cover problem, defined by S. Arora, L. Babai, J. Stern, Z. Sweedyk [Proceedings of 34th IEEE Symposium on Foundations of Computer Science, 1993, pp. 724–733], serves as a starting point for numerous hardness of approximation reductions. It is one of six ‘canonical’ approximation problems in the survey of Arora and Lund [Hardness of Approximations, in: Approximation Algorithms for NP-Hard Problems, PWS Publishing Company, 1996, Chapter 10]. In this paper we present a direct combinatorial reduction from low error-probability PCP [Proceedings of 31st ACM Symposium on Theory of Computing, 1999, pp. 29–40] to
Label-Cover showing it NP-hard to approximate to within 2
(log
n)
1−o(1)
. This improves upon the best previous hardness of approximation results known for this problem.
We also consider the
Minimum-Monotone-Satisfying-Assignment (MMSA) problem of finding a satisfying assignment to a monotone formula with the least number of 1's, introduced by M. Alekhnovich, S. Buss, S. Moran, T. Pitassi [Minimum propositional proof length is NP-hard to linearly approximate, 1998]. We define a hierarchy of approximation problems obtained by restricting the number of alternations of the monotone formula. This hierarchy turns out to be equivalent to an AND/OR scheduling hierarchy suggested by M.H. Goldwasser, R. Motwani [Lecture Notes in Comput. Sci., Vol. 1272, Springer-Verlag, 1997, pp. 307–320]. We show some hardness results for certain levels in this hierarchy, and place
Label-Cover between levels 3 and 4. This partially answers an open problem from M.H. Goldwasser, R. Motwani regarding the precise complexity of each level in the hierarchy, and the place of
Label-Cover in it. |
|---|---|
| AbstractList | The Label-Cover problem, defined by S. Arora, L. Babai, J. Stern, Z. Sweedyk [Proceedings of 34th IEEE Symposium on Foundations of Computer Science, 1993, pp. 724-733], serves as a starting point for numerous hardness of approximation reductions. It is one of six 'canonical' approximation problems in the survey of Arora and Lund [Hardness of Approximations, in: Approximation Algorithms for NP-Hard Problems, PWS Publishing Company, 1996, Chapter 10]. In this paper we present a direct combinatorial reduction from low error-probability PCP [Proceedings of 31st ACM Symposium on Theory of Computing, 1999, pp. 29-40] to Label-Cover showing it NP-hard to approximate to within 2^(logn)^1-o(1). This improves upon the best previous hardness of approximation results known for this problem. We also consider the Minimum-Monotone-Satisfying-Assignment (MMSA) problem of finding a satisfying assignment to a monotone formula with the least number of 1's, introduced by M. Alekhnovich, S. Buss, S. Moran, T. Pitassi [Minimum propositional proof length is NP-hard to linearly approximate, 1998]. We define a hierarchy of approximation problems obtained by restricting the number of alternations of the monotone formula. This hierarchy turns out to be equivalent to an AND/OR scheduling hierarchy suggested by M.H. Goldwasser, R. Motwani [Lecture Notes in Comput. Sci., Vol. 1272, Springer-Verlag, 1997, pp. 307-320]. We show some hardness results for certain levels in this hierarchy, and place between levels 3 and 4. This partially answers an open problem from M.H. Goldwasser, R. Motwani regarding the precise complexity of each level in the hierarchy, and the place of Label-Cover on it. [PUBLICATION ABSTRACT] The Label-Cover problem, defined by S. Arora, L. Babai, J. Stern, Z. Sweedyk [Proceedings of 34th IEEE Symposium on Foundations of Computer Science, 1993, pp. 724–733], serves as a starting point for numerous hardness of approximation reductions. It is one of six ‘canonical’ approximation problems in the survey of Arora and Lund [Hardness of Approximations, in: Approximation Algorithms for NP-Hard Problems, PWS Publishing Company, 1996, Chapter 10]. In this paper we present a direct combinatorial reduction from low error-probability PCP [Proceedings of 31st ACM Symposium on Theory of Computing, 1999, pp. 29–40] to Label-Cover showing it NP-hard to approximate to within 2 (log n) 1−o(1) . This improves upon the best previous hardness of approximation results known for this problem. We also consider the Minimum-Monotone-Satisfying-Assignment (MMSA) problem of finding a satisfying assignment to a monotone formula with the least number of 1's, introduced by M. Alekhnovich, S. Buss, S. Moran, T. Pitassi [Minimum propositional proof length is NP-hard to linearly approximate, 1998]. We define a hierarchy of approximation problems obtained by restricting the number of alternations of the monotone formula. This hierarchy turns out to be equivalent to an AND/OR scheduling hierarchy suggested by M.H. Goldwasser, R. Motwani [Lecture Notes in Comput. Sci., Vol. 1272, Springer-Verlag, 1997, pp. 307–320]. We show some hardness results for certain levels in this hierarchy, and place Label-Cover between levels 3 and 4. This partially answers an open problem from M.H. Goldwasser, R. Motwani regarding the precise complexity of each level in the hierarchy, and the place of Label-Cover in it. |
| Author | Safra, Shmuel Dinur, Irit |
| Author_xml | – sequence: 1 givenname: Irit surname: Dinur fullname: Dinur, Irit email: iritd@eecs.berkeley.edu – sequence: 2 givenname: Shmuel surname: Safra fullname: Safra, Shmuel email: safra@post.tau.ac.il |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=15495113$$DView record in Pascal Francis |
| BookMark | eNp9kE1LxDAQhoOs4Lr6A7wVwZutM_noB55E_ALBi55Dmk41S03XpIr-e7Ps4sHDnobA-8y8eQ7ZzI-eGDtBKBCwvFgWbjUUHEAUiAVAtcfmWFc8LxGbGZsDcMgBGzhghzEuAaCUopqz8yefTW-UvZnQeYoxG_vMrFZh_HbvZnL-NRtMS0Nuxy8KR2y_N0Ok4-1csJfbm-fr-_zx6e7h-uoxtxLrKbeqFW3X9DU1ikNVy6YH2coShaoFKS45tWTqTlllselAyZK3KNK7T_2VFAt2utmbenx8Upz0cvwMPp3UXFS85lWFKXS2DZlozdAH462LehVS8fCjUclGIYqUqzY5G8YYA_Xauil9bfRTMG7QCHptUC91MqjXBjWiTgYTif_Iv-U7mMsNQ8nPl6Ogo3XkLXUukJ10N7od9C_CQIhs |
| CODEN | IFPLAT |
| CitedBy_id | crossref_primary_10_1016_j_jda_2006_03_008 crossref_primary_10_1016_j_ipl_2024_106556 crossref_primary_10_1016_j_ipl_2012_03_004 crossref_primary_10_1016_j_orl_2009_05_006 crossref_primary_10_1109_TCBB_2012_165 crossref_primary_10_1016_j_ipl_2008_05_007 crossref_primary_10_1137_06066850X crossref_primary_10_1137_23M1608483 crossref_primary_10_1007_s10472_014_9415_9 crossref_primary_10_1145_1159892_1159901 crossref_primary_10_1007_s10878_005_1413_8 crossref_primary_10_1016_j_tcs_2021_06_018 crossref_primary_10_1155_2011_895398 crossref_primary_10_1016_j_apal_2011_09_009 crossref_primary_10_1007_s00453_016_0222_z crossref_primary_10_1007_s10878_009_9222_0 crossref_primary_10_1109_TIT_2018_2822267 |
| Cites_doi | 10.1007/BFb0055766 10.1145/185675.306789 10.1137/S0097539795280895 10.1016/0012-365X(75)90058-8 10.1016/S0022-0000(74)80044-9 |
| ContentType | Journal Article |
| Copyright | 2003 Elsevier B.V. 2004 INIST-CNRS Copyright Elsevier Sequoia S.A. Mar 16, 2004 |
| Copyright_xml | – notice: 2003 Elsevier B.V. – notice: 2004 INIST-CNRS – notice: Copyright Elsevier Sequoia S.A. Mar 16, 2004 |
| DBID | AAYXX CITATION IQODW 7SC 8FD JQ2 L7M L~C L~D |
| DOI | 10.1016/j.ipl.2003.11.007 |
| DatabaseName | CrossRef Pascal-Francis Computer and Information Systems Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Computer and Information Systems Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Advanced Technologies Database with Aerospace ProQuest Computer Science Collection Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Computer and Information Systems Abstracts |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science Applied Sciences |
