High-multiplicity N-fold IP via configuration LP

N -fold integer programs (IPs) form an important class of block-structured IPs for which increasingly fast algorithms have recently been developed and successfully applied. We study high-multiplicity N -fold IPs, which encode IPs succinctly by presenting a description of each block type and a vector...

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Published in:Mathematical programming Vol. 200; no. 1; pp. 199 - 227
Main Authors: Knop, Dušan, Koutecký, Martin, Levin, Asaf, Mnich, Matthias, Onn, Shmuel
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2023
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ISSN:0025-5610, 1436-4646
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Abstract N -fold integer programs (IPs) form an important class of block-structured IPs for which increasingly fast algorithms have recently been developed and successfully applied. We study high-multiplicity N -fold IPs, which encode IPs succinctly by presenting a description of each block type and a vector of block multiplicities. Our goal is to design algorithms which solve N -fold IPs in time polynomial in the size of the succinct encoding, which may be significantly smaller than the size of the explicit (non-succinct) instance. We present the first fixed-parameter algorithm for high-multiplicity N -fold IPs, which even works for convex objectives. Our key contribution is a novel proximity theorem which relates fractional and integer optima of the Configuration LP, a fundamental notion by Gilmore and Gomory [Oper. Res., 1961] which we generalize. Our algorithm for N -fold IP is faster than previous algorithms whenever the number of blocks is much larger than the number of block types, such as in N -fold IP models for various scheduling problems.
AbstractList N -fold integer programs (IPs) form an important class of block-structured IPs for which increasingly fast algorithms have recently been developed and successfully applied. We study high-multiplicity N -fold IPs, which encode IPs succinctly by presenting a description of each block type and a vector of block multiplicities. Our goal is to design algorithms which solve N -fold IPs in time polynomial in the size of the succinct encoding, which may be significantly smaller than the size of the explicit (non-succinct) instance. We present the first fixed-parameter algorithm for high-multiplicity N -fold IPs, which even works for convex objectives. Our key contribution is a novel proximity theorem which relates fractional and integer optima of the Configuration LP, a fundamental notion by Gilmore and Gomory [Oper. Res., 1961] which we generalize. Our algorithm for N -fold IP is faster than previous algorithms whenever the number of blocks is much larger than the number of block types, such as in N -fold IP models for various scheduling problems.
N-fold integer programs (IPs) form an important class of block-structured IPs for which increasingly fast algorithms have recently been developed and successfully applied. We study high-multiplicityN-fold IPs, which encode IPs succinctly by presenting a description of each block type and a vector of block multiplicities. Our goal is to design algorithms which solve N-fold IPs in time polynomial in the size of the succinct encoding, which may be significantly smaller than the size of the explicit (non-succinct) instance. We present the first fixed-parameter algorithm for high-multiplicity N-fold IPs, which even works for convex objectives. Our key contribution is a novel proximity theorem which relates fractional and integer optima of the Configuration LP, a fundamental notion by Gilmore and Gomory [Oper. Res., 1961] which we generalize. Our algorithm for N-fold IP is faster than previous algorithms whenever the number of blocks is much larger than the number of block types, such as in N-fold IP models for various scheduling problems.
