Streaming Algorithms for Maximizing Monotone Submodular Functions Under a Knapsack Constraint
In this paper, we consider the problem of maximizing a monotone submodular function subject to a knapsack constraint in the streaming setting. In particular, the elements arrive sequentially and at any point of time, the algorithm has access only to a small fraction of the data stored in primary mem...
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| Vydáno v: | Algorithmica Ročník 82; číslo 4; s. 1006 - 1032 |
|---|---|
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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01.04.2020
Springer Nature B.V |
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| ISSN: | 0178-4617, 1432-0541 |
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| Abstract | In this paper, we consider the problem of maximizing a monotone submodular function subject to a knapsack constraint in the streaming setting. In particular, the elements arrive sequentially and at any point of time, the algorithm has access only to a small fraction of the data stored in primary memory. For this problem, we propose a
(
0.363
-
ε
)
-approximation algorithm, requiring only a single pass through the data; moreover, we propose a
(
0.4
-
ε
)
-approximation algorithm requiring a constant number of passes through the data. The required memory space of both algorithms depends only on the size of the knapsack capacity and
ε
. |
|---|---|
| AbstractList | In this paper, we consider the problem of maximizing a monotone submodular function subject to a knapsack constraint in the streaming setting. In particular, the elements arrive sequentially and at any point of time, the algorithm has access only to a small fraction of the data stored in primary memory. For this problem, we propose a
(
0.363
-
ε
)
-approximation algorithm, requiring only a single pass through the data; moreover, we propose a
(
0.4
-
ε
)
-approximation algorithm requiring a constant number of passes through the data. The required memory space of both algorithms depends only on the size of the knapsack capacity and
ε
. In this paper, we consider the problem of maximizing a monotone submodular function subject to a knapsack constraint in the streaming setting. In particular, the elements arrive sequentially and at any point of time, the algorithm has access only to a small fraction of the data stored in primary memory. For this problem, we propose a (0.363-ε)-approximation algorithm, requiring only a single pass through the data; moreover, we propose a (0.4-ε)-approximation algorithm requiring a constant number of passes through the data. The required memory space of both algorithms depends only on the size of the knapsack capacity and ε. |
| Author | Kakimura, Naonori Huang, Chien-Chung Yoshida, Yuichi |
| Author_xml | – sequence: 1 givenname: Chien-Chung surname: Huang fullname: Huang, Chien-Chung organization: DIENS, École Normale Supérieure, Université PSL – sequence: 2 givenname: Naonori orcidid: 0000-0002-3918-3479 surname: Kakimura fullname: Kakimura, Naonori email: kakimura@math.keio.ac.jp organization: Department of Mathematics, Keio University – sequence: 3 givenname: Yuichi surname: Yoshida fullname: Yoshida, Yuichi organization: National Institute of Informatics |
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| Cites_doi | 10.1137/130920277 10.1145/2187836.2187888 10.1137/1.9781611973402.110 10.1145/956750.956769 10.1007/s10107-015-0900-7 10.1287/moor.1100.0463 10.1016/S0167-6377(03)00062-2 10.1007/BFb0121195 10.1145/2623330.2623637 10.1137/080733991 10.1137/110839655 10.1287/moor.7.3.410 10.1137/1.9781611974782.78 10.1007/978-3-662-47672-7_26 |
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| Keywords | Multiple-pass streaming Submodular functions Single-pass streaming Constant approximation |
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| References | Badanidiyuru, A., Mirzasoleiman, B., Karbasi, A., Krause, A.: Streaming submodular maximization: massive data summarization on the fly. In: Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), pp. 671–680 (2014) FilmusYWardJA tight combinatorial algorithm for submodular maximization subject to a matroid constraintSIAM J. Comput.2014432514542318305010.1137/130920277 Kempe, D., Kleinberg, J., Tardos, É.: Maximizing the spread of influence through a social network. In: Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), pp. 137–146 (2003) Kulik, A., Shachnai, H., Tamir, T.: Maximizing submodular set functions subject to multiple linear constraints. In: Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 545–554 (2013) CalinescuGChekuriCPálMVondrákJMaximizing a monotone submodular function subject to a