Integer Linear Programming Models for Global Routing

Modern integrated circuit design involves the layout of circuits consisting of millions of switching elements or transistors. Due to the sheer complexity of the problem, optimizing the connectivity between transistors is very difficult. The circuit interconnection is the single most important factor...

Full description

Saved in:
Bibliographic Details
Published in:INFORMS journal on computing Vol. 18; no. 2; pp. 137 - 150
Main Authors: Behjat, Laleh, Vannelli, Anthony, Rosehart, William
Format: Journal Article
Language:English
Published: Linthicum INFORMS 22.03.2006
Institute for Operations Research and the Management Sciences
Subjects:
Design and construction
Design engineering
global routing
Heuristic
Integer programming
Integrated circuit fabrication
Integrated circuits
Linear programming
linear relaxation
Methods
Semiconductor chips
Studies
Technology application
Transistors
Very-large-scale integration
VLSI layout
United States
ISSN:1091-9856, 1526-5528, 1091-9856
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract Modern integrated circuit design involves the layout of circuits consisting of millions of switching elements or transistors. Due to the sheer complexity of the problem, optimizing the connectivity between transistors is very difficult. The circuit interconnection is the single most important factor in performance criteria such as signal delay, power dissipation, circuit size, and cost. These factors dictate that interconnections, i.e., wires, be made as short as possible. The wire-minimization problem is generally formulated as a sequence of discrete optimization subproblems that are known to be NP-hard. Hence, they can only be solved approximately using meta-heuristics. These methods are computationally expensive and the quality of the solution depends to a great extent on an appropriate choice of starting configuration and modeling techniques. In this paper, new modeling techniques are used to solve the routing problem formulated as an integer programming problem. The main contribution of this paper is a proposed global routing heuristic that combines the wire length, channel congestion, and number of pins in routes to find the best wiring layout of a circuit. By adding information such as channel congestion and the number of pins in each route as well as the wire length, the quality of the solution is improved. In addition, the solutions of the large relaxed linear programming problems are skewed towards a zero-one solution, resulting in faster convergence. The developed LP models in this paper are useful when solving the global routing problem for two reasons; first, the new interior-point algorithms to solve the LP problem are polynomial in time. Second, "near optimal wiring" is obtained in polynomial time without performing randomized rounding.
AbstractList Modern integrated circuit design involves the layout of circuits consisting of millions of switching elements or transistors. Due to the sheer complexity of the problem, optimizing the connectivity between transistors is very difficult. The circuit interconnection is the single most important factor in performance criteria such as signal delay, power dissipation, circuit size, and cost. These factors dictate that interconnections, i.e., wires, be made as short as possible. The wire-minimization problem is generally formulated as a sequence of discrete optimization subproblems that are known to be NP-hard. Hence, they can only be solved approximately using meta-heuristics. These methods are computationally expensive and the quality of the solution depends to a great extent on an appropriate choice of starting configuration and modeling techniques. In this paper, new modeling techniques are used to solve the routing problem formulated as an integer programming problem. The main contribution of this paper is a proposed global routing heuristic that combines the wire length, channel congestion, and number of pins in routes to find the best wiring layout of a circuit. By adding information such as channel congestion and the number of pins in each route as well as the wire length, the quality of the solution is improved. In addition, the solutions of the large relaxed linear programming problems are skewed towards a zero-one solution, resulting in faster convergence. The developed LP models in this paper are useful when solving the global routing problem for two reasons; first, the new interior-point algorithms to solve the LP problem are polynomial in time. Second, "near optimal wiring" is obtained in polynomial time without performing randomized rounding.