Audience Academic
Author Knop, Dušan
Koutecký, Martin
Onn, Shmuel
Mnich, Matthias
Levin, Asaf
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Cites_doi 10.1287/moor.1110.0515
10.1007/BF02579456
10.1287/opre.28.6.1347
10.1007/s10107-014-0761-5
10.1002/(SICI)1099-1425(199806)1:1<55::AID-JOS2>3.0.CO;2-J
10.1007/BF01582130
10.1016/0377-2217(95)00022-I
10.1287/mnsc.18.1.98
10.1287/opre.39.4.648
10.1287/opre.9.6.849
10.1007/s10107-019-01402-2
10.1287/opre.47.6.862
10.1007/s10951-017-0550-0
10.1145/96559.96597
10.1145/3340322
10.1016/j.disopt.2014.07.003
10.1016/j.disopt.2006.06.006
10.1137/S1064827502401953
10.1016/j.jcss.2016.07.004
10.1112/blms/17.1.21
10.1145/7531.7535
10.1515/crll.1916.146.1
10.1287/ijoc.2017.0797
10.1145/3330137
10.1137/0213007
10.1137/S1052623497318682
10.1137/19M1303873
10.1016/0012-365X(94)00240-J
10.4171/093
10.1109/SFCS.1982.61
10.1137/1.9781611972443
10.1007/978-3-540-68279-0_13
10.1137/1.9781611976465.101
10.1007/978-3-642-13193-6_21
10.1007/978-3-642-78240-4
10.1007/s10107-013-0638-z
10.1007/978-3-642-38171-3_31
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Issue 1
Keywords Integer programming
90C10
Fixed-parameter algorithms
Scheduling
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Configuration IP
Language English
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References Hochbaum, Shmoys (CR22) 1987; 34
Jansen, Lassota, Rohwedder (CR26) 2020; 34
Onn (CR36) 2017; 83
Ferris, Horn (CR15) 1998; 80
Knop, Koutecký (CR29) 2018; 21
CR19
CR18
CR16
Chen, Marx (CR6) 2018; 2018
CR13
De Loera, Hemmecke, Onn, Weismantel (CR9) 2008; 5
CR12
CR34
CR33
Sevast’janov, Banaszczyk (CR39) 1997; 169
CR10
van den Akker, Hoogeveen, van de Velde (CR41) 1999; 47
CR31
Jansen, Solis-Oba (CR24) 2011; 36
CR30
Onn (CR35) 2014; 14
Psaraftis (CR37) 1980; 28
Bergner, Caprara, Ceselli, Furini, Lübbecke, Malaguti, Traversi (CR4) 2015; 149
Hochbaum, Shantikumar (CR21) 1990; 37
Hochbaum, Shamir (CR20) 1991; 39
Altmanová, Knop, Koutecký (CR2) 2019; 24
Fernandez de la Vega, Lueker (CR14) 1981; 1
Borndörfer, Ferreira, Martin (CR5) 1998; 9
CR8
Steinitz (CR40) 1916; 146
Alon, Azar, Woeginger, Yadid (CR1) 1998; 1
CR27
Weil, Kettler (CR45) 1971; 18
Aykanat, Pinar, Çatalyürek (CR3) 2004; 25
CR25
Knop, Koutecký, Mnich (CR32) 2020; 184
CR23
CR44
CR42
Khaniyev, Elhedhli, Erenay (CR28) 2018; 30
Vose (CR43) 1985; 17
Cosmadakis, Papadimitriou (CR7) 1984; 13
Scheithauer, Terno (CR38) 1995; 84
Gilmore, Gomory (CR17) 1961; 9
Eisenbrand, Weismantel (CR11) 2020; 16
SS Cosmadakis (1882_CR7) 1984; 13
K Jansen (1882_CR26) 2020; 34
M Bergner (1882_CR4) 2015; 149
K Altmanová (1882_CR2) 2019; 24
W Fernandez de la Vega (1882_CR14) 1981; 1
C Aykanat (1882_CR3) 2004; 25
1882_CR10
1882_CR33
G Scheithauer (1882_CR38) 1995; 84
1882_CR12
1882_CR34
F Eisenbrand (1882_CR11) 2020; 16
1882_CR13
S Onn (1882_CR35) 2014; 14
1882_CR30
1882_CR31
1882_CR18
D Knop (1882_CR32) 2020; 184
JA De Loera (1882_CR9) 2008; 5
MC Ferris (1882_CR15) 1998; 80
1882_CR19
DS Hochbaum (1882_CR20) 1991; 39
DS Hochbaum (1882_CR21) 1990; 37
T Khaniyev (1882_CR28) 2018; 30
1882_CR16
DS Hochbaum (1882_CR22) 1987; 34
S Sevast’janov (1882_CR39) 1997; 169
N Alon (1882_CR1) 1998; 1
JM van den Akker (1882_CR41) 1999; 47
D Knop (1882_CR29) 2018; 21
R Borndörfer (1882_CR5) 1998; 9
MD Vose (1882_CR43) 1985; 17
1882_CR44
1882_CR23
1882_CR42
PC Gilmore (1882_CR17) 1961; 9
K Jansen (1882_CR24) 2011; 36
1882_CR25
1882_CR27
RL Weil (1882_CR45) 1971; 18
1882_CR8
L Chen (1882_CR6) 2018; 2018
S Onn (1882_CR36) 2017; 83
HN Psaraftis (1882_CR37) 1980; 28
E Steinitz (1882_CR40) 1916; 146
References_xml – ident: CR18
– volume: 36
  start-page: 743
  issue: 4
  year: 2011
  end-page: 753
  ident: CR24
  article-title: A polynomial time algorithm for the cutting stock problem with a constant number of object lengths
  publication-title: Math. Oper. Res.
