Layered graph models and exact algorithms for the generalized hop-constrained minimum spanning tree problem

This paper studies the generalized hop-constrained minimum spanning tree problem (GHMSTP) which has applications in backbone network design subject to quality-of-service constraints that restrict the maximum number of intermediate routers along each communication path. Different possibilities to mod...

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Published in:Computers & operations research Vol. 65; pp. 1 - 18
Main Author: Leitner, Markus
Format: Journal Article
Language:English
Published: New York Elsevier Ltd 01.01.2016
Pergamon Press Inc
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ISSN:0305-0548, 1873-765X, 0305-0548
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Abstract This paper studies the generalized hop-constrained minimum spanning tree problem (GHMSTP) which has applications in backbone network design subject to quality-of-service constraints that restrict the maximum number of intermediate routers along each communication path. Different possibilities to model the GHMSTP as an integer linear program and strengthening valid inequalities are studied. The obtained formulations are compared theoretically, i.e., by means of their linear programming relaxation. In addition, branch-and-cut approaches based on these formulations are developed and compared in a computational study. •New optimization problem generalizing the generalized minimum spanning tree problem and the hop constrained minimum spanning tree problem.•Extended formulations based on layered graph reformulations and strength- ening valid inequalities.•Theoretical and computational comparisons between all formulations.
AbstractList This paper studies the generalized hop-constrained minimum spanning tree problem (GHMSTP) which has applications in backbone network design subject to quality-of-service constraints that restrict the maximum number of intermediate routers along each communication path. Different possibilities to model the GHMSTP as an integer linear program and strengthening valid inequalities are studied. The obtained formulations are compared theoretically, i.e., by means of their linear programming relaxation. In addition, branch-and-cut approaches based on these formulations are developed and compared in a computational study.
This paper studies the generalized hop-constrained minimum spanning tree problem (GHMSTP) which has applications in backbone network design subject to quality-of-service constraints that restrict the maximum number of intermediate routers along each communication path. Different possibilities to model the GHMSTP as an integer linear program and strengthening valid inequalities are studied. The obtained formulations are compared theoretically, i.e., by means of their linear programming relaxation. In addition, branch-and-cut approaches based on these formulations are developed and compared in a computational study. •New optimization problem generalizing the generalized minimum spanning tree problem and the hop constrained minimum spanning tree problem.•Extended formulations based on layered graph reformulations and strength- ening valid inequalities.•Theoretical and computational comparisons between all formulations.
Author Leitner, Markus
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Cites_doi 10.1016/S0377-2217(00)00143-0
10.1023/A:1018967121276
10.1016/0377-2217(95)00090-9
10.1007/s10107-013-0743-z
10.1007/PL00009180
10.1016/S0167-6377(98)00029-7
10.1002/net.3230260407
10.1016/0305-0548(88)90033-0
10.1287/opre.45.3.378
10.1287/ijoc.3.4.376
10.1016/j.ejor.2007.08.021
10.1016/j.ejor.2004.07.058
10.1007/s10107-009-0297-2
10.1007/s10479-006-0049-0
10.1287/ijoc.1040.0077
10.1007/978-3-642-20807-2_30
10.1016/0305-0548(94)00074-I
10.1002/net.10105
10.1016/j.ejor.2010.08.011
10.1287/ijoc.1110.0472
10.1016/S0377-2217(00)00267-8
10.1002/(SICI)1097-0037(199810)32:3<207::AID-NET5>3.0.CO;2-O
10.1287/ijoc.11.2.188
10.1016/j.ejor.2013.11.029
10.1007/s10732-007-9047-x
10.1287/ijoc.1120.0500
10.1007/s10732-009-9123-5
10.1002/net.20370
10.1007/978-0-387-48793-9_11
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Keywords Integer programming
Generalized network design
Hop-constraints
Layered graph
Branch-and-cut
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References Gouveia (bib9) 1995; 22
Gouveia, Requejo (bib11) 2001; 132
Gouveia, Leitner, Ljubić (bib15) 2014; 236
Gouveia (bib10) 1996; 95
Mario Ruthmair. On solving constrained tree problems and an adaptive layers framework [Ph.D. thesis]. Vienna University of Technology; 2008.