Modern integrated circuit design involves the layout of circuits consisting of millions of switching elements or transistors. The circuit interconnection is the single most important factor in performance criteria such as signal delay, power dissipation, circuit size, and cost. Due to the sheer complexity of the problem, optimizing the connectivity between transistors is very difficult. In this paper, new modeling techniques are used to solve the routing problem formulated as an integer programming problem. The main contribution of this paper is a proposed global muting heuristic that combines the wire length, channel congestion, and number of pins in routes to find the best wiring layout of a circuit. The developed linear programming (LP) models in this paper are useful when solving the global routing problem for two reasons; first, the new interior-point algorithms to solve the LP problem are polynomial in time. Second, "near optimal wiring" is obtained in polynomial time without performing randomized rounding.
Audience Academic
Author Vannelli, Anthony
Behjat, Laleh
Rosehart, William
Author_xml – sequence: 1
  fullname: Behjat, Laleh
– sequence: 2
  fullname: Vannelli, Anthony
– sequence: 3
  fullname: Rosehart, William
BookMark eNqFkc1L5DAYh4O44Oh69Vx0rx3z1TQ5irgqjCii55CmSSdDm2jSQfa_33QrijCy5JCv58mb5HcI9n3wBoATBJcI8_rcbYJeIkjhEiJc74EFqjArqwrz_TyGApWCV-wAHKa0gRBSQsUC0Fs_ms7EYuW8UbF4iKGLahic74q70Jo-FTbE4roPjeqLx7Ad885P8MOqPpnj9_4IPP--erq8KVf317eXF6tSU8LHElvORNNyw4SBVmAriMKaNpwwzZFFVFMFm6ZhuK2gYFWVJ4hhJkTNoCEtOQKn87kvMbxuTRrlJmyjzyUlhrDCkPE6Q2cz1KneSOdtGKPSg0taXiBaY4YIppkqd1Cd8SaqPv-jdXn5C7_cwefWmsHpnQKdBR1DStFYqd2oRhd8Fl0vEZRTSnJKSU4pySmlzzof2kt0g4p_vhfeHzLdKQ7p__yvmV-7bv3m4vyYSfzHcYklIjX5C3LdrlU
CitedBy_id crossref_primary_10_1007_s11704_015_4107_1
crossref_primary_10_1109_TCAD_2010_2066030
crossref_primary_10_1155_2009_537341
crossref_primary_10_1109_TVLSI_2012_2205717
crossref_primary_10_1007_s11704_015_4017_1
crossref_primary_10_1038_s41598_024_82226_9
Cites_doi 10.1109/43.331403
10.1109/43.602477
10.1145/369691.369699
10.1007/BFb0121044
10.1007/978-3-322-92106-2
10.1137/0802028
10.1109/TCAD.2002.801083
10.1109/TEC.1961.5219222
10.1109/43.68406
10.1007/978-1-4684-2001-2_9
10.1137/0204019
10.1137/0114025
10.1109/TCAD.1983.1270039
10.1109/DAC.1982.1585535
10.1007/BF02579150
10.1137/S1052623497331786
10.1109/CCECE.2001.933590
10.1023/A:1014847925683
10.1109/ICCAD.1999.810613
10.1093/oso/9780195100563.001.0001
10.1109/43.673630
10.1145/369691.369711
10.1007/BF01582166
10.1007/BF01759035
10.1145/127601.127678
10.1109/DAC.1978.1585154
ContentType Journal Article
Copyright COPYRIGHT 2006 Institute for Operations Research and the Management Sciences
Copyright Institute for Operations Research and the Management Sciences Spring 2006
Copyright_xml – notice: COPYRIGHT 2006 Institute for Operations Research and the Management Sciences
– notice: Copyright Institute for Operations Research and the Management Sciences Spring 2006
DBID AAYXX
CITATION
3V.