  doi: 10.1287/moor.1110.0515
– volume: 1
  start-page: 349
  issue: 4
  year: 1981
  end-page: 355
  ident: CR14
  article-title: Bin packing can be solved within in linear time
  publication-title: Combinatorica
  doi: 10.1007/BF02579456
– volume: 28
  start-page: 1347
  issue: 6
  year: 1980
  end-page: 1359
  ident: CR37
  article-title: A dynamic programming approach for sequencing groups of identical jobs
  publication-title: Oper. Res.
  doi: 10.1287/opre.28.6.1347
– ident: CR16
– volume: 149
  start-page: 391
  issue: 1–2
  year: 2015
  end-page: 424
  ident: CR4
  article-title: Automatic Dantzig-Wolfe reformulation of mixed integer programs
  publication-title: Math. Prog.
  doi: 10.1007/s10107-014-0761-5
– volume: 1
  start-page: 55
  issue: 1
  year: 1998
  end-page: 66
  ident: CR1
  article-title: Approximation schemes for scheduling on parallel machines
  publication-title: J. Sched.
  doi: 10.1002/(SICI)1099-1425(199806)1:1<55::AID-JOS2>3.0.CO;2-J
– ident: CR12
– volume: 80
  start-page: 35
  issue: 1
  year: 1998
  end-page: 61
  ident: CR15
  article-title: Partitioning mathematical programs for parallel solution
  publication-title: Math. Prog.
  doi: 10.1007/BF01582130
– ident: CR30
– volume: 84
  start-page: 562
  issue: 3
  year: 1995
  end-page: 571
  ident: CR38
  article-title: The modified integer round-up property of the one-dimensional cutting stock problem
  publication-title: European J. Oper. Res.
  doi: 10.1016/0377-2217(95)00022-I
– volume: 18
  start-page: 98
  issue: 1
  year: 1971
  end-page: 108
  ident: CR45
  article-title: Rearranging matrices to block-angular form for decomposition (and other) algorithms
  publication-title: Mgmt. Sci.
  doi: 10.1287/mnsc.18.1.98
– volume: 39
  start-page: 648
  issue: 4
  year: 1991
  end-page: 653
  ident: CR20
  article-title: Strongly polynomial algorithms for the high multiplicity scheduling problem
  publication-title: Oper. Res.
  doi: 10.1287/opre.39.4.648
– ident: CR10
– volume: 9
  start-page: 849
  year: 1961
  end-page: 859
  ident: CR17
  article-title: A linear programming approach to the cutting-stock problem
  publication-title: Oper. Res.
  doi: 10.1287/opre.9.6.849
– volume: 184
  start-page: 1
  issue: 1
  year: 2020
  end-page: 34
  ident: CR32
  article-title: Combinatorial -fold integer programming and applications
  publication-title: Math. Program.