| EISSN | 1872-6119 |
| EndPage | 254 |
| ExternalDocumentID | 547307981 15495113 10_1016_j_ipl_2003_11_007 S0020019003005167 |
| Genre | Feature |
| GroupedDBID | --K --M -~X .DC .~1 0R~ 1B1 1RT 1~. 1~5 29I 4.4 457 4G. 5GY 5VS 7-5 71M 8P~ 9JN AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO AAYFN ABBOA ABEFU ABFNM ABFSI ABJNI ABMAC ABTAH ABXDB ABYKQ ACDAQ ACGFS ACNNM ACRLP ACZNC ADBBV ADEZE ADJOM ADMUD AEBSH AEKER AENEX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHZHX AIALX AIEXJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD ASPBG AVWKF AXJTR AZFZN BKOJK BKOMP BLXMC CS3 DU5 E.L EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q G8K GBLVA GBOLZ HLZ HMJ HVGLF HZ~ IHE J1W KOM LG9 M26 M41 MO0 MS~ O-L O9- OAUVE OZT P-8 P-9 P2P PC. PQQKQ Q38 R2- RIG ROL RPZ SBC SDF SDG SDP SES SEW SME SPC SPCBC SSV SSZ T5K TN5 UQL WH7 WUQ XPP ZMT ZY4 ~G- 9DU AATTM AAXKI AAYWO AAYXX ABDPE ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD AFXIZ AGCQF AGRNS BNPGV IQODW SSH 7SC 8FD JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c418t-c5b3bd9f8e95207849f04b4613583e5242ebea8d5c5c19d05462b13d5cf003543 |
| ISICitedReferencesCount | 29 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000188934900006&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0020-0190 |
| IngestDate | Mon Jul 14 08:13:28 EDT 2025 Mon Jul 21 09:14:41 EDT 2025 Tue Nov 18 21:12:24 EST 2025 Sat Nov 29 03:44:12 EST 2025 Fri Feb 23 02:30:02 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 5 |
| Keywords | Label-cover PCP Computational complexity Hardness of approximation Computer theory NP hard problem Information processing Approximation algorithm Label cover |
| Language | English |
| License | https://www.elsevier.com/tdm/userlicense/1.0 CC BY 4.0 |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c418t-c5b3bd9f8e95207849f04b4613583e5242ebea8d5c5c19d05462b13d5cf003543 |
| Notes | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 |
| PQID | 237282771 |
| PQPubID | 45522 |
| PageCount | 8 |
| ParticipantIDs | proquest_journals_237282771 pascalfrancis_primary_15495113 crossref_citationtrail_10_1016_j_ipl_2003_11_007 crossref_primary_10_1016_j_ipl_2003_11_007 elsevier_sciencedirect_doi_10_1016_j_ipl_2003_11_007 |
| PublicationCentury | 2000 |
| PublicationDate | 2004-03-16 |
| PublicationDateYYYYMMDD | 2004-03-16 |
| PublicationDate_xml | – month: 03 year: 2004 text: 2004-03-16 day: 16 |
| PublicationDecade | 2000 |
| PublicationPlace | Amsterdam |
| PublicationPlace_xml | – name: Amsterdam |
| PublicationTitle | Information processing letters |
| PublicationYear | 2004 |
| Publisher | Elsevier B.V Elsevier Science Elsevier Sequoia S.A |
| Publisher_xml | – name: Elsevier B.V – name: Elsevier Science – name: Elsevier Sequoia S.A |
| References | Dinur, Fischer, Kindler, Raz, Safra (BIB004) 1999 Umans (BIB013) 1999 Johnson (BIB007) 1974; 9 Lund, Yannakakis (BIB010) 1994; 41 M. Alekhnovich, S. Buss, S. Moran, T. Pitassi, Minimum propositional proof length is NP-hard to linearly approximate, manuscript, 1998 Lapidot, Shamir (BIB008) 1991 Raz (BIB011) 1998; 27 Lovász (BIB009) 1975; 13 Raz, Safra (BIB012) 1997 Feige, Lovász (BIB005) 1992 Goldwasser, Motwani (BIB006) 1997; vol. 1272 Bellare, Goldwasser, Lund, Russell (BIB003) 1993 Arora, Babai, Stern, Sweedyk (BIB002) 1993 Dinur (10.1016/j.ipl.2003.11.007_BIB004) 1999 Raz (10.1016/j.ipl.2003.11.007_BIB011) 1998; 27 Umans (10.1016/j.ipl.2003.11.007_BIB013) 1999 Bellare (10.1016/j.ipl.2003.11.007_BIB003) 1993 Lovász (10.1016/j.ipl.2003.11.007_BIB009) 1975; 13 Feige (10.1016/j.ipl.2003.11.007_BIB005) 1992 Raz (10.1016/j.ipl.2003.11.007_BIB012) 1997 Lund (10.1016/j.ipl.2003.11.007_BIB010) 1994; 41 Goldwasser (10.1016/j.ipl.2003.11.007_BIB006) 1997; vol. 1272 10.1016/j.ipl.2003.11.007_BIB001 Lapidot (10.1016/j.ipl.2003.11.007_BIB008) 1991 Arora (10.1016/j.ipl.2003.11.007_BIB002) 1993 Johnson (10.1016/j.ipl.2003.11.007_BIB007) 1974; 9 |