Gouveia, Magnanti, Requejo (bib12) 2006; 146
Botton, Fortz, Goueia, Poss (bib1) 2013; 25
Cherkassky, Goldberg (bib2) 1994; 19
Corinne Feremans. Generalized spanning trees and extensions [Ph.D. thesis]. Universite Libre de Bruxelles, 2001.
Gouveia, Paias, Sharma (bib13) 2011; 17
Reinelt (bib28) 1991; 3
Öncan, Cordeau, Laporte (bib25) 2008; 191
Fischetti, José, González, Toth (bib7) 1997; 45
Dahl, Gouveia, Requejo (bib4) 2006
Pop, Kern, Still. (bib27) 2006; 170
Ljubić, Gollowitzer (bib23) 2013; 25
Gouveia, Simonetti, Uchoa (bib14) 2011; 128
Feremans, Labbé, Laporte (bib6) 2004; 43
Woolston, Albin (bib33) 1988; 15
LeBlanc, Chifflet, Mahey (bib22) 1999; 11
Dahl (bib3) 1998; 23
Ruthmair M, Raidl GR A layered graph model and an adaptive layers framework to solve delay-constrained minimum tree problems. In: Proceedings of the 15th Conference on Integer Programming and Combinatorial Optimization (IPCO XV), vol. 6655 of LNCS; 2011. p. 376–388.
Golden, Raghavan, Stanojević (bib8) 2005; 17
Myung, Lee, Tcha (bib24) 1995; 26
John Silberholz, Bruce Golden. The generalized traveling salesman problem: a new genetic algorithm approach. In: Edward K Baker, Anito Joseph, Anuj Mehrotra, Michael A. Trick, editors. Extending the horizons: advances in computing, optimization, and decision technologies. Operations research/computer science interfaces series, vol. 37; 2007. p. 165–81.
Gouveia, Leitner, Ljubić (bib16) 2015; 150
Bin Hu. Hybrid Metaheuristics for generalized network design problems [Ph.D. thesis]. Vienna University of Technology, 2008.
Voß (bib32) 1999; 86
Hu, Leitner, Raidl (bib18) 2008; 14
Hu, Leitner, Raidl (bib19) 2010; 55
Koch, Martin (bib21) 1998; 32
Petrica C. Pop. The generalized minimum spanning tree problem [Ph.D. thesis]. University of Twente; 2002.
Karapetyan, Gutin (bib20) 2011; 208
Gouveia (10.1016/j.cor.2015.06.012_bib13) 2011; 17
10.1016/j.cor.2015.06.012_bib5
Koch (10.1016/j.cor.2015.06.012_bib21) 1998; 32
Voß (10.1016/j.cor.2015.06.012_bib32) 1999; 86
Hu (10.1016/j.cor.2015.06.012_bib18) 2008; 14
Karapetyan (10.1016/j.cor.2015.06.012_bib20) 2011; 208
Gouveia (10.1016/j.cor.2015.06.012_bib15) 2014; 236
Ljubić (10.1016/j.cor.2015.06.012_bib23) 2013; 25
Gouveia (10.1016/j.cor.2015.06.012_bib16) 2015; 150
Pop (10.1016/j.cor.2015.06.012_bib27) 2006; 170
10.1016/j.cor.2015.06.012_bib17
Gouveia (10.1016/j.cor.2015.06.012_bib14) 2011; 128
Gouveia (10.1016/j.cor.2015.06.012_bib11) 2001; 132
10.1016/j.cor.2015.06.012_bib31
10.1016/j.cor.2015.06.012_bib30
Golden (10.1016/j.cor.2015.06.012_bib8) 2005; 17
Botton (10.1016/j.cor.2015.06.012_bib1) 2013; 25
Gouveia (10.1016/j.cor.2015.06.012_bib9) 1995; 22
LeBlanc (10.1016/j.cor.2015.06.012_bib22) 1999; 11
Cherkassky (10.1016/j.cor.2015.06.012_bib2) 1994; 19
Öncan (10.1016/j.cor.2015.06.012_bib25) 2008; 191
Gouveia (10.1016/j.cor.2015.06.012_bib10) 1996; 95
Myung (10.1016/j.cor.2015.06.012_bib24) 1995; 26
Woolston (10.1016/j.cor.2015.06.012_bib33) 1988; 15
10.1016/j.cor.2015.06.012_bib29
10.1016/j.cor.2015.06.012_bib26
Fischetti (10.1016/j.cor.2015.06.012_bib7) 1997; 45
Dahl (10.1016/j.cor.2015.06.012_bib4) 2006
Reinelt (10.1016/j.cor.2015.06.012_bib28) 1991; 3
Feremans (10.1016/j.cor.2015.06.012_bib6) 2004; 43
Hu (10.1016/j.cor.2015.06.012_bib19) 2010; 55
Dahl (10.1016/j.cor.2015.06.012_bib3) 1998; 23
Gouveia (10.1016/j.cor.2015.06.012_bib12) 2006; 146
References_xml – volume: 128
  start-page: 123
  year: 2011
  end-page: 148
  ident: bib14
  article-title: Modeling hop-constrained and diameter-constrained minimum spanning tree problems as Steiner tree problems over layered graphs