  doi: 10.1007/s10107-019-01402-2
– ident: CR33
– volume: 47
  start-page: 862
  issue: 6
  year: 1999
  end-page: 872
  ident: CR41
  article-title: Parallel machine scheduling by column generation
  publication-title: Oper. Res.
  doi: 10.1287/opre.47.6.862
– volume: 21
  start-page: 493
  issue: 5
  year: 2018
  end-page: 503
  ident: CR29
  article-title: Scheduling meets -fold integer programming
  publication-title: J. Sched.
  doi: 10.1007/s10951-017-0550-0
– volume: 37
  start-page: 843
  issue: 4
  year: 1990
  end-page: 862
  ident: CR21
  article-title: Convex separable optimization is not much harder than linear optimization
  publication-title: J. ACM
  doi: 10.1145/96559.96597
– volume: 16
  start-page: 5:1
  issue: 1
  year: 2020
  end-page: 5:14
  ident: CR11
  article-title: Proximity results and faster algorithms for integer programming using the Steinitz lemma
  publication-title: ACM Trans. Algorithms
  doi: 10.1145/3340322
– ident: CR8
– volume: 14
  start-page: 72
  year: 2014
  end-page: 77
  ident: CR35
  article-title: Huge multiway table problems
  publication-title: Discrete Optim.
  doi: 10.1016/j.disopt.2014.07.003
– ident: CR25
– ident: CR27
– ident: CR42
– volume: 5
  start-page: 231
  issue: 2
  year: 2008
  end-page: 241
  ident: CR9
  article-title: -fold integer programming
  publication-title: Discrete Optim.
  doi: 10.1016/j.disopt.2006.06.006
– ident: CR23
– ident: CR19
– ident: CR44
– volume: 25
  start-page: 1860
  issue: 6
  year: 2004
  end-page: 1879
  ident: CR3
  article-title: Permuting sparse rectangular matrices into block-diagonal form
  publication-title: SIAM J. Scientific Comput.
  doi: 10.1137/S1064827502401953
– volume: 83
  start-page: 207
  issue: 1
  year: 2017
  end-page: 214
  ident: CR36
  article-title: Huge tables and multicommodity flows are fixed-parameter tractable via unimodular integer Carathéodory
  publication-title: J. Comput. Syst. Sci.
  doi: 10.1016/j.jcss.2016.07.004
– volume: 17
  start-page: 21
  issue: 1
  year: 1985
  end-page: 24
  ident: CR43
  article-title: Egyptian fractions
  publication-title: Bull. London Math. Soc.
  doi: 10.1112/blms/17.1.21
– volume: 34
  start-page: 144
  issue: 1
  year: 1987
  end-page: 162
  ident: CR22
  article-title: Using dual approximation algorithms for scheduling problems: theoretical and practical results
  publication-title: J. Assoc. Comput. Mach.
  doi: 10.1145/7531.7535
– ident: CR31
– ident: CR13
– volume: 146
  start-page: 1
  year: 1916
  end-page: 52
  ident: CR40
  article-title: Bedingt konvergente Reihen und konvexe Systeme
  publication-title: J. Reine Angew. Math.
  doi: 10.1515/crll.1916.146.1
– ident: CR34
– volume: 30
  start-page: 570
  issue: 3
  year: 2018
  end-page: 587
  ident: CR28
  article-title: Structure detection in mixed-integer programs
  publication-title: INFORMS J. Comput.
  doi: 10.1287/ijoc.2017.0797
– volume: 24
  start-page: 1
  issue: 1
  year: 2019
  end-page: 22
  ident: CR2
  article-title: Evaluating and tuning -fold integer programming
  publication-title: ACM J. Exp. Algorithmics
  doi: 10.1145/3330137
– volume: 13
  start-page: 99
  issue: 1
  year: 1984
  end-page: 108
  ident: CR7
  article-title: The traveling salesman problem with many visits to few cities
  publication-title: SIAM J. Comput.