7WY
7WZ
7XB
87Z
8AL
8AO
8FE
8FG
8FK
8FL
ABUWG
AFKRA
ARAPS
AZQEC
BENPR
BEZIV
BGLVJ
CCPQU
DWQXO
FRNLG
F~G
GNUQQ
HCIFZ
JQ2
K60
K6~
K7-
L.-
M0C
M0N
P5Z
P62
PHGZM
PHGZT
PKEHL
PQBIZ
PQBZA
PQEST
PQGLB
PQQKQ
PQUKI
PYYUZ
Q9U
DOI 10.1287/ijoc.1040.0127
DatabaseName CrossRef
ProQuest Central (Corporate)
ABI/INFORM Collection
ABI/INFORM Global (PDF only)
ProQuest Central (purchase pre-March 2016)
ABI/INFORM Global (Alumni Edition)
Computing Database (Alumni Edition)
ProQuest Pharma Collection
ProQuest SciTech Collection
ProQuest Technology Collection
ProQuest Central (Alumni) (purchase pre-March 2016)
ABI/INFORM Collection (Alumni Edition)
ProQuest Central (Alumni)
ProQuest Central UK/Ireland
Advanced Technologies & Computer Science Collection
ProQuest Central Essentials
ProQuest Central
Business Premium Collection
Technology collection
ProQuest One Community College
ProQuest Central
Business Premium Collection (Alumni)
ABI/INFORM Global (Corporate)
ProQuest Central Student
SciTech Premium Collection
ProQuest Computer Science Collection
ProQuest Business Collection (Alumni Edition)
ProQuest Business Collection
Computer Science Database
ABI/INFORM Professional Advanced
ABI/INFORM Global
Computing Database
ProQuest advanced technologies & aerospace journals
ProQuest Advanced Technologies & Aerospace Collection
ProQuest Central Premium
ProQuest One Academic
ProQuest One Academic Middle East (New)
ProQuest One Business (OCUL)
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
ABI/INFORM Collection China
ProQuest Central Basic
DatabaseTitle CrossRef
ABI/INFORM Global (Corporate)
ProQuest Business Collection (Alumni Edition)
ProQuest One Business
Computer Science Database
ProQuest Central Student
Technology Collection
ProQuest One Academic Middle East (New)
ProQuest Advanced Technologies & Aerospace Collection
ProQuest Central Essentials
ProQuest Computer Science Collection
ProQuest Central (Alumni Edition)
SciTech Premium Collection
ProQuest One Community College
ProQuest Pharma Collection
ABI/INFORM Complete
ProQuest Central
ABI/INFORM Professional Advanced
ProQuest One Applied & Life Sciences
ProQuest Central Korea
ProQuest Central (New)
ABI/INFORM Complete (Alumni Edition)
Advanced Technologies & Aerospace Collection
Business Premium Collection
ABI/INFORM Global
ProQuest Computing
ABI/INFORM Global (Alumni Edition)
ProQuest Central Basic
ProQuest Computing (Alumni Edition)
ProQuest One Academic Eastern Edition
ABI/INFORM China
ProQuest Technology Collection
ProQuest SciTech Collection
ProQuest Business Collection
Advanced Technologies & Aerospace Database
ProQuest One Academic UKI Edition
ProQuest One Business (Alumni)
ProQuest One Academic
ProQuest Central (Alumni)
ProQuest One Academic (New)
Business Premium Collection (Alumni)
DatabaseTitleList
ABI/INFORM Global (Corporate)
CrossRef
Database_xml – sequence: 1
  dbid: BENPR
  name: ProQuest Central
  url: https://www.proquest.com/central
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
Computer Science
EISSN 1526-5528
1091-9856
EndPage 150
ExternalDocumentID 1069188021
A147261324
10_1287_ijoc_1040_0127
ijoc.1040.0127
joc_18_2_137
Genre Research Article - Special Cluster on Operations Research in Electrical and Computer Engineering
Feature
GeographicLocations United States
GeographicLocations_xml – name: United States
GroupedDBID 1AW
29I
3V.
