Practical Approximation Algorithms for Zero- and Bounded-Skew Trees

The skew of an edge-weighted rooted tree is the maximum difference between any two root-to-leaf path weights. Zero- or bounded-skew trees are needed for achieving synchronization in many applications, including network multicasting [G. N. Rouskas and I. Baldine, IEEE J. on Selected Areas in Communic...

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on discrete mathematics Vol. 15; no. 1; pp. 97 - 111
Main Authors: Zelikovsky, Alexander Z., Mandoiu, Ion I.
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.01.2001
Subjects:
Algorithms
Approximation
Computer science
Leaves
R&D
Research & development
ISSN:0895-4801, 1095-7146
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract The skew of an edge-weighted rooted tree is the maximum difference between any two root-to-leaf path weights. Zero- or bounded-skew trees are needed for achieving synchronization in many applications, including network multicasting [G. N. Rouskas and I. Baldine, IEEE J. on Selected Areas in Communication, 15 (1997), pp. 346--356] and VLSI clock routing [H. Bakoglu, Circuits, Interconnections, and Packaging for VSLI, Addison-Wesley, Reading, MA, 1990, A. B. Kahng and G. Robins, On Optimal Interconnections for VSLI, Kluwer Academic Publishers, Norwell, MA, 1995]. In these applications edge weights represent propagation delays, and a signal generated at the root should be received by multiple recipients located at the leaves (almost) simultaneously. The objective is to find zero- or bounded-skew trees of minimum total weight, since the weight of the tree is directly proportional to the amount of resources (bandwidth and buffers for network multicasting, power and chip area for clock routing in VLSI) that must be allocated to the tree. Charikar et al. in [Proceedings of the Tenth ACM-SIAM Symposium on Discrete Algorithms, Baltimore, MD, 1999, ACM, New York, 1999, pp. 177--184] have recently proposed the first strongly polynomial algorithms with proven constant approximation factors, $2e\approx 5.44 and 16.86, for finding minimum weight zero- and bounded-skew trees, respectively. In this paper we introduce a new approach to these problems, based on zero-skew "stretching" of spanning trees, and obtain algorithms with improved approximation factors of 4 and 14. For the case when tree nodes are points in the plane and edge weights are given by the rectilinear metric our algorithms find zero- and bounded-skew trees of length at most 3 and 9 times the optimum. This case is of special interest in VLSI clock routing. An important feature of our algorithms is their practical running time, which is asymptotically the same as the time needed for computing the minimum spanning tree.
AbstractList The skew of an edge-weighted rooted tree is the maximum difference between any two root-to-leaf path weights. Zero- or bounded-skew trees are needed for achieving synchronization in many applications, including network multicasting [G. N. Rouskas and I. Baldine, IEEE J. on Selected Areas in Communication, 15 (1997), pp. 346--356] and VLSI clock routing [H. Bakoglu, Circuits, Interconnections, and Packaging for VSLI, Addison-Wesley, Reading, MA, 1990, A. B. Kahng and G. Robins, On Optimal Interconnections for VSLI, Kluwer Academic Publishers, Norwell, MA, 1995]. In these applications edge weights represent propagation delays, and a signal generated at the root should be received by multiple recipients located at the leaves (almost) simultaneously. The objective is to find zero- or bounded-skew trees of minimum total weight, since the weight of the tree is directly proportional to the amount of resources (bandwidth and buffers for network multicasting, power and chip area for clock routing in VLSI) that must be allocated to the tree. Charikar et al. in [Proceedings of the Tenth ACM-SIAM Symposium on Discrete Algorithms, Baltimore, MD, 1999, ACM, New York, 1999, pp. 177--184] have recently proposed the first strongly polynomial algorithms with proven constant approximation factors, $2e\approx 5.44 and 16.86, for finding minimum weight zero- and bounded-skew trees, respectively. In this paper we introduce a new approach to these problems, based on zero-skew "stretching" of spanning trees, and obtain algorithms with improved approximation factors of 4 and 14. For the case when tree nodes are points in the plane and edge weights are given by the rectilinear metric our algorithms find zero- and bounded-skew trees of length at most 3 and 9 times the optimum. This case is of special interest in VLSI clock routing. An important feature of our algorithms is their practical running time, which is asymptotically the same as the time needed for computing the minimum spanning tree.