  doi: 10.1137/0213007
– volume: 2018
  start-page: 2801
  year: 2018
  end-page: 2820
  ident: CR6
  article-title: Covering a tree with rooted subtrees—parameterized and approximation algorithms
  publication-title: In Proc. SODA
– volume: 9
  start-page: 236
  issue: 1
  year: 1998
  end-page: 269
  ident: CR5
  article-title: Decomposing matrices into blocks
  publication-title: SIAM J. Optim.
  doi: 10.1137/S1052623497318682
– volume: 34
  start-page: 2282
  issue: 4
  year: 2020
  end-page: 2299
  ident: CR26
  article-title: Near-linear time algorithm for -fold ilps via color coding
  publication-title: SIAM J. Discret. Math.
  doi: 10.1137/19M1303873
– volume: 169
  start-page: 145
  issue: 1–3
  year: 1997
  end-page: 152
  ident: CR39
  article-title: To the Steinitz lemma in coordinate form
  publication-title: Discrete Math.
  doi: 10.1016/0012-365X(94)00240-J
– ident: 1882_CR34
  doi: 10.4171/093
– ident: 1882_CR27
  doi: 10.1109/SFCS.1982.61
– ident: 1882_CR12
– ident: 1882_CR33
– volume: 39
  start-page: 648
  issue: 4
  year: 1991
  ident: 1882_CR20
  publication-title: Oper. Res.
  doi: 10.1287/opre.39.4.648
– volume: 17
  start-page: 21
  issue: 1
  year: 1985
  ident: 1882_CR43
  publication-title: Bull. London Math. Soc.
  doi: 10.1112/blms/17.1.21
– volume: 34
  start-page: 2282
  issue: 4
  year: 2020
  ident: 1882_CR26
  publication-title: SIAM J. Discret. Math.
  doi: 10.1137/19M1303873
– volume: 13
  start-page: 99
  issue: 1
  year: 1984
  ident: 1882_CR7
  publication-title: SIAM J. Comput.
  doi: 10.1137/0213007
– volume: 25
  start-page: 1860
  issue: 6
  year: 2004
  ident: 1882_CR3
  publication-title: SIAM J. Scientific Comput.
  doi: 10.1137/S1064827502401953
– volume: 5
  start-page: 231
  issue: 2
  year: 2008
  ident: 1882_CR9
  publication-title: Discrete Optim.
  doi: 10.1016/j.disopt.2006.06.006
– ident: 1882_CR30
– volume: 34
  start-page: 144
  issue: 1
  year: 1987
  ident: 1882_CR22
  publication-title: J. Assoc. Comput. Mach.
  doi: 10.1145/7531.7535
– volume: 9
  start-page: 236
  issue: 1
  year: 1998
  ident: 1882_CR5
  publication-title: SIAM J. Optim.
  doi: 10.1137/S1052623497318682
– ident: 1882_CR10
  doi: 10.1137/1.9781611972443
– volume: 149
  start-page: 391
  issue: 1–2
  year: 2015
  ident: 1882_CR4
  publication-title: Math. Prog.
  doi: 10.1007/s10107-014-0761-5
– ident: 1882_CR42
  doi: 10.1007/978-3-540-68279-0_13
– volume: 14
  start-page: 72
  year: 2014
  ident: 1882_CR35
  publication-title: Discrete Optim.
  doi: 10.1016/j.disopt.2014.07.003
– volume: 36
  start-page: 743
  issue: 4
  year: 2011
  ident: 1882_CR24
  publication-title: Math. Oper. Res.
  doi: 10.1287/moor.1110.0515
– volume: 146
  start-page: 1
  year: 1916
  ident: 1882_CR40
  publication-title: J. Reine Angew. Math.
  doi: 10.1515/crll.1916.146.1
– ident: 1882_CR13
– volume: 9
  start-page: 849
  year: 1961
  ident: 1882_CR17
  publication-title: Oper. Res.