4.4
4S
5GY
7WY
8AL
8AO
8FE
8FG
8FL
8VB
AAPBV
ABDBF
ABFLS
ABPTK
ABUWG
ACNCT
ADCOW
AEILP
AENEX
AFKRA
AKVCP
ALMA_UNASSIGNED_HOLDINGS
ARAPS
ARCSS
AZQEC
BENPR
BEZIV
BGLVJ
BPHCQ
CS3
DU5
DWQXO
EAD
EAP
EBA
EBE
EBR
EBS
EBU
ECS
EDO
EHE
EJD
EMI
EMK
EPL
EST
ESX
F5P
FRNLG
GNUQQ
GROUPED_ABI_INFORM_COMPLETE
GROUPED_ABI_INFORM_RESEARCH
HCIFZ
I-F
IAO
ICD
IEA
IGS
IL9
IOF
ITC
K6
K60
K6V
K7-
M0C
M0N
MV1
N95
NIEAY
P2P
P62
PQEST
PQQKQ
PQUKI
PRINS
PROAC
QWB
RPU
TH9
TN5
TUS
XI7
Y99
ZL0
ZY4
ACYGS
XFK
.4S
.DC
18M
AADHG
AAYXX
ABDNZ
ACGFO
AEGXH
AEMOZ
AFFHD
AHQJS
AIAGR
BAAKF
CCPQU
CITATION
EBO
K1G
K6~
PHGZM
PHGZT
PQBIZ
PQBZA
PQGLB
XOL
7XB
8FK
JQ2
L.-
PKEHL
Q9U
ID FETCH-LOGICAL-c438t-2f869bd8e69e0f92f93a2c4b836c81f14c4a0bbb62d5096550bb162699760e3d3
IEDL.DBID M0C
ISICitedReferencesCount 8
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000238428600002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 1091-9856
IngestDate Fri Jul 25 23:52:54 EDT 2025
Tue Nov 11 11:16:06 EST 2025
Sat Nov 29 12:05:32 EST 2025
Tue Nov 04 18:41:29 EST 2025
Sat Nov 29 03:32:06 EST 2025
Tue Nov 18 22:23:58 EST 2025
Wed Jan 06 02:47:42 EST 2021
Fri Jan 15 03:35:51 EST 2021
IsPeerReviewed true
IsScholarly true
Issue 2
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c438t-2f869bd8e69e0f92f93a2c4b836c81f14c4a0bbb62d5096550bb162699760e3d3
Notes SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
PQID 200520687
PQPubID 46392
PageCount 14
ParticipantIDs gale_infotracmisc_A147261324
highwire_informs_joc_18_2_137
crossref_primary_10_1287_ijoc_1040_0127
crossref_citationtrail_10_1287_ijoc_1040_0127
informs_primary_10_1287_ijoc_1040_0127
proquest_journals_200520687
gale_infotracgeneralonefile_A147261324
gale_infotracacademiconefile_A147261324
ProviderPackageCode Y99
RPU
NIEAY
PublicationCentury 2000
PublicationDate 20060322
PublicationDateYYYYMMDD 2006-03-22
PublicationDate_xml – month: 03
  year: 2006
  text: 20060322
  day: 22
PublicationDecade 2000
PublicationPlace Linthicum
PublicationPlace_xml – name: Linthicum
PublicationTitle INFORMS journal on computing
PublicationYear 2006
Publisher INFORMS
Institute for Operations Research and the Management Sciences
Publisher_xml – name: INFORMS
– name: Institute for Operations Research and the Management Sciences
References B20
B21
B22
B23
B24
B25
B26
B27
B28
B29
B30
B31
B10
B32
B11
B33
B12
B34
B13
B35
B14
B36
B15
B37
B16
B17
B18
B19
B1
B2
B3
B4
B5
B6
B7
B8
B9
Lengauer T. (B23) 1990
Ng A. P. (B28) 1987; 6
Sherwani N. (B31) 1999
Shragowitz E. (B32) 1987; 5
Bertsekas D. P. (B6) 1995
Andersen E. D. (B3) 1996
Aarts E. H. L. (B1) 1985; 4
Raghavan P. (B29) 1988; 37
Madden P. (B26) 2004
Floundas C. A. (B12) 1995
References_xml – ident: B12
– ident: B9
– ident: B35
– ident: B14
– ident: B10
– ident: B3
– ident: B20
– ident: B1