Author Zelikovsky, Alexander Z.
Mandoiu, Ion I.
Author_xml – sequence: 1
  givenname: Alexander Z.
  surname: Zelikovsky
  fullname: Zelikovsky, Alexander Z.
– sequence: 2
  givenname: Ion I.
  surname: Mandoiu
  fullname: Mandoiu, Ion I.
BookMark eNp9kDtPAzEQhC0UJJLAD6Cz6A3eO_tslyHiJUUCKaGhOTl-wIXLOdiOgH_PhVCBRLXFzLe7MyM06ELnEDoFeg5Qios5lYozSYHSUsiyEgdoCFRxIoBVAzTcyWSnH6FRSitKgTHgQzR9iNrkxugWTzabGD6atc5N6PCkfQ6xyS_rhH2I-MnFQLDuLL4M2846S-av7h0vonPpGB163SZ38jPH6PH6ajG9JbP7m7vpZEYMSJ4JgFVWmgqYrrwQTPplwZaVtiBL7ZSGwltplWRKa-a9F8aIkhZFIbgXUrhyjM72e_s_37Yu5XoVtrHrT9aq4JUAELw3ib3JxJBSdL42Tf6OlKNu2hpovSus_lNYT8IvchP7NuLnP8wXiI9t4g
CitedBy_id crossref_primary_10_1109_TVT_2007_912605
crossref_primary_10_1137_S0895480199352622
crossref_primary_10_1109_TCAD_2003_814238
Cites_doi 10.1145/293625.293628
10.1109/82.204128
10.1007/PL00009340
10.1137/0130013
10.1109/49.564133
10.1145/290179.290180
10.1145/322123.322124
10.1007/BF00288961
ContentType Journal Article
Copyright [Copyright] © 2002 Society for Industrial and Applied Mathematics
Copyright_xml – notice: [Copyright] © 2002 Society for Industrial and Applied Mathematics
DBID AAYXX
CITATION
3V.
7WY
7WZ
7X2
7XB
87Z
88A
88F
88I
88K
8AL
8FE
8FG
8FH
8FK
8FL
8G5
ABJCF
ABUWG
AFKRA
ARAPS
ATCPS
AZQEC
BBNVY
BENPR
BEZIV
BGLVJ
BHPHI
CCPQU
D1I
DWQXO
FRNLG
F~G
GNUQQ
GUQSH
HCIFZ
JQ2
K60
K6~
K7-
KB.
