Multiple knapsack-constrained monotone DR-submodular maximization on distributive lattice Continuous Greedy Algorithm on Median Complex

We consider a problem of maximizing a monotone DR-submodular function under multiple order-consistent knapsack constraints on a distributive lattice. Because a distributive lattice is used to represent a dependency constraint, the problem can represent a dependency constrained version of a submodula...

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Vydáno v:	Mathematical programming Ročník 194; číslo 1-2; s. 85 - 119
Hlavní autoři:	Maehara, Takanori, Nakashima, So, Yamaguchi, Yutaro
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2022
Témata:	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 90C27 (Mathematical programming; Combinatorial Optimization) Distributive lattices Continuous greedy Median complex Submodular maximization 68W25 (Algorithms in computer science; Approximation Algorithm) 06D99 (Distributive lattices; None of the above, but in this section)
ISSN:	0025-5610, 1436-4646
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Abstract	We consider a problem of maximizing a monotone DR-submodular function under multiple order-consistent knapsack constraints on a distributive lattice. Because a distributive lattice is used to represent a dependency constraint, the problem can represent a dependency constrained version of a submodular maximization problem on a set. We propose a ( 1 - 1 / e )-approximation algorithm for this problem. To achieve this result, we generalize the continuous greedy algorithm to distributive lattices: We choose a median complex as a continuous relaxation of the distributive lattice and define the multilinear extension on it. We show that the median complex admits special curves, named uniform linear motions . The multilinear extension of a DR-submodular function is concave along a positive uniform linear motion, which is a key property used in the continuous greedy algorithm.
AbstractList	We consider a problem of maximizing a monotone DR-submodular function under multiple order-consistent knapsack constraints on a distributive lattice. Because a distributive lattice is used to represent a dependency constraint, the problem can represent a dependency constrained version of a submodular maximization problem on a set. We propose a ( 1 - 1 / e )-approximation algorithm for this problem. To achieve this result, we generalize the continuous greedy algorithm to distributive lattices: We choose a median complex as a continuous relaxation of the distributive lattice and define the multilinear extension on it. We show that the median complex admits special curves, named uniform linear motions . The multilinear extension of a DR-submodular function is concave along a positive uniform linear motion, which is a key property used in the continuous greedy algorithm.
Author	Maehara, Takanori Nakashima, So Yamaguchi, Yutaro
Author_xml	– sequence: 1 givenname: Takanori orcidid: 0000-0002-2101-1484 surname: Maehara fullname: Maehara, Takanori email: takanori.maehara@riken.jp organization: RIKEN AIP – sequence: 2 givenname: So surname: Nakashima fullname: Nakashima, So organization: The University of Tokyo – sequence: 3 givenname: Yutaro surname: Yamaguchi fullname: Yamaguchi, Yutaro organization: Kyushu University
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Cites_doi	10.1177/0278364904045468 10.1016/0166-218X(84)90003-9 10.1007/s10107-018-1324-y 10.1137/080733991 10.1007/BF01588971 10.1090/conm/453/08795 10.1006/aama.1998.0583 10.1287/opre.26.2.305 10.1007/978-3-662-12494-9 10.1023/B:JOCO.0000038913.96607.c2 10.2140/agt.2010.10.2277 10.1137/110839655 10.1016/S0167-6377(03)00062-2 10.1287/mnsc.23.8.789 10.1137/1.9781611973068.60 10.1017/CBO9781139177801.004 10.1109/CDC.2010.5717225 10.1145/1374376.1374389 10.1007/978-3-319-28684-6_12 10.1006/aama.1999.0677 10.1007/978-3-642-68874-4_10 10.1198/000313002119 10.1080/01621459.1963.10500830 10.1145/2187836.2187888 10.1609/aaai.v33i01.33014618
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Keywords	90C27 (Mathematical programming; Combinatorial Optimization) Distributive lattices Continuous greedy Median complex Submodular maximization 68W25 (Algorithms in computer science; Approximation Algorithm) 06D99 (Distributive lattices; None of the above, but in this section)