| References_xml | – start-page: 733 year: 1992 end-page: 741 ident: BIB005 article-title: Two-prover one-round proof systems: Their power and their problems publication-title: Proceedings of 24th ACM Symposium on Theory of Computing – start-page: 29 year: 1999 end-page: 40 ident: BIB004 article-title: PCP characterizations of NP: Towards a polynomially-small error-probability publication-title: Proceedings of 31st ACM Symposium on Theory of Computing – volume: 13 start-page: 383 year: 1975 end-page: 390 ident: BIB009 article-title: On the ratio of optimal integral and fractional covers publication-title: Discrete Math. – start-page: 465 year: 1999 end-page: 474 ident: BIB013 article-title: Hardness of approximating Σ publication-title: 40th Annual IEEE Symposium on Foundations of Computer Science (FOCS '99) – volume: 27 start-page: 763 year: 1998 end-page: 803 ident: BIB011 article-title: A parallel repetition theorem publication-title: SIAM J. Comput. – start-page: 724 year: 1993 end-page: 733 ident: BIB002 article-title: The hardness of approximate optima in lattices, codes and linear equations publication-title: Proceedings of 34th IEEE Symposium on Foundations of Computer Science – start-page: 113 year: 1993 end-page: 131 ident: BIB003 article-title: Efficient multi-prover interactive proofs with applications to approximation problems publication-title: Proceedings of 25th ACM Symposium on Theory of Computing – volume: 41 start-page: 960 year: 1994 end-page: 981 ident: BIB010 article-title: On the hardness of approximating minimization problems publication-title: J. ACM – reference: M. Alekhnovich, S. Buss, S. Moran, T. Pitassi, Minimum propositional proof length is NP-hard to linearly approximate, manuscript, 1998 – start-page: 13 year: 1991 end-page: 18 ident: BIB008 article-title: Fully parallelized multi prover protocols for NEXPTIME publication-title: Proceedings of 32nd IEEE Symposium on Foundations of Computer Science – start-page: 475 year: 1997 end-page: 484 ident: BIB012 article-title: A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP publication-title: Proceedings of 29th ACM Symposium on Theory of Computing – volume: vol. 1272 start-page: 307 year: 1997 end-page: 320 ident: BIB006 article-title: Intractability of assembly sequencing: Unit disks in the plane publication-title: Lecture Notes in Comput. Sci. – volume: 9 start-page: 256 year: 1974 end-page: 278 ident: BIB007 article-title: Approximation algorithms for combinatorial problems publication-title: J. Comput. System Sci. – start-page: 465 year: 1999 ident: 10.1016/j.ipl.2003.11.007_BIB013 article-title: Hardness of approximating Σp2 minimization problems – start-page: 733 year: 1992 ident: 10.1016/j.ipl.2003.11.007_BIB005 article-title: Two-prover one-round proof systems: Their power and their problems – start-page: 13 year: 1991 ident: 10.1016/j.ipl.2003.11.007_BIB008 article-title: Fully parallelized multi prover protocols for NEXPTIME – ident: 10.1016/j.ipl.2003.11.007_BIB001 doi: 10.1007/BFb0055766 – volume: 41 start-page: 960 issue: 5 year: 1994 ident: 10.1016/j.ipl.2003.11.007_BIB010 article-title: On the hardness of approximating minimization problems publication-title: J. ACM doi: 10.1145/185675.306789 – start-page: 475 year: 1997 ident: 10.1016/j.ipl.2003.11.007_BIB012 article-title: A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP – start-page: 29 year: 1999 ident: 10.1016/j.ipl.2003.11.007_BIB004 article-title: PCP characterizations