L.-
L6V
LK8
M0C
M0K
M0N
M1Q
M2O
M2P
M2T
M7P
M7S
MBDVC
P5Z
P62
PATMY
PDBOC
PHGZM
PHGZT
PKEHL
PQBIZ
PQBZA
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PTHSS
PYCSY
Q9U
DOI 10.1137/S0895480100378367
DatabaseName CrossRef
ProQuest Central (Corporate)
ABI/INFORM Collection
ABI/INFORM Global (PDF only)
Agricultural Science Collection
ProQuest Central (purchase pre-March 2016)
ABI/INFORM Collection
Biology Database (Alumni Edition)
Military Database (Alumni Edition)
Science Database (Alumni Edition)
Telecommunications (Alumni Edition)
Computing Database (Alumni Edition)
ProQuest SciTech Collection
ProQuest Technology Collection
ProQuest Natural Science Collection
ProQuest Central (Alumni) (purchase pre-March 2016)
ABI/INFORM Collection (Alumni)
Research Library (Alumni)
Materials Science & Engineering Collection
ProQuest Central (Alumni)
ProQuest Central UK/Ireland
Advanced Technologies & Computer Science Collection
Agricultural & Environmental Science Collection
ProQuest Central Essentials
Biological Science Collection
ProQuest Central
Business Premium Collection
ProQuest Technology Collection
Natural Science Collection
ProQuest One Community College
ProQuest Materials Science Collection
ProQuest Central Korea
Business Premium Collection (Alumni)
ABI/INFORM Global (Corporate)
ProQuest Central Student
ProQuest Research Library
SciTech Premium Collection
ProQuest Computer Science Collection
ProQuest Business Collection (Alumni Edition)
ProQuest Business Collection
Computer Science Database
Materials Science Database
ABI/INFORM Professional Advanced
ProQuest Engineering Collection
ProQuest Biological Science Collection
ABI/INFORM Global
Agricultural Science Database
Computing Database
Military Database
Research Library
Science Database (ProQuest)
Telecommunications Database
Biological Science Database (ProQuest)
Engineering Database
Research Library (Corporate)
ProQuest advanced technologies & aerospace journals
ProQuest Advanced Technologies & Aerospace Collection
Environmental Science Database
Materials Science Collection
ProQuest Central Premium
ProQuest One Academic (New)
ProQuest One Academic Middle East (New)
ProQuest One Business
ProQuest One Business (Alumni)
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Applied & Life Sciences
ProQuest One Academic (retired)
ProQuest One Academic UKI Edition
ProQuest Central China
Engineering collection
Environmental Science Collection
ProQuest Central Basic
DatabaseTitle CrossRef
Agricultural Science Database
ProQuest Business Collection (Alumni Edition)
Research Library Prep
Computer Science Database
ProQuest Central Student
ProQuest Advanced Technologies & Aerospace Collection
ProQuest Central Essentials
ProQuest Computer Science Collection
SciTech Premium Collection
ProQuest Military Collection
ProQuest Central China
ABI/INFORM Complete
ProQuest Telecommunications
ProQuest One Applied & Life Sciences
Natural Science Collection
Biological Science Collection
ProQuest Central (New)
Engineering Collection
Advanced Technologies & Aerospace Collection
Business Premium Collection
ABI/INFORM Global
Engineering Database
ProQuest Science Journals (Alumni Edition)
ProQuest Biological Science Collection
ProQuest One Academic Eastern Edition
Agricultural Science Collection
ProQuest Technology Collection
ProQuest Telecommunications (Alumni Edition)
Biological Science Database
ProQuest Business Collection
Environmental Science Collection
ProQuest One Academic UKI Edition
Environmental Science Database
ProQuest One Academic
ProQuest One Academic (New)
ABI/INFORM Global (Corporate)
ProQuest One Business
Technology Collection
ProQuest One Academic Middle East (New)
Materials Science Collection
ProQuest Central (Alumni Edition)
ProQuest One Community College
Research Library (Alumni Edition)
ProQuest Natural Science Collection
ProQuest Biology Journals (Alumni Edition)
ProQuest Central
ABI/INFORM Professional Advanced
ProQuest Engineering Collection
ProQuest Central Korea
Agricultural & Environmental Science Collection
Materials Science Database
ProQuest Research Library
ABI/INFORM Complete (Alumni Edition)
ProQuest Materials Science Collection
ProQuest Computing
ABI/INFORM Global (Alumni Edition)
ProQuest Central Basic
ProQuest Science Journals
ProQuest Computing (Alumni Edition)
ProQuest Military Collection (Alumni Edition)
ProQuest SciTech Collection
Advanced Technologies & Aerospace Database
Materials Science & Engineering Collection
ProQuest One Business (Alumni)
ProQuest Central (Alumni)
Business Premium Collection (Alumni)
DatabaseTitleList Agricultural Science Database
Database_xml – sequence: 1
  dbid: BENPR
  name: ProQuest Central
  url: https://www.proquest.com/central
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Computer Science
EISSN 1095-7146
EndPage 111
ExternalDocumentID 2599696541
10_1137_S0895480100378367
GroupedDBID .4S
.DC
123
4.4
6TJ
7WY
7X2
7XC
88I
8CJ
8FE
8FG
8FH
8FL
8G5
AALVN
AASXH
AAYXX
ABDBF
ABDPE
ABJCF
ABKAD
ABMZU
ABUWG
ACGFO
ACGOD
ACIWK
ACPRK
ACUHS
ADBBV
ADNWM
ADXHL
AENEX
AFFHD
AFFNX
AFKRA
AFRAH
ALMA_UNASSIGNED_HOLDINGS
ANXRF
ARAPS
ARCSS
ATCPS
AZQEC
BBNVY
BENPR
BEZIV
BGLVJ
BHPHI
BPHCQ
CCPQU
CITATION
CS3
CZ9
D1I
D1J
D1K
DQ2
DU5
DWQXO
EAP
EBS
EDO
EJD
EMK
EST
ESX
FRNLG
GNUQQ
GUQSH
H13
HCIFZ
H~9
I-F
K6-
K60
K6V
K6~
K7-
KB.