  doi: 10.1287/opre.9.6.849
– ident: 1882_CR8
  doi: 10.1137/1.9781611976465.101
– volume: 30
  start-page: 570
  issue: 3
  year: 2018
  ident: 1882_CR28
  publication-title: INFORMS J. Comput.
  doi: 10.1287/ijoc.2017.0797
– volume: 28
  start-page: 1347
  issue: 6
  year: 1980
  ident: 1882_CR37
  publication-title: Oper. Res.
  doi: 10.1287/opre.28.6.1347
– volume: 80
  start-page: 35
  issue: 1
  year: 1998
  ident: 1882_CR15
  publication-title: Math. Prog.
  doi: 10.1007/BF01582130
– ident: 1882_CR16
  doi: 10.1007/978-3-642-13193-6_21
– volume: 16
  start-page: 5:1
  issue: 1
  year: 2020
  ident: 1882_CR11
  publication-title: ACM Trans. Algorithms
  doi: 10.1145/3340322
– ident: 1882_CR18
  doi: 10.1007/978-3-642-78240-4
– volume: 21
  start-page: 493
  issue: 5
  year: 2018
  ident: 1882_CR29
  publication-title: J. Sched.
  doi: 10.1007/s10951-017-0550-0
– volume: 184
  start-page: 1
  issue: 1
  year: 2020
  ident: 1882_CR32
  publication-title: Math. Program.
  doi: 10.1007/s10107-019-01402-2
– volume: 83
  start-page: 207
  issue: 1
  year: 2017
  ident: 1882_CR36
  publication-title: J. Comput. Syst. Sci.
  doi: 10.1016/j.jcss.2016.07.004
– volume: 169
  start-page: 145
  issue: 1–3
  year: 1997
  ident: 1882_CR39
  publication-title: Discrete Math.
  doi: 10.1016/0012-365X(94)00240-J
– volume: 37
  start-page: 843
  issue: 4
  year: 1990
  ident: 1882_CR21
  publication-title: J. ACM
  doi: 10.1145/96559.96597
– volume: 24
  start-page: 1
  issue: 1
  year: 2019
  ident: 1882_CR2
  publication-title: ACM J. Exp. Algorithmics
  doi: 10.1145/3330137
– volume: 84
  start-page: 562
  issue: 3
  year: 1995
  ident: 1882_CR38
  publication-title: European J. Oper. Res.
  doi: 10.1016/0377-2217(95)00022-I
– ident: 1882_CR19
  doi: 10.1007/s10107-013-0638-z
– ident: 1882_CR23
– ident: 1882_CR31
– volume: 2018
  start-page: 2801
  year: 2018
  ident: 1882_CR6
  publication-title: In Proc. SODA
– ident: 1882_CR25
– volume: 1
  start-page: 349
  issue: 4
  year: 1981
  ident: 1882_CR14
  publication-title: Combinatorica
  doi: 10.1007/BF02579456
– volume: 1
  start-page: 55
  issue: 1
  year: 1998
  ident: 1882_CR1
  publication-title: J. Sched.
  doi: 10.1002/(SICI)1099-1425(199806)1:1<55::AID-JOS2>3.0.CO;2-J
– volume: 47
  start-page: 862
  issue: 6
  year: 1999
  ident: 1882_CR41
  publication-title: Oper. Res.
  doi: 10.1287/opre.47.6.862
– ident: 1882_CR44
  doi: 10.1007/978-3-642-38171-3_31
– volume: 18
  start-page: 98
  issue: 1
  year: 1971
  ident: 1882_CR45
  publication-title: Mgmt. Sci.
  doi: 10.1287/mnsc.18.1.98
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Snippet N -fold integer programs (IPs) form an important class of block-structured IPs for which increasingly fast algorithms have recently been developed and...
N-fold integer programs (IPs) form an important class of block-structured IPs for which increasingly fast algorithms have recently been developed and...
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SubjectTerms Algorithms
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Full Length Paper
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Theoretical
Title High-multiplicity N-fold IP via configuration LP
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