Submodular maximization subject to a knapsack constraint: Combinatorial algorithms with near-optimal adaptive complexity
Submodular maximization is a classic algorithmic problem with multiple applications in data mining and machine learning; there, the growing need to deal with massive instances motivates the design of algorithms balancing the quality of the solution with applicability. For the latter, an important me...
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| Published in: | Theoretical computer science Vol. 1060; p. 115629 |
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| Main Authors: | , , , , , |
| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
18.01.2026
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| ISSN: | 0304-3975 |
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| Abstract | Submodular maximization is a classic algorithmic problem with multiple applications in data mining and machine learning; there, the growing need to deal with massive instances motivates the design of algorithms balancing the quality of the solution with applicability. For the latter, an important measure is the adaptive complexity, which captures the number of sequential rounds of parallel computation needed by an algorithm to terminate. In this work, we obtain the first constant factor approximation algorithm for non-monotone submodular maximization subject to a knapsack constraint with near-optimal O(log n) adaptive complexity. Low adaptivity by itself, however, is not enough: a crucial feature to account for is represented by the total number of function evaluations (or value queries). Our algorithm asks O˜(n2) value queries but can be modified to run with only O˜(n), while retaining a low adaptive complexity of O(log2n). Besides the above improvement in adaptivity, this is also the first combinatorial approach with sublinear adaptive complexity for the problem and yields algorithms comparable to the state-of-the-art even for the special cases of cardinality constraints or monotone objectives. |
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| AbstractList | Submodular maximization is a classic algorithmic problem with multiple applications in data mining and machine learning; there, the growing need to deal with massive instances motivates the design of algorithms balancing the quality of the solution with applicability. For the latter, an important measure is the adaptive complexity, which captures the number of sequential rounds of parallel computation needed by an algorithm to terminate. In this work, we obtain the first constant factor approximation algorithm for non-monotone submodular maximization subject to a knapsack constraint with near-optimal O(log n) adaptive complexity. Low adaptivity by itself, however, is not enough: a crucial feature to account for is represented by the total number of function evaluations (or value queries). Our algorithm asks O˜(n2) value queries but can be modified to run with only O˜(n), while retaining a low adaptive complexity of O(log2n). Besides the above improvement in adaptivity, this is also the first combinatorial approach with sublinear adaptive complexity for the problem and yields algorithms comparable to the state-of-the-art even for the special cases of cardinality constraints or monotone objectives. |
| ArticleNumber | 115629 |
| Author | Leonardi, Stefano Amanatidis, Georgios Reiffenhäuser, Rebecca Fusco, Federico Lazos, Philip Marchetti-Spaccamela, Alberto |