KC.
L6V
LK5
LK8
M0C
M0K
M1Q
M2O
M2P
M7P
M7R
M7S
P1Q
P2P
P62
PATMY
PDBOC
PHGZM
PHGZT
PQBIZ
PQBZA
PQGLB
PQQKQ
PROAC
PTHSS
PYCSY
RJG
RNS
RSI
TN5
TUS
UQL
YNT
YYP
3V.
7XB
88A
88K
8AL
8FK
JQ2
L.-
M0N
M2T
MBDVC
PKEHL
PQEST
PQUKI
PRINS
Q9U
ID FETCH-LOGICAL-c185t-11d9d8c614a6f7748fb24b6ad183ae9a12fd8d9849aa4fff7cc73022275f787e3
IEDL.DBID M1Q
ISSN 0895-4801
IngestDate Thu Aug 21 10:40:32 EDT 2025
Sat Nov 29 05:36:58 EST 2025
Tue Nov 18 21:51:51 EST 2025
IsPeerReviewed true
IsScholarly true
Issue 1
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c185t-11d9d8c614a6f7748fb24b6ad183ae9a12fd8d9849aa4fff7cc73022275f787e3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
PQID 925671175
PQPubID 666311
PageCount 15
ParticipantIDs proquest_journals_925671175
crossref_citationtrail_10_1137_S0895480100378367
crossref_primary_10_1137_S0895480100378367
PublicationCentury 2000
PublicationDate 20010101
PublicationDateYYYYMMDD 2001-01-01
PublicationDate_xml – month: 01
  year: 2001
  text: 20010101
  day: 01
PublicationDecade 2000
PublicationPlace Philadelphia
PublicationPlace_xml – name: Philadelphia
PublicationTitle SIAM journal on discrete mathematics
PublicationYear 2001
Publisher Society for Industrial and Applied Mathematics
Publisher_xml – name: Society for Industrial and Applied Mathematics
References R20
R4
R14
R7
Edahiro M. (R10) 1991; 32
R13
R9
R18
Eppstein David (R12) 2000; 5
R1
References_xml – ident: R9
  doi: 10.1145/293625.293628
– ident: R7
  doi: 10.1109/82.204128
– ident: R4
  doi: 10.1007/PL00009340
– volume: 5
  start-page: 0
  year: 2000
  ident: R12
  publication-title: ACM J. Exp. Algorithmics
– ident: R13
  doi: 10.1137/0130013
– ident: R20
  doi: 10.1109/49.564133
– volume: 32
  start-page: 569
  issn: 0547-051X
  year: 1991
  ident: R10
  publication-title: NEC Res. Development
– ident: R1
  doi: 10.1145/290179.290180
– ident: R14
  doi: 10.1145/322123.322124
– ident: R18
  doi: 10.1007/BF00288961
SSID ssj0014415
Score 1.5733114
Snippet The skew of an edge-weighted rooted tree is the maximum difference between any two root-to-leaf path weights. Zero- or bounded-skew trees are needed for...