– ident: B27
– ident: B7
– ident: B5
– ident: B29
– ident: B25
– ident: B23
– ident: B21
– ident: B18
– ident: B16
– ident: B31
– ident: B33
– ident: B37
– ident: B8
– ident: B36
– ident: B11
– ident: B13
– ident: B2
– ident: B26
– ident: B4
– ident: B28
– ident: B6
– ident: B24
– ident: B22
– ident: B17
– ident: B32
– ident: B15
– ident: B30
– ident: B34
– ident: B19
– ident: B7
  doi: 10.1109/43.331403
– ident: B8
  doi: 10.1109/43.602477
– ident: B2
  doi: 10.1145/369691.369699
– ident: B16
  doi: 10.1007/BFb0121044
– volume-title: Combinatorial Algorithms for Integrated Circuit Layout
  year: 1990
  ident: B23
  doi: 10.1007/978-3-322-92106-2
– volume-title: Nonlinear Programming
  year: 1995
  ident: B6
– ident: B27
  doi: 10.1137/0802028
– ident: B15
  doi: 10.1109/TCAD.2002.801083
– ident: B22
  doi: 10.1109/TEC.1961.5219222
– ident: B36
  doi: 10.1109/43.68406
– ident: B18
  doi: 10.1007/978-1-4684-2001-2_9
– volume: 6
  start-page: 130
  year: 1987
  ident: B28
  publication-title: Comput. Artificial Intelligence
– ident: B13
  doi: 10.1137/0204019
– ident: B14
  doi: 10.1137/0114025
– ident: B37
  doi: 10.1109/TCAD.1983.1270039
– volume: 4
  start-page: 193
  year: 1985
  ident: B1
  publication-title: Phillips J. Res.
– ident: B10
  doi: 10.1109/DAC.1982.1585535
– ident: B17
  doi: 10.1007/BF02579150
– ident: B24
  doi: 10.1137/S1052623497331786
– ident: B4
  doi: 10.1109/CCECE.2001.933590
– ident: B5
  doi: 10.1023/A:1014847925683
– ident: B11
  doi: 10.1109/ICCAD.1999.810613
– volume-title: Implementation of Interior-Point Methods for Large Scale Linear Programming
  year: 1996
  ident: B3
– volume-title: Nonlinear and Mixed-Integer Optimization
  year: 1995
  ident: B12
  doi: 10.1093/oso/9780195100563.001.0001
– ident: B9
  doi: 10.1109/43.673630
– volume-title: Algorithms for VLSI Physical Design Automation
  year: 1999
  ident: B31
– volume: 37
  start-page: 130
  year: 1988
  ident: B29
  publication-title: J. Comput. Sci.
– volume-title: BLAC CAD Binghamton Laboratory for Algorithms, Circuits, and Computer-Aided Design
  year: 2004
  ident: B26
– ident: B19
  doi: 10.1145/369691.369711
– ident: B25
  doi: 10.1007/BF01582166
– ident: B30
  doi: 10.1007/BF01759035
– ident: B20
  doi: 10.1145/127601.127678
– ident: B33
  doi: 10.1109/DAC.1978.1585154
– volume: 5
  start-page: 3
  year: 1987
  ident: B32
  publication-title: Interaction
SSID ssj0004349
Score 1.7850428
Snippet Modern integrated circuit design involves the layout of circuits consisting of millions of switching elements or transistors. Due to the sheer complexity of...
Modern integrated circuit design involves the layout of circuits consisting of millions of switching elements or transistors. The circuit interconnection is...