matroid constraintSIAM J. Comput.201140617401766286319310.1137/080733991 LeeJSviridenkoMVondrákJSubmodular maximization over multiple matroids via generalized exchange propertiesMath. Oper. Res.2010354795806277751510.1287/moor.1100.0463 Soma, T., Kakimura, N., Inaba, K., Kawarabayashi, K.: Optimal budget allocation: theoretical guarantee and efficient algorithm. In: Proceedings of the 31st International Conference on Machine Learning (ICML), pp. 351–359 (2014) WolseyLMaximising real-valued submodular functions: primal and dual heuristics for location problemsMath. Oper. Res.1982741042566793210.1287/moor.7.3.410 KrauseASinghAPGuestrinCNear-optimal sensor placements in gaussian processes: theory, efficient algorithms and empirical studiesJ. Mach. Learn. Res.200892352841225.68192 Yu, Q., Xu, E.L., Cui, S.: Streaming algorithms for news and scientific literature recommendation: submodular maximization with a d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d$$\end{document}-knapsack constraint. In: IEEE Global Conference on Signal and Information Processing (2016) Badanidiyuru, A., Vondrák, J.: Fast algorithms for maximizing submodular functions. In: Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1497–1514 (2013) Lin, H., Bilmes, J.: Multi-document summarization via budgeted maximization of submodular functions. In: Proceedings of the 2010 Annual Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (NAACL-HLT), pp. 912–920 (2010) ChakrabartiAKaleSSubmodular maximization meets streaming: matchings, matroids, and moreMath. Program.20151541–2225247342193410.1007/s10107-015-0900-7 FisherMLNemhauserGLWolseyLAAn analysis of approximations for maximizing submodular set functions IIMath. Program. Study19788738751036910.1007/BFb0121195 Lin, H., Bilmes, J.: A class of submodular functions for document summarization. In: Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics: Human Language Technologies (ACL-HLT), pp. 510–520 (2011) LeeJMaximum Entropy Sampling, Encyclopedia of Environmetrics2006New YorkWiley12291234 Alon, N., Gamzu, I., Tennenholtz, M.: Optimizing budget allocation among channels and influencers. In: Proceedings of the 21st International Conference on World Wide Web (WWW), pp. 381–388 (2012) Chan, T.H.H., Huang, Z., Jiang, S.H.C., Kang, N., Tang, Z.G.: Online submodular maximization with free disposal: Randomization beats for partition matroids online. In: Proceedings of the 28th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1204–1223 (2017) ChekuriChandraGuptaShalmoliQuanrudKentStreaming Algorithms for Submodular Function MaximizationAutomata, Languages, and Programming2015Berlin, HeidelbergSpringer Berlin Heidelberg31833010.1007/978-3-662-47672-7_26 ChekuriCVondrákJZenklusenRSubmodular function maximization via the multilinear relaxation and contention resolution schemesSIAM J. Comput.201443618311879328128710.1137/110839655 SviridenkoMA note on maximizing a submodular set function subject to a knapsack constraintOper. Res. Lett.20043214143201710710.1016/S0167-6377(03)00062-2 628_CR6 G Calinescu (628_CR4) 2011; 40 A Krause (628_CR12) 2008; 9 628_CR2 628_CR3 J Lee (628_CR14) 2006 L Wolsey (628_CR20) 1982; 7 Chandra Chekuri (628_CR7) 2015 ML Fisher (628_CR10) 1978; 8 C Chekuri (628_CR8) 2014; 43 628_CR21 628_CR11 628_CR13 M Sviridenko (628_CR19) 2004; 32 628_CR16 628_CR17 Y Filmus (628_CR9) 2014; 43 628_CR18 628_CR1 A Chakrabarti (628_CR5) 2015; 154 J Lee (628_CR15) 2010; 35 |
| References_xml | – reference: Badanidiyuru, A., Mirzasoleiman, B., Karbasi, A., Krause, A.: Streaming submodular maximization: massive data summarization on the fly. In: Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), pp. 671–680 (2014) – reference: Lin, H., Bilmes, J.: Multi-document summarization via budgeted maximization of submodular functions. In: Proceedings of the 2010 Annual Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies (NAACL-HLT), pp. 912–920 (2010) – reference: SviridenkoMA note on maximizing a submodular set function subject to a knapsack constraintOper. Res. Lett.20043214143201710710.1016/S0167-6377(03)00062-2 – reference: LeeJSviridenkoMVondrákJSubmodular maximization over multiple matroids via generalized exchange propertiesMath. Oper. Res.2010354795806277751510.1287/moor.1100.0463 – reference: Badanidiyuru, A., Vondrák, J.: Fast algorithms for maximizing submodular functions. In: Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1497–1514 (2013) – reference: KrauseASinghAPGuestrinCNear-optimal sensor placements in gaussian processes: theory, efficient algorithms and empirical studiesJ. Mach. Learn. Res.200892352841225.68192 – reference: ChekuriCVondrákJZenklusenRSubmodular function maximization via the multilinear relaxation and contention