of NP: Towards a polynomially-small error-probability – volume: 27 start-page: 763 issue: 3 year: 1998 ident: 10.1016/j.ipl.2003.11.007_BIB011 article-title: A parallel repetition theorem publication-title: SIAM J. Comput. doi: 10.1137/S0097539795280895 – volume: 13 start-page: 383 year: 1975 ident: 10.1016/j.ipl.2003.11.007_BIB009 article-title: On the ratio of optimal integral and fractional covers publication-title: Discrete Math. doi: 10.1016/0012-365X(75)90058-8 – start-page: 113 year: 1993 ident: 10.1016/j.ipl.2003.11.007_BIB003 article-title: Efficient multi-prover interactive proofs with applications to approximation problems – volume: 9 start-page: 256 year: 1974 ident: 10.1016/j.ipl.2003.11.007_BIB007 article-title: Approximation algorithms for combinatorial problems publication-title: J. Comput. System Sci. doi: 10.1016/S0022-0000(74)80044-9 – start-page: 724 year: 1993 ident: 10.1016/j.ipl.2003.11.007_BIB002 article-title: The hardness of approximate optima in lattices, codes and linear equations – volume: vol. 1272 start-page: 307 year: 1997 ident: 10.1016/j.ipl.2003.11.007_BIB006 article-title: Intractability of assembly sequencing: Unit disks in the plane |
| SSID | ssj0006437 |
| Score | 1.8555613 |
| Snippet | The
Label-Cover problem, defined by S. Arora, L. Babai, J. Stern, Z. Sweedyk [Proceedings of 34th IEEE Symposium on Foundations of Computer Science, 1993, pp.... The Label-Cover problem, defined by S. Arora, L. Babai, J. Stern, Z. Sweedyk [Proceedings of 34th IEEE Symposium on Foundations of Computer Science, 1993, pp.... |
| SourceID | proquest pascalfrancis crossref elsevier |
| SourceType | Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 247 |
| SubjectTerms | Applied sciences Approximation Computational complexity Computer science Computer science; control theory; systems Estimates Exact sciences and technology Hardness of approximation Label-cover Miscellaneous PCP Studies Theoretical computing |
| Title | On the hardness of approximating label-cover |
| URI | https://dx.doi.org/10.1016/j.ipl.2003.11.007 https://www.proquest.com/docview/237282771 |
| Volume | 89 |
| WOSCitedRecordID | wos000188934900006&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: 1872-6119 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0006437 issn: 0020-0190 databaseCode: AIEXJ dateStart: 19950113 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1LT9wwELYQcKhUtVBadUtBOfRUCIode20fUUVVegAkqLS3aOM4bRAN0T6q_fmd8SO7gEDl0Eu0GyXZbD575nPm8RHyCRi0rgzFVojWpHysRVoqaVLUB5QVN0JVxolNyLMzNRrpiyD8N3VyArJt1WKhu_8KNewDsLF09hlw9xeFHfAZQIctwA7bfwL-3CcuYjWVM2MY6MfG4YsGyWn78wBwtzepwdzNVWoaCpPceOh8-YA72tX7LOXnm3buQD6dNH3GzOW4dnJFB5e_fs9DDn58k8AxlcoXOvaZ_Zik5uU7o3X0Aj9hFIhVU-c7ZQavyXwr6AcG2b8buD5qOhfnyY-wZWoml94nRtzvOaU-VTBmoV0XcAkUzcxh0VK4BgIbTAoNxnjj-PRk9L33vxiK9Ik9_t_EWLbL6rt3H4-xkZfdeApzpPbiJg_8tCMfV1vkVVg1JMce7W2yZts35HVU5EiCgd4hh-dtAuAnEfzktk7ugJ-sgP-W_Ph6cvXlWxr0MFLDqZqlRpR5WelaWS0YUDuu64yXHAiZULkVQLZgRo5VJYwwVFdAxoespDl8rzFgzPN3ZL29be17kqgKlq2s5BbtMVVZaVWth3SY2ZphO6cByeJzKUxoFo-aJTfFo3gMyOf-lM53SnnqYB4fdhGonqdwBQycp07bvwPM8ocELPQpzQdkNyJVhDk5LVgumWJS0g_PucVd8mI5ST6S9dlkbvfIpvkza6aT_TDo_gLmx4WL |
| 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=On+the+hardness+of+approximating+label-cover&rft.jtitle=Information+processing+letters&rft.au=Dinur%2C+Irit&rft.au=Safra%2C+Shmuel&rft.date=2004-03-16&rft.issn=0020-0190&rft.volume=89&rft.issue=5&rft.spage=247&rft.epage=254&rft_id=info:doi/10.1016%2Fj.ipl.2003.11.007&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_ipl_2003_11_007 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0020-0190&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0020-0190&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0020-0190&client=summon |