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References	Grätzer (CR18) 2002 Cornnejols, Fisher, Nemhauser (CR13) 1977; 23 Ageev, Sviridenko (CR2) 2004; 8 Calinescu, Chekuri, Pál, Vondrák (CR8) 2011; 40 CR19 CR17 CR16 CR14 CR35 CR11 CR31 Hirai (CR20) 2018; 61 CR30 Chekuri, Vondrák, Zenklusen (CR10) 2014; 43 Bandelt, Chepoi (CR4) 2008; 453 Abrams, Ghrist (CR1) 2004; 23 Bridson, Haefliger (CR7) 1999 CR3 Brady, McCammond (CR6) 2010; 10 CR28 CR9 CR26 Soma, Yoshida (CR32) 2018; 172 Fujishige, Tomizawa (CR15) 1983; 26 CR25 CR24 Nemhauser, Wolsey, Fisher (CR29) 1978; 14 CR23 CR22 CR21 Murota (CR27) 2016; 1 Topkis (CR34) 1978; 26 Sviridenko (CR33) 2004; 32 Conforti, Cornuéjols (CR12) 1984; 7 Barnabei, Nicoletti, Pezzoli (CR5) 1998; 21 AA Ageev (1620_CR2) 2004; 8 G Grätzer (1620_CR18) 2002 1620_CR28 MR Bridson (1620_CR7) 1999 1620_CR9 HJ Bandelt (1620_CR4) 2008; 453 1620_CR3 T Soma (1620_CR32) 2018; 172 G Cornnejols (1620_CR13) 1977; 23 M Sviridenko (1620_CR33) 2004; 32 C Chekuri (1620_CR10) 2014; 43 S Fujishige (1620_CR15) 1983; 26 GL Nemhauser (1620_CR29) 1978; 14 DM Topkis (1620_CR34) 1978; 26 H Hirai (1620_CR20) 2018; 61 1620_CR22 1620_CR21 M Conforti (1620_CR12) 1984; 7 1620_CR26 M Barnabei (1620_CR5) 1998; 21 1620_CR25 1620_CR24 A Abrams (1620_CR1) 2004; 23 1620_CR23 1620_CR19 1620_CR17 1620_CR16 G Calinescu (1620_CR8) 2011; 40 T Brady (1620_CR6) 2010; 10 K Murota (1620_CR27) 2016; 1 1620_CR11 1620_CR31 1620_CR30 1620_CR14 1620_CR35
References_xml	– ident: CR22 – volume: 23 start-page: 811 issue: 7–8 year: 2004 end-page: 826 ident: CR1 article-title: State complexes for metamorphic robots publication-title: Int. J. Robot. Res. doi: 10.1177/0278364904045468 – volume: 7 start-page: 251 issue: 3 year: 1984 end-page: 274 ident: CR12 article-title: Submodular set functions, matroids and the greedy algorithm: tight worst-case bounds and some generalizations of the rado-edmonds theorem publication-title: Discrete Appl. Math. doi: 10.1016/0166-218X(84)90003-9 – ident: CR14 – ident: CR16 – ident: CR30 – volume: 172 start-page: 539 issue: 1–2 year: 2018 end-page: 563 ident: CR32 article-title: Maximizing monotone submodular functions over the integer lattice publication-title: Math. Program. doi: 10.1007/s10107-018-1324-y – volume: 40 start-page: 1740 issue: 6 year: 2011 end-page: 1766 ident: CR8 article-title: Maximizing a monotone submodular function subject to a matroid constraint publication-title: SIAM J. Comput. doi: 10.1137/080733991 – ident: CR35 – ident: CR25 – ident: CR23 – volume: 26 start-page: 309 issue: 4 year: 1983 end-page: 318 ident: CR15 article-title: A note on submodular functions on distributive lattices publication-title: J. Oper. Res. Soc. Jpn. – ident: CR21 – ident: CR19 – volume: 1 start-page: 151 issue: 1 year: 2016 end-page: 273 ident: CR27 article-title: Discrete convex analysis: a tool for economics and game theory publication-title: J. Mech. Inst. Des. – volume: 14 start-page: 265 issue: 1 year: 1978 end-page: 294 ident: CR29 article-title: An analysis of approximations for maximizing submodular set functions-I publication-title: Math. Program. doi: 10.1007/BF01588971 – ident: CR3 – volume: 453 start-page: 49 year: 2008 end-page: 86 ident: CR4 article-title: Metric graph theory and geometry: a survey publication-title: Contemp. Math. doi: 10.1090/conm/453/08795 – ident: CR17 – volume: 21 start-page: 78 issue: 1 year: 1998 end-page: 112 ident: CR5 article-title: Matroids on partially ordered sets publication-title: Adv. Appl. Math. doi: 10.1006/aama.1998.0583 – ident: CR31 – volume: 26 start-page: 305 issue: 2 year: 1978 end-page: 321 ident: CR34 article-title: Minimizing a submodular function on a lattice publication-title: Oper. Res. doi: 10.1287/opre.26.2.305 – ident: CR11 – year: 1999 ident: CR7 publication-title: Metric Spaces of Non-positive Curvature doi: 10.1007/978-3-662-12494-9 – ident: CR9 – volume: 8 start-page: 307 issue: 3 year: 2004 end-page: 328 ident: CR2 article-title: Pipage rounding: a new method of constructing algorithms with proven performance guarantee publication-title: J. Comb. Optim. doi: 10.1023/B:JOCO.0000038913.96607.c2 – year: 2002 ident: CR18 publication-title: General Lattice Theory – volume: 10 start-page: 2277 issue: 4 year: 2010 end-page: 2314 ident: CR6 article-title: Braids, posets and orthoschemes publication-title: Algebraic