SourceID proquest
crossref
SourceType Aggregation Database
Enrichment Source
Index Database
StartPage 97
SubjectTerms Algorithms
Approximation
Computer science
Leaves
R&D
Research & development
Title Practical Approximation Algorithms for Zero- and Bounded-Skew Trees
URI https://www.proquest.com/docview/925671175
Volume 15
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVPQU
  databaseName: ABI/INFORM Collection
  customDbUrl:
  eissn: 1095-7146
  dateEnd: 20140731
  omitProxy: false
  ssIdentifier: ssj0014415
  issn: 0895-4801
  databaseCode: 7WY
  dateStart: 19880201
  isFulltext: true
  titleUrlDefault: https://www.proquest.com/abicomplete
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ABI/INFORM Global
  customDbUrl:
  eissn: 1095-7146
  dateEnd: 20140731
  omitProxy: false
  ssIdentifier: ssj0014415
  issn: 0895-4801
  databaseCode: M0C
  dateStart: 19880201
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/abiglobal
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Agricultural Science Database
  customDbUrl:
  eissn: 1095-7146
  dateEnd: 20140731
  omitProxy: false
  ssIdentifier: ssj0014415
  issn: 0895-4801
  databaseCode: M0K
  dateStart: 19880201
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/agriculturejournals
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Biological Science Database
  customDbUrl:
  eissn: 1095-7146
  dateEnd: 20140731
  omitProxy: false
  ssIdentifier: ssj0014415
  issn: 0895-4801
  databaseCode: M7P
  dateStart: 19880201
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/biologicalscijournals
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Computer Science Database
  customDbUrl:
  eissn: 1095-7146
  dateEnd: 20140731
  omitProxy: false
  ssIdentifier: ssj0014415
  issn: 0895-4801
  databaseCode: K7-
  dateStart: 19880201
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/compscijour
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Engineering Database
  customDbUrl:
  eissn: 1095-7146
  dateEnd: 20140731
  omitProxy: false
  ssIdentifier: ssj0014415
  issn: 0895-4801
  databaseCode: M7S
  dateStart: 19880201
  isFulltext: true
  titleUrlDefault: http://search.proquest.com
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Environmental Science Database
  customDbUrl:
  eissn: 1095-7146
  dateEnd: 20140731
  omitProxy: false
  ssIdentifier: ssj0014415
  issn: 0895-4801
  databaseCode: PATMY
  dateStart: 19880201
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/environmentalscience
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Materials Science Database
  customDbUrl:
  eissn: 1095-7146
  dateEnd: 20140731
  omitProxy: false
  ssIdentifier: ssj0014415
  issn: 0895-4801
  databaseCode: KB.