resolution schemesSIAM J. Comput.201443618311879328128710.1137/110839655 – reference: Lin, H., Bilmes, J.: A class of submodular functions for document summarization. In: Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics: Human Language Technologies (ACL-HLT), pp. 510–520 (2011) – reference: CalinescuGChekuriCPálMVondrákJMaximizing a monotone submodular function subject to a matroid constraintSIAM J. Comput.201140617401766286319310.1137/080733991 – reference: Chan, T.H.H., Huang, Z., Jiang, S.H.C., Kang, N., Tang, Z.G.: Online submodular maximization with free disposal: Randomization beats for partition matroids online. In: Proceedings of the 28th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 1204–1223 (2017) – reference: Kempe, D., Kleinberg, J., Tardos, É.: Maximizing the spread of influence through a social network. In: Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), pp. 137–146 (2003) – reference: Soma, T., Kakimura, N., Inaba, K., Kawarabayashi, K.: Optimal budget allocation: theoretical guarantee and efficient algorithm. In: Proceedings of the 31st International Conference on Machine Learning (ICML), pp. 351–359 (2014) – reference: ChakrabartiAKaleSSubmodular maximization meets streaming: matchings, matroids, and moreMath. Program.20151541–2225247342193410.1007/s10107-015-0900-7 – reference: WolseyLMaximising real-valued submodular functions: primal and dual heuristics for location problemsMath. Oper. Res.1982741042566793210.1287/moor.7.3.410 – reference: Yu, Q., Xu, E.L., Cui, S.: Streaming algorithms for news and scientific literature recommendation: submodular maximization with a d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d$$\end{document}-knapsack constraint. In: IEEE Global Conference on Signal and Information Processing (2016) – reference: LeeJMaximum Entropy Sampling, Encyclopedia of Environmetrics2006New YorkWiley12291234 – reference: ChekuriChandraGuptaShalmoliQuanrudKentStreaming Algorithms for Submodular Function MaximizationAutomata, Languages, and Programming2015Berlin, HeidelbergSpringer Berlin Heidelberg31833010.1007/978-3-662-47672-7_26 – reference: Kulik, A., Shachnai, H., Tamir, T.: Maximizing submodular set functions subject to multiple linear constraints. In: Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 545–554 (2013) – reference: FilmusYWardJA tight combinatorial algorithm for submodular maximization subject to a matroid constraintSIAM J. Comput.2014432514542318305010.1137/130920277 – reference: FisherMLNemhauserGLWolseyLAAn analysis of approximations for maximizing submodular set functions IIMath. Program. Study19788738751036910.1007/BFb0121195 – reference: Alon, N., Gamzu, I., Tennenholtz, M.: Optimizing budget allocation among channels and influencers. In: Proceedings of the 21st International Conference on World Wide Web (WWW), pp. 381–388 (2012) – volume: 9 start-page: 235 year: 2008 ident: 628_CR12 publication-title: J. Mach. Learn. Res. – volume: 43 start-page: 514 issue: 2 year: 2014 ident: 628_CR9 publication-title: SIAM J. Comput. doi: 10.1137/130920277 – ident: 628_CR1 doi: 10.1145/2187836.2187888 – ident: 628_CR3 doi: 10.1137/1.9781611973402.110 – ident: 628_CR11 doi: 10.1145/956750.956769 – volume: 154 start-page: 225 issue: 1–2 year: 2015 ident: 628_CR5 publication-title: Math. Program. doi: 10.1007/s10107-015-0900-7 – volume: 35 start-page: 795 issue: 4 year: 2010 ident: 628_CR15 publication-title: Math. Oper. Res. doi: 10.1287/moor.1100.0463 – volume: 32 start-page: 41 issue: 1 year: 2004 ident: 628_CR19 publication-title: Oper. Res. Lett. doi: 10.1016/S0167-6377(03)00062-2 – volume: 8 start-page: 73 year: 1978 ident: 628_CR10 publication-title: Math. Program. Study doi: 10.1007/BFb0121195 – ident: 628_CR21 – ident: 628_CR16 – start-page: 1229 volume-title: Maximum Entropy Sampling, Encyclopedia of Environmetrics year: 2006 ident: 628_CR14 – ident: 628_CR2 doi: 10.1145/2623330.2623637 – volume: 40 start-page: 1740 issue: 6 year: 2011 ident: 628_CR4 publication-title: SIAM J. Comput. doi: 10.1137/080733991 – ident: 628_CR17 – ident: 628_CR18 – volume: 43 start-page: 1831 issue: 6 year: 2014 ident: 628_CR8 publication-title: SIAM J. Comput. doi: 10.1137/110839655 – ident: 628_CR13 – volume: 7 start-page: 410 year: 1982 ident: 628_CR20 publication-title: Math. Oper. Res. doi: 10.1287/moor.7.3.410 – ident: 628_CR6 doi: 10.1137/1.9781611974782.78 – start-page: 318 volume-title: Automata, Languages, and Programming year: 2015 ident: 628_CR7 doi: 10.1007/978-3-662-47672-7_26 |
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| Title | Streaming Algorithms for Maximizing Monotone Submodular Functions Under a Knapsack Constraint |
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