Geom. Topol. doi: 10.2140/agt.2010.10.2277 – volume: 43 start-page: 1831 issue: 6 year: 2014 end-page: 1879 ident: CR10 article-title: Submodular function maximization via the multilinear relaxation and contention resolution schemes publication-title: SIAM J. Comput. doi: 10.1137/110839655 – volume: 32 start-page: 41 issue: 1 year: 2004 end-page: 43 ident: CR33 article-title: A note on maximizing a submodular set function subject to a knapsack constraint publication-title: Oper. Res. Lett. doi: 10.1016/S0167-6377(03)00062-2 – volume: 61 start-page: 71 issue: 1 year: 2018 end-page: 109 ident: CR20 article-title: L-convexity on graph structures publication-title: J. Oper. Res. Soc. Jpn. – ident: CR28 – ident: CR26 – ident: CR24 – volume: 23 start-page: 789 year: 1977 end-page: 810 ident: CR13 article-title: Location of bank accounts of optimize float: an analytic study of exact and approximate algorithm publication-title: Manag. Sci. doi: 10.1287/mnsc.23.8.789 – ident: 1620_CR23 doi: 10.1137/1.9781611973068.60 – volume-title: General Lattice Theory year: 2002 ident: 1620_CR18 – volume: 7 start-page: 251 issue: 3 year: 1984 ident: 1620_CR12 publication-title: Discrete Appl. Math. doi: 10.1016/0166-218X(84)90003-9 – volume: 26 start-page: 309 issue: 4 year: 1983 ident: 1620_CR15 publication-title: J. Oper. Res. Soc. Jpn. – volume: 61 start-page: 71 issue: 1 year: 2018 ident: 1620_CR20 publication-title: J. Oper. Res. Soc. Jpn. – volume: 40 start-page: 1740 issue: 6 year: 2011 ident: 1620_CR8 publication-title: SIAM J. Comput. doi: 10.1137/080733991 – volume: 453 start-page: 49 year: 2008 ident: 1620_CR4 publication-title: Contemp. Math. doi: 10.1090/conm/453/08795 – ident: 1620_CR26 – ident: 1620_CR24 – ident: 1620_CR22 doi: 10.1017/CBO9781139177801.004 – volume: 10 start-page: 2277 issue: 4 year: 2010 ident: 1620_CR6 publication-title: Algebraic Geom. Topol. doi: 10.2140/agt.2010.10.2277 – ident: 1620_CR31 doi: 10.1109/CDC.2010.5717225 – volume: 8 start-page: 307 issue: 3 year: 2004 ident: 1620_CR2 publication-title: J. Comb. Optim. doi: 10.1023/B:JOCO.0000038913.96607.c2 – ident: 1620_CR35 doi: 10.1145/1374376.1374389 – ident: 1620_CR9 – volume: 14 start-page: 265 issue: 1 year: 1978 ident: 1620_CR29 publication-title: Math. Program. doi: 10.1007/BF01588971 – volume: 21 start-page: 78 issue: 1 year: 1998 ident: 1620_CR5 publication-title: Adv. Appl. Math. doi: 10.1006/aama.1998.0583 – ident: 1620_CR19 – volume: 172 start-page: 539 issue: 1–2 year: 2018 ident: 1620_CR32 publication-title: Math. Program. doi: 10.1007/s10107-018-1324-y – volume: 43 start-page: 1831 issue: 6 year: 2014 ident: 1620_CR10 publication-title: SIAM J. Comput. doi: 10.1137/110839655 – ident: 1620_CR30 – ident: 1620_CR17 doi: 10.1007/978-3-319-28684-6_12 – ident: 1620_CR11 doi: 10.1006/aama.1999.0677 – volume: 26 start-page: 305 issue: 2 year: 1978 ident: 1620_CR34 publication-title: Oper. Res. doi: 10.1287/opre.26.2.305 – volume: 1 start-page: 151 issue: 1 year: 2016 ident: 1620_CR27 publication-title: J. Mech. Inst. Des. – ident: 1620_CR25 doi: 10.1007/978-3-642-68874-4_10 – ident: 1620_CR16 doi: 10.1198/000313002119 – ident: 1620_CR21 doi: 10.1080/01621459.1963.10500830 – volume: 23 start-page: 789 year: 1977 ident: 1620_CR13 publication-title: Manag. Sci. doi: 10.1287/mnsc.23.8.789 – volume: 23 start-page: 811 issue: 7–8 year: 2004 ident: 1620_CR1 publication-title: Int. J. Robot. Res. doi: 10.1177/0278364904045468 – ident: 1620_CR3 doi: 10.1145/2187836.2187888 – volume: 32 start-page: 41 issue: 1 year: 2004 ident: 1620_CR33 publication-title: Oper. Res. Lett. doi: 10.1016/S0167-6377(03)00062-2 – volume-title: Metric Spaces of Non-positive Curvature year: 1999 ident: 1620_CR7 doi: 10.1007/978-3-662-12494-9 – ident: 1620_CR14 – ident: 1620_CR28 doi: 10.1609/aaai.v33i01.33014618
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Snippet	We consider a problem of maximizing a monotone DR-submodular function under multiple order-consistent knapsack constraints on a distributive lattice. Because a...
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SubjectTerms	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
Subtitle	Continuous Greedy Algorithm on Median Complex
Title	Multiple knapsack-constrained monotone DR-submodular maximization on distributive lattice
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