  publication-title: Math Progr
– volume: 32
  start-page: 207
  year: 1998
  end-page: 232
  ident: bib21
  article-title: Solving Steiner tree problems in graphs to optimality
  publication-title: Networks
– volume: 22
  start-page: 959
  year: 1995
  end-page: 970
  ident: bib9
  article-title: Using the Miller–Tucker–Zemlin constraints to formulate a minimal spanning tree problem with hop constraints
  publication-title: Comput Oper Res
– start-page: 493
  year: 2006
  end-page: 515
  ident: bib4
  article-title: On formulations and methods for the hop-constrained minimum spanning tree problem
  publication-title: Handbook of optimization in telecommunications
– reference: Corinne Feremans. Generalized spanning trees and extensions [Ph.D. thesis]. Universite Libre de Bruxelles, 2001.
– volume: 15
  start-page: 207
  year: 1988
  end-page: 217
  ident: bib33
  article-title: The design of centralized networks with reliability and availability constraints
  publication-title: Comput Oper Res
– volume: 208
  start-page: 221
  year: 2011
  end-page: 232
  ident: bib20
  article-title: Lin–Kernighan heuristic adaptations for the generalized traveling salesman problem
  publication-title: Eur J Oper Res
– reference: Ruthmair M, Raidl GR A layered graph model and an adaptive layers framework to solve delay-constrained minimum tree problems. In: Proceedings of the 15th Conference on Integer Programming and Combinatorial Optimization (IPCO XV), vol. 6655 of LNCS; 2011. p. 376–388.
– volume: 25
  start-page: 13
  year: 2013
  end-page: 26
  ident: bib1
  article-title: Benders decomposition for the hop-constrained survivable network design problem
  publication-title: INFORMS J Comput
– reference: Mario Ruthmair. On solving constrained tree problems and an adaptive layers framework [Ph.D. thesis]. Vienna University of Technology; 2008.
– volume: 14
  start-page: 473
  year: 2008
  end-page: 499
  ident: bib18
  article-title: Combining variable neighborhood search with integer linear programming for the generalized minimum spanning tree problem
  publication-title: J Heuristics
– volume: 43
  start-page: 71
  year: 2004
  end-page: 86
  ident: bib6
  article-title: The generalized minimum spanning tree problem
  publication-title: Networks
– volume: 95
  start-page: 178
  year: 1996
  end-page: 190
  ident: bib10
  article-title: Multicommodity flow models for spanning trees with hop constraints
  publication-title: Eur J Oper Res
– volume: 17
  start-page: 290
  year: 2005
  end-page: 304
  ident: bib8
  article-title: Heuristic search for the generalized minimum spanning tree problem
  publication-title: INFORMS J Comput
– volume: 11
  start-page: 188
  year: 1999
  end-page: 197
  ident: bib22
  article-title: Packet routing in telecommunication networks with path and flow restrictions
  publication-title: INFORMS J Comput
– volume: 170
  start-page: 900
  year: 2006
  end-page: 908
  ident: bib27
  article-title: A new relaxation method for the generalized minimum spanning tree problem
  publication-title: Eur J Oper Res
– volume: 150
  start-page: 49
  year: 2015
  end-page: 78
  ident: bib16
  article-title: The two-level diameter constrained spanning tree problem
  publication-title: Math Progr
– volume: 19
  start-page: 390
  year: 1994
  end-page: 410
  ident: bib2
  article-title: On implementing push-relabel method for the maximum flow problem
  publication-title: Algorithmica
– reference: Bin Hu. Hybrid Metaheuristics for generalized network design problems [Ph.D. thesis]. Vienna University of Technology, 2008.