SourceID proquest
gale
crossref
informs
highwire
SourceType Aggregation Database
Enrichment Source
Index Database
Publisher
StartPage 137
SubjectTerms Design and construction
Design engineering
global routing
Heuristic
Integer programming
Integrated circuit fabrication
Integrated circuits
Linear programming
linear relaxation
Methods
Semiconductor chips
Studies
Technology application
Transistors
Very-large-scale integration
VLSI layout
Title Integer Linear Programming Models for Global Routing
URI http://joc.journal.informs.org/cgi/content/abstract/18/2/137
https://www.proquest.com/docview/200520687
Volume 18
WOSCitedRecordID wos000238428600002&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: PRVPQU
  databaseName: ABI/INFORM Collection
  customDbUrl:
  eissn: 1526-5528
  dateEnd: 20091031
  omitProxy: false
  ssIdentifier: ssj0004349
  issn: 1091-9856
  databaseCode: 7WY
  dateStart: 19990401
  isFulltext: true
  titleUrlDefault: https://www.proquest.com/abicomplete
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ABI/INFORM Global
  customDbUrl:
  eissn: 1526-5528
  dateEnd: 20091031
  omitProxy: false
  ssIdentifier: ssj0004349
  issn: 1091-9856
  databaseCode: M0C
  dateStart: 19990401
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/abiglobal
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Advanced Technologies & Aerospace Database
  customDbUrl:
  eissn: 1526-5528
  dateEnd: 20091031
  omitProxy: false
  ssIdentifier: ssj0004349
  issn: 1091-9856
  databaseCode: P5Z
  dateStart: 19990401
  isFulltext: true
  titleUrlDefault: https://search.proquest.com/hightechjournals
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Computer Science Database
  customDbUrl:
  eissn: 1526-5528
  dateEnd: 20091031
  omitProxy: false
  ssIdentifier: ssj0004349
  issn: 1091-9856
  databaseCode: K7-
  dateStart: 19990401
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/compscijour
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: ProQuest Central
  customDbUrl:
  eissn: 1526-5528
  dateEnd: 20091031
  omitProxy: false
  ssIdentifier: ssj0004349
  issn: 1091-9856
  databaseCode: BENPR
  dateStart: 19990401
  isFulltext: true
  titleUrlDefault: https://www.proquest.com/central
  providerName: ProQuest