  dateStart: 19880201
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/materialsscijournals
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Military Database
  customDbUrl:
  eissn: 1095-7146
  dateEnd: 20140731
  omitProxy: false
  ssIdentifier: ssj0014415
  issn: 0895-4801
  databaseCode: M1Q
  dateStart: 19880201
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/military
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ProQuest advanced technologies & aerospace journals
  customDbUrl:
  eissn: 1095-7146
  dateEnd: 20140731
  omitProxy: false
  ssIdentifier: ssj0014415
  issn: 0895-4801
  databaseCode: P5Z
  dateStart: 19880201
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/hightechjournals
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ProQuest Central
  customDbUrl:
  eissn: 1095-7146
  dateEnd: 20140731
  omitProxy: false
  ssIdentifier: ssj0014415
  issn: 0895-4801
  databaseCode: BENPR
  dateStart: 19880201
  isFulltext: true
  titleUrlDefault: https://www.proquest.com/central
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Research Library
  customDbUrl:
  eissn: 1095-7146
  dateEnd: 20140731
  omitProxy: false
  ssIdentifier: ssj0014415
  issn: 0895-4801
  databaseCode: M2O
  dateStart: 19880201
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/pqrl
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Science Database
  customDbUrl:
  eissn: 1095-7146
  dateEnd: 20140731
  omitProxy: false
  ssIdentifier: ssj0014415
  issn: 0895-4801
  databaseCode: M2P
  dateStart: 19880201
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/sciencejournals
  providerName: ProQuest
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1NT9wwEB0V6KEXoF8qUFY-9IRkGudjHZ8QuwIhIbZLWVTKJXI8dosKu7BZ2v58PI53BarEpVL0lCiOFWU8nnFsvwfwCR3qMhMhc9M87yJyjabmtbJJXSdZhkUrNiEHg_LiQg3j2pwmLquc94mho8aJoX_kn5WPzZJ4Jfdu7ziJRtHkalTQWIIVnycros4_EaeLSQQaKoQkUhWcWFLipKbIiDG6DExngvhXyiyozD8KS0975RBqDtf-8yXXYTXmmGy_bRSv4YUdv4G1uX4Di-78FvotWZGhskQt_veq3cfI9q9_-GpnP28a5nNadmmnE870GFmPRJgs8rNf9g8bTa1t3sH54cGof8SjqAI3PjTPuBCosDQ-Kuuu87lf6eo0r7savW9rq7RIHZaoylxpnTvnpDG-E6Ads4Xzzm2z97A8noztB2CZS9CkSapVgjkKoZPCSuMrsloLb_ANSObftDKRcZyEL66rMPLIZPWPGTZgZ_HIbUu38VzhrbkVquh5TbUwweazd7fgVbuajI6PsDyb3ttteGl-z66aaQeW5LfvHVjpHQyGX_3VseSEvV2PJ0k_4HEntDbC9EvAYcARoQzn8szjsLh8AM-w2ho
linkProvider ProQuest
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1LaxsxEB7ctNBc4j7Js9GhvQREV6tdr3QoIXVqbOyaQlwIvWy1GqkJSdaJ10maH5X_WGkfpqWQmw-Bva0k0M6nmdGO9H0A79GiEpyVmZuiUQeRKtQZzaQJsizgHONKbCIZj8XxsfzWgvvmLow_Vtn4xNJR41T7f-QfpYvNieeV3L-8ol40yhdXGwWNChVDc3frdmzFp8GhM--HMOx9mXT7tBYVoNqFpjllDCUK7aKS6liX-wibhVHWUeiwrYxULLQoUIpIKhVZaxOt3SLwN0Zj68BtuBv3CTyNuEj8shomdFG08FuTMmmVMfWsLHURlXHPUC1KZjXm-V4EL1Xt_wqD_0aBMrT12o_so7yAtTqHJgcV6F9Cy-SvoN3oU5DaXb2GbkXGpH1bT53--7S6p0kOzn-5acxPLgricnbyw8ymlKgcyWcvMmWQHp2ZWzKZGVO8ge9LmcpbWMmnuVkHwm2AOgxCJQOMkDEVxCbRbiCjFHOA3oCgsWGqa0Z1L-xxnpY7K56k_5l9A_YWXS4rOpGHGm81Vk9rz1KkC5NvPvh2F573J19H6WgwHm7BanVyzj_bsDKfXZsdeKZv5qfF7F2JYQI_l42PP1_dK5M
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=Practical+Approximation+Algorithms+for+Zero-+and+Bounded-Skew+Trees&rft.jtitle=SIAM+journal+on+discrete+mathematics&rft.au=Zelikovsky%2C+Alexander+Z.&rft.au=Mandoiu%2C+Ion+I.&rft.date=2001-01-01&rft.issn=0895-4801&rft.eissn=1095-7146&rft.volume=15&rft.issue=1&rft.spage=97&rft.epage=111&rft_id=info:doi/10.1137%2FS0895480100378367&rft.externalDBID=n%2Fa&rft.externalDocID=10_1137_S0895480100378367
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0895-4801&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0895-4801&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0895-4801&client=summon