– volume: 132
  start-page: 539
  year: 2001
  end-page: 552
  ident: bib11
  article-title: A new Lagrangian relaxation approach for the hop-constrained minimum spanning tree problem
  publication-title: Eur J Oper Res
– volume: 17
  start-page: 23
  year: 2011
  end-page: 37
  ident: bib13
  article-title: Restricted dynamic programming based neighborhoods for the hop-constrained minimum spanning tree problem
  publication-title: J Heuristics
– volume: 26
  start-page: 231
  year: 1995
  end-page: 241
  ident: bib24
  article-title: On the generalized minimum spanning tree problem
  publication-title: Networks
– volume: 45
  start-page: 378
  year: 1997
  end-page: 394
  ident: bib7
  article-title: A branch-and-cut algorithm for the symmetric generalized traveling salesman problem
  publication-title: Oper Res
– volume: 55
  start-page: 257
  year: 2010
  end-page: 275
  ident: bib19
  article-title: The generalized minimum edge biconnected network problem
  publication-title: Networks
– volume: 86
  start-page: 271
  year: 1999
  end-page: 294
  ident: bib32
  article-title: The Steiner tree problem with hop constraints
  publication-title: Ann Oper Res
– volume: 3
  start-page: 376
  year: 1991
  end-page: 384
  ident: bib28
  article-title: TSPLIB—a traveling salesman problem library
  publication-title: INFORMS J Comput
– volume: 191
  start-page: 306
  year: 2008
  end-page: 319
  ident: bib25
  article-title: A tabu search heuristic for the generalized minimum spanning tree problem
  publication-title: Eur J Oper Res
– volume: 236
  start-page: 100
  year: 2014
  end-page: 112
  ident: bib15
  article-title: Hop constrained Steiner trees with multiple root nodes
  publication-title: Eur J Oper Res
– volume: 25
  start-page: 256
  year: 2013
  end-page: 270
  ident: bib23
  article-title: Layered graph approaches to the hop constrained connected facility location problem
  publication-title: INFORMS J Comput
– volume: 23
  start-page: 21
  year: 1998
  end-page: 26
  ident: bib3
  article-title: The 2-hop spanning tree problem
  publication-title: Oper Res Lett
– reference: Petrica C. Pop. The generalized minimum spanning tree problem [Ph.D. thesis]. University of Twente; 2002.
– volume: 146
  start-page: 19
  year: 2006
  end-page: 39
  ident: bib12
  article-title: An intersecting tree model for odd-diameter-constrained minimum spanning and Steiner trees
  publication-title: Ann Oper Res
– reference: John Silberholz, Bruce Golden. The generalized traveling salesman problem: a new genetic algorithm approach. In: Edward K Baker, Anito Joseph, Anuj Mehrotra, Michael A. Trick, editors. Extending the horizons: advances in computing, optimization, and decision technologies. Operations research/computer science interfaces series, vol. 37; 2007. p. 165–81.