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3fTxQxEJ4I-KAPoijxBC77YPCp0m73R_tEgEBMjJeL0Yi-NG13SzB4h-zp3-9Mt4tcFHzw5ZK9mWwmO9PZme70-wBe6mC5t7lmJXeKFehl5jAsWLBNWbdC-jI0kWyinkzU6ameptmcLo1VDjkxJupm7mmPfK9HCKpUvX_5nRFpFH1cTQwaK7BGhQ1N9L3jR7-PRcpY_RL0JdOqrBJmI_YIe-df554-b_LXPBLK3HgnDZl5gAuOx5yogOz-SNfxHXSy_p_WP4ZHqfjMDvpoeQL32tkGrA_EDlla5xvw8AZK4VMoaNfwDOXYt-K6yKb9SNc3FGZEpXbRZWh41rMHZDRihJJn8PHk-MPRG5bIFpgvpFqwPKhKu0a1lW550HnQ0ua-cEpWXokgCl9Y7pyr8iYixqBvncBuSGM9w1vZyE1Ync1n7XPISmGdszzw0IoiiMqGymIukdiMulKEcgRseNzGJyRyIsS4MNSRoHsMuceQewy5ZwSvrvUvewyO2zXJe4Ychnf0Np0xQLsI5sociKLGlhGLyBHsLmme9SDff1PcXlLE1eeXxDtDoJgUJiaapExuhESLdoe__2X61hA5JqWRzlyHzYs7pVvwoN8ZkizPt2F1cfWj3YH7_ufivLsaw0r96fMY1g6PJ9P3ePW2ZuO4UPB3Wn75BbquFcE
linkProvider ProQuest
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1LTxRBEK4gmggHUZS4AjoHxVNLP-bRczCGqASyuOGACbe2u2eaQGAXmUXjj_I_WjUzjWx8nTh4nap0aqa_rkdP91cAz8tgubeyZBl3mqU4y8whLFiwVVbUQvksVG2ziWI00oeH5f4cfI93YehYZfSJraOuJp72yDc7hqBcF2_OPzNqGkU_V2MHjQ4Vw_rbV6zYmte773B6X0i5_f7g7Q7rmwownyo9ZTLovHSVrvOy5qGUoVRW-tRplXstgkh9arlzLpdVy4yC7-AEZv0lxm1eq0rhuLfgNo5V0LIaFuznNUzVZttEtclKneU9RyTWJJvHJxNPv1P5K942sLkWA2MkiPTE7bUqSlibX8JDG_O2l_6zr3Uf7vXJdbLVrYYHMFePl2EpNq5Iej-2DIvXWBgfQkq7okcox7ocbU72uyNrZyhMqFXcaZPgh0q67ggJHaFCySP4eCNvsgLz48m4fgxJJqxzlgceapEGkduQW_SVCottl4mQDYDF6TW-Z1qnhh-nhiouhIMhOBiCgyE4DODllf55xzHyZ01CiyGA4Ije9nco0C6i8TJbIi2wJMYkeQAbM5pHHYn57xTXZhTRu_gZ8XoEpulhaVqTtJFGKLRoIz7-l-mrEammd5ONuYLpk79Kn8HdnYMPe2ZvdzRchYVuF0wxKddgfnpxWa_DHf9letxcPG0XZAKfbhrTPwBEqmzm
linkToPdf http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1Lb9QwEB6VghA9UCgglraQA5ST2djOwzkgVFFWVEWrPYBUcTG2E1dFZbc0WxA_rf-uM4lduuJ16oFrZhSN488zHmf8DcDTypvUGVGxPLWKZTjLzCIsmDd1XjZcutzXXbOJcjxW-_vVZAnO4l0YKquMPrFz1PXM0Rn5sGcIKlQ59KEqYrIzenX8lVEDKfrRGrtp9AjZa358x-ytfbm7g1P9TIjRm_ev37LQYIC5TKo5E14Vla1VU1RN6ivhK2mEy6yShVPc88xlJrXWFqLuWFJwPJZjBlBhDE8bWUt87zW4XmKKSdWEk_zjzyuZstt5E-0mq1ReBL5IzE-Gh59njn6tpi_SrpnNpXgYo0KkKu6uWNHmtf0lVHTxb7T6H3-5O3A7bLqT7X6V3IWlZroGq7GhRRL82xqsXGJnvAcZnZYeoBzzdbQ5mfSlbF9QmFALuaM2wY-W9F0TEiqtQsl9-HAlI3kAy9PZtHkISc6NtSb1qW945nlhfGHQh0pMwm3OfT4AFqdau8DATo1AjjRlYggNTdDQBA1N0BjA8wv945575M-ahBxNYME3OhPuVqBdRO-lt3lWYqqMm-cBbC1oHvTk5r9T3FhQRK_jFsSbEaQ6QFR3JiktNJdo0VZ8_C_T1yNqdXCfrb6A7KO_Sp_ATYSyfrc73luHW_3hmGRCbMDy_OS02YQb7tv8sD153K3NBD5dNaTPAVb6dgo
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=Integer+Linear+Programming+Models+for+Global+Routing&rft.jtitle=INFORMS+journal+on+computing&rft.au=Behjat%2C+Laleh&rft.au=Vannelli%2C+Anthony&rft.au=Rosehart%2C+William&rft.date=2006-03-22&rft.issn=1091-9856&rft.eissn=1526-5528&rft.volume=18&rft.issue=2&rft.spage=137&rft.epage=150&rft_id=info:doi/10.1287%2Fijoc.1040.0127&rft.externalDBID=n%2Fa&rft.externalDocID=10_1287_ijoc_1040_0127
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1091-9856&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1091-9856&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1091-9856&client=summon