– volume: 132
  start-page: 539
  issue: 3
  year: 2001
  ident: 10.1016/j.cor.2015.06.012_bib11
  article-title: A new Lagrangian relaxation approach for the hop-constrained minimum spanning tree problem
  publication-title: Eur J Oper Res
  doi: 10.1016/S0377-2217(00)00143-0
– volume: 86
  start-page: 271
  year: 1999
  ident: 10.1016/j.cor.2015.06.012_bib32
  article-title: The Steiner tree problem with hop constraints
  publication-title: Ann Oper Res
  doi: 10.1023/A:1018967121276
– volume: 95
  start-page: 178
  year: 1996
  ident: 10.1016/j.cor.2015.06.012_bib10
  article-title: Multicommodity flow models for spanning trees with hop constraints
  publication-title: Eur J Oper Res
  doi: 10.1016/0377-2217(95)00090-9
– volume: 150
  start-page: 49
  issue: 1
  year: 2015
  ident: 10.1016/j.cor.2015.06.012_bib16
  article-title: The two-level diameter constrained spanning tree problem
  publication-title: Math Progr
  doi: 10.1007/s10107-013-0743-z
– ident: 10.1016/j.cor.2015.06.012_bib26
– volume: 19
  start-page: 390
  year: 1994
  ident: 10.1016/j.cor.2015.06.012_bib2
  article-title: On implementing push-relabel method for the maximum flow problem
  publication-title: Algorithmica
  doi: 10.1007/PL00009180
– volume: 23
  start-page: 21
  issue: 1–2
  year: 1998
  ident: 10.1016/j.cor.2015.06.012_bib3
  article-title: The 2-hop spanning tree problem
  publication-title: Oper Res Lett
  doi: 10.1016/S0167-6377(98)00029-7
– volume: 26
  start-page: 231
  issue: 4
  year: 1995
  ident: 10.1016/j.cor.2015.06.012_bib24
  article-title: On the generalized minimum spanning tree problem
  publication-title: Networks
  doi: 10.1002/net.3230260407
– volume: 15
  start-page: 207
  year: 1988
  ident: 10.1016/j.cor.2015.06.012_bib33
  article-title: The design of centralized networks with reliability and availability constraints
  publication-title: Comput Oper Res
  doi: 10.1016/0305-0548(88)90033-0
– volume: 45
  start-page: 378
  issue: 3
  year: 1997
  ident: 10.1016/j.cor.2015.06.012_bib7
  article-title: A branch-and-cut algorithm for the symmetric generalized traveling salesman problem
  publication-title: Oper Res
  doi: 10.1287/opre.45.3.378
– volume: 3
  start-page: 376
  issue: 4
  year: 1991
  ident: 10.1016/j.cor.2015.06.012_bib28
  article-title: TSPLIB—a traveling salesman problem library
  publication-title: INFORMS J Comput
  doi: 10.1287/ijoc.3.4.376
– volume: 191
  start-page: 306
  issue: 2
  year: 2008
  ident: 10.1016/j.cor.2015.06.012_bib25
  article-title: A tabu search heuristic for the generalized minimum spanning tree problem
  publication-title: Eur J Oper Res
  doi: 10.1016/j.ejor.2007.08.021
– volume: 170
  start-page: 900
  issue: 3
  year: 2006
  ident: 10.1016/j.cor.2015.06.012_bib27
  article-title: A new relaxation method for the generalized minimum spanning tree problem
  publication-title: Eur J Oper Res
  doi: 10.1016/j.ejor.2004.07.058
– volume: 128
  start-page: 123
  year: 2011
  ident: 10.1016/j.cor.2015.06.012_bib14
  article-title: Modeling hop-constrained and diameter-constrained minimum spanning tree problems as Steiner tree problems over layered graphs
  publication-title: Math Progr
  doi: 10.1007/s10107-009-0297-2
– volume: 146
  start-page: 19
  issue: 1
  year: 2006
  ident: 10.1016/j.cor.2015.06.012_bib12
  article-title: An intersecting tree model for odd-diameter-constrained minimum spanning and Steiner trees
  publication-title: Ann Oper Res
  doi: 10.1007/s10479-006-0049-0
– volume: 17
  start-page: 290
  issue: 3
  year: 2005
  ident: 10.1016/j.cor.2015.06.012_bib8
  article-title: Heuristic search for the generalized minimum spanning tree problem
  publication-title: INFORMS J Comput
  doi: 10.1287/ijoc.1040.0077
– ident: 10.1016/j.cor.2015.06.012_bib30
  doi: 10.1007/978-3-642-20807-2_30
– volume: 22
  start-page: 959
  year: 1995
  ident: 10.1016/j.cor.2015.06.012_bib9
  article-title: Using the Miller–Tucker–Zemlin constraints to formulate a minimal spanning tree problem with hop constraints
  publication-title: Comput Oper Res
  doi: 10.1016/0305-0548(94)00074-I
– ident: 10.1016/j.cor.2015.06.012_bib17
– volume: 43
  start-page: 71
  issue: 2
  year: 2004
  ident: 10.1016/j.cor.2015.06.012_bib6
  article-title: The generalized minimum spanning tree problem
  publication-title: Networks
  doi: 10.1002/net.10105
– ident: 10.1016/j.cor.2015.06.012_bib29
– volume: 208
  start-page: 221
  issue: 3
  year: 2011
  ident: 10.1016/j.cor.2015.06.012_bib20
  article-title: Lin–Kernighan heuristic adaptations for the generalized traveling salesman problem
  publication-title: Eur J Oper Res
  doi: 10.1016/j.ejor.2010.08.011
– volume: 25
  start-page: 13
  issue: 1
  year: 2013
  ident: 10.1016/j.cor.2015.06.012_bib1
  article-title: Benders decomposition for the hop-constrained survivable network design problem
  publication-title: INFORMS J Comput
  doi: 10.1287/ijoc.1110.0472
– ident: 10.1016/j.cor.2015.06.012_bib5
  doi: 10.1016/S0377-2217(00)00267-8
– volume: 32
  start-page: 207
  issue: 3
  year: 1998
  ident: 10.1016/j.cor.2015.06.012_bib21
  article-title: Solving Steiner tree problems in graphs to optimality
  publication-title: Networks
  doi: 10.1002/(SICI)1097-0037(199810)32:3<207::AID-NET5>3.0.CO;2-O
– volume: 11
  start-page: 188
  issue: 2
  year: 1999
  ident: 10.1016/j.cor.2015.06.012_bib22
  article-title: Packet routing in telecommunication networks with path and flow restrictions
  publication-title: INFORMS J Comput
  doi: 10.1287/ijoc.11.2.188
– start-page: 493
  year: 2006
  ident: 10.1016/j.cor.2015.06.012_bib4
  article-title: On formulations and methods for the hop-constrained minimum spanning tree problem
– volume: 236
  start-page: 100
  year: 2014
  ident: 10.1016/j.cor.2015.06.012_bib15
  article-title: Hop constrained Steiner trees with multiple root nodes
  publication-title: Eur J Oper Res
  doi: 10.1016/j.ejor.2013.11.029
– volume: 14
  start-page: 473
  issue: 5
  year: 2008
  ident: 10.1016/j.cor.2015.06.012_bib18
  article-title: Combining variable neighborhood search with integer linear programming for the generalized minimum spanning tree problem
  publication-title: J Heuristics
  doi: 10.1007/s10732-007-9047-x
– volume: 25
  start-page: 256
  year: 2013
  ident: 10.1016/j.cor.2015.06.012_bib23
  article-title: Layered graph approaches to the hop constrained connected facility location problem
  publication-title: INFORMS J Comput
  doi: 10.1287/ijoc.1120.0500
– volume: 17
  start-page: 23
  issue: 1
  year: 2011
  ident: 10.1016/j.cor.2015.06.012_bib13
  article-title: Restricted dynamic programming based neighborhoods for the hop-constrained minimum spanning tree problem
  publication-title: J Heuristics
  doi: 10.1007/s10732-009-9123-5
– volume: 55
  start-page: 257
  issue: 3
  year: 2010
  ident: 10.1016/j.cor.2015.06.012_bib19
  article-title: The generalized minimum edge biconnected network problem
  publication-title: Networks
  doi: 10.1002/net.20370
– ident: 10.1016/j.cor.2015.06.012_bib31
  doi: 10.1007/978-0-387-48793-9_11
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Snippet This paper studies the generalized hop-constrained minimum spanning tree problem (GHMSTP) which has applications in backbone network design subject to...
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SubjectTerms Algorithms
Branch-and-cut
Computer simulation
Generalized network design
Graph algorithms
Graph theory
Graphs
Hop-constraints
Inequalities
Integer programming
Layered graph
Linear programming
Mathematical models
Operations research
Quality of service
Routers
Studies
Title Layered graph models and exact algorithms for the generalized hop-constrained minimum spanning tree problem
URI https://dx.doi.org/10.1016/j.cor.2015.06.012
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https://www.proquest.com/docview/1816077801
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