| Author_xml | – sequence: 1 givenname: Georgios orcidid: 0000-0002-4341-5439 surname: Amanatidis fullname: Amanatidis, Georgios email: g.d.amanatidis@gmail.com organization: Department of Informatics, Athens University of Economics and Business, Greece; Archimedes Unit, Athena Research Center, Greece – sequence: 2 givenname: Federico orcidid: 0000-0001-6250-945X surname: Fusco fullname: Fusco, Federico email: federico.fusco@uniroma1.it organization: Department of Computer, Control, and Management Engineering “Antonio Ruberti”, Sapienza University of Rome, Italy – sequence: 3 givenname: Philip orcidid: 0000-0001-9684-7609 surname: Lazos fullname: Lazos, Philip email: plazos@gmail.com organization: Independent Researcher, London, United Kingdom – sequence: 4 givenname: Stefano orcidid: 0000-0002-9809-7191 surname: Leonardi fullname: Leonardi, Stefano email: leonardi@diag.uniroma1.it organization: Department of Computer, Control, and Management Engineering “Antonio Ruberti”, Sapienza University of Rome, Italy – sequence: 5 givenname: Alberto orcidid: 0000-0002-7991-4416 surname: Marchetti-Spaccamela fullname: Marchetti-Spaccamela, Alberto email: alberto@diag.uniroma1.it organization: Department of Computer, Control, and Management Engineering “Antonio Ruberti”, Sapienza University of Rome, Italy – sequence: 6 givenname: Rebecca orcidid: 0000-0002-0959-2589 surname: Reiffenhäuser fullname: Reiffenhäuser, Rebecca email: r.e.m.reiffenhauser@uva.nl organization: Institute for Logic, Language and Computation, University of Amsterdam, The Netherlands |
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| Cites_doi | 10.4086/toc.2015.v011a004 10.1007/BF01588971 10.1613/jair.1.13472 10.1613/jair.1.16801 10.1137/110839655 10.1287/moor.2013.0592 10.1145/285055.285059 10.1287/opre.2021.2170 10.1137/090779346 10.1016/S0167-6377(03)00062-2 |
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| References | Das, Kempe (bib0006) 2018; 19 Chen, Dey, Kuhnle (bib0035) 2021 Das, Kempe (bib0005) 2008 Nemhauser, Wolsey, Fisher (bib0013) 1978; 14 Breuer, Balkanski, Singer (bib0011) 2020; 119 Ene, Nguyen, Vladu (bib0037) 2018 Kulik, Shachnai, Tamir (bib0029) 2013; 38 Kempe, Kleinberg, Tardos (bib0002) 2015; 11 Amanatidis, Fusco, Lazos, Leonardi, Marchetti-Spaccamela, Reiffenhäuser (bib0042) 2021; 139 Dütting, Fusco, Lattanzi, Norouzi-Fard, Zadimoghaddam (bib0047) 2025; 26 Hartline, Mirrokni, Sundararajan (bib0001) 2008 Balkanski, Singer (bib0018) 2018 Feldman, Naor, Schwartz (bib0028) 2011 Feige (bib0027) 1998; 45 Cui, Han, Tang, Huang, Li, Zhiyuli (bib0023) 2023 Fahrbach, Mirrokni, Zadimoghaddam (bib0034) 2019 Chekuri, Quanrud (bib0039) 2019 Esfandiari, Karbasi, Mirrokni (bib0040) 2021; 134 Schrijver (bib0009) 2003; 24 Kazemi, Zadimoghaddam, Karbasi (bib0015) 2018; 80 Kuhnle (bib0025) 2021 Tschiatschek, Iyer, Wei, Bilmes (bib0003) 2014 Khanna, Elenberg, Dimakis, Negahban, Ghosh (bib0016) 2017; 54 Balkanski, Breuer, Singer (bib0017) 2018 Ene, Nguyen (bib0033) 2019 Minoux (bib0046) 1978 Mirzasoleiman, Bilmes, Leskovec (bib0007) 2020; 119 Balkanski, Rubinstein, Singer (bib0019) 2019 Buchbinder, Feldman (bib0010) 2018 Dueck, Frey (bib0014) 2007 Sviridenko (bib0026) 2004; 32 Ene, Nguyen, Vladu (bib0021) 2019 Buchbinder, Feldman, Naor, Schwartz (bib0045) 2014 Buchbinder, Feldman (bib0031) 2024 Chen, Feldman, Karbasi (bib0038) 2019 Balkanski, Rubinstein, Singer (bib0020) 2022; 70 Cui, Han, Tang, Li, Zhiyuli, Li (bib0043) 2025; 82 Dütting, Fusco, Lattanzi, Norouzi-Fard, Svensson, Zadimoghaddam (bib0049) 2025 Dütting, Fusco, Lattanzi, Norouzi-Fard, Zadimoghaddam (bib0048) 2025; 21 Mirzasoleiman, Badanidiyuru, Karbasi (bib0004) 2016; 48 Fahrbach, Mirrokni, Zadimoghaddam (bib0036) 2019; 97 Lattanzi, Mitrovic, Norouzi-Fard, Tarnawski, Zadimoghaddam (bib0041) 2020 Chekuri, Vondrák, Zenklusen (bib0030) 2014; 43 Mirzasoleiman, Karbasi, Sarkar, Krause (bib0008) 2013 Gupta, Roth, Schoenebeck, Talwar (bib0032) 2010; 6484 Ene, Nguyen (bib0024) 2020; 119 Amanatidis, Fusco, Lazos, Leonardi, Reiffenhäuser (bib0012) 2022; 74 Chekuri, Quanrud (bib0022) 2019 Feige, Mirrokni, Vondrák (bib0044) 2011; 40 Lattanzi (10.1016/j.tcs.2025.115629_bib0041) 2020 Tschiatschek (10.1016/j.tcs.2025.115629_bib0003) 2014 Esfandiari (10.1016/j.tcs.2025.115629_bib0040) 2021; 134 Dütting (10.1016/j.tcs.2025.115629_bib0048) 2025; 21 Gupta (10.1016/j.tcs.2025.115629_bib0032) 2010; 6484 Chen (10.1016/j.tcs.2025.115629_bib0035) 2021 Chen (10.1016/j.tcs.2025.115629_bib0038) 2019 Feige (10.1016/j.tcs.2025.115629_bib0044) 2011; 40 Breuer (10.1016/j.tcs.2025.115629_bib0011) 2020; 119 Feige (10.1016/j.tcs.2025.115629_bib0027) 1998; 45 Balkanski (10.1016/j.tcs.2025.115629_bib0018) 2018 Ene (10.1016/j.tcs.2025.115629_bib0021) 2019 Mirzasoleiman (10.1016/j.tcs.2025.115629_bib0007) 2020; 119 Minoux (10.1016/j.tcs.2025.115629_bib0046) 1978 Kazemi (10.1016/j.tcs.2025.115629_bib0015) 2018; 80 Cui (10.1016/j.tcs.2025.115629_bib0043) 2025; 82 Hartline (10.1016/j.tcs.2025.115629_bib0001) 2008 Balkanski (10.1016/j.tcs.2025.115629_bib0019) 2019 Fahrbach (10.1016/j.tcs.2025.115629_bib0034) 2019 Kuhnle (10.1016/j.tcs.2025.115629_bib0025) 2021 Ene (10.1016/j.tcs.2025.115629_bib0033) 2019 Kulik (10.1016/j.tcs.2025.115629_bib0029) 2013; 38 Buchbinder (10.1016/j.tcs.2025.115629_bib0045) 2014 Buchbinder (10.1016/j.tcs.2025.115629_bib0010) 2018 Feldman (10.1016/j.tcs.2025.115629_bib0028) 2011 Mirzasoleiman (10.1016/j.tcs.2025.115629_bib0004) 2016; 48 Das (10.1016/j.tcs.2025.115629_bib0006) 2018; 19 Amanatidis (10.1016/j.tcs.2025.115629_bib0042) 2021; 139 Chekuri (10.1016/j.tcs.2025.115629_bib0039) 2019 Dütting (10.1016/j.tcs.2025.115629_bib0049) 2025 Dueck (10.1016/j.tcs.2025.115629_bib0014) 2007 Ene (10.1016/j.tcs.2025.115629_bib0037) 2018 Mirzasoleiman (10.1016/j.tcs.2025.115629_bib0008) 2013 Fahrbach (10.1016/j.tcs.2025.115629_bib0036) 2019; 97 Amanatidis (10.1016/j.tcs.2025.115629_bib0012) 2022; 74 Das (10.1016/j.tcs.2025.115629_bib0005) 2008 Ene (10.1016/j.tcs.2025.115629_bib0024) 2020; 119 Nemhauser (10.1016/j.tcs.2025.115629_bib0013) 1978; 14 Buchbinder (10.1016/j.tcs.2025.115629_bib0031) 2024 Cui (10.1016/j.tcs.2025.115629_bib0023) 2023 Kempe (10.1016/j.tcs.2025.115629_bib0002) 2015; 11 Sviridenko (10.1016/j.tcs.2025.115629_bib0026) 2004; 32 Schrijver (10.1016/j.tcs.2025.115629_bib0009) 2003; 24 Dütting (10.1016/j.tcs.2025.115629_bib0047) 2025; 26 Chekuri (10.1016/j.tcs.2025.115629_bib0030) 2014; 43 Khanna (10.1016/j.tcs.2025.115629_bib0016) 2017; 54 Balkanski (10.1016/j.tcs.2025.115629_bib0017) 2018 Chekuri (10.1016/j.tcs.2025.115629_bib0022) 2019 Balkanski (10.1016/j.tcs.2025.115629_bib0020) 2022; 70 |
| References_xml | – start-page: 570 year: 2011 end-page: 579 ident: bib0028 article-title: A unified continuous greedy algorithm for submodular maximization publication-title: FOCS – volume: 19 start-page: 3:1 year: 2018 end-page: 3:34 ident: bib0006 article-title: Approximate submodularity and its applications: subset selection, sparse approximation and dictionary selection publication-title: J. Mach. Learn. Res. – start-page: 78 year: 2019 end-page: 89 ident: bib0039 article-title: Parallelizing greedy for submodular set function maximization in matroids and beyond publication-title: STOC – start-page: 189 year: 2008 end-page: 198 ident: bib0001 article-title: Optimal marketing strategies over social networks publication-title: WWW – volume: 45 start-page: 634 year: 1998 end-page: 652 ident: bib0027 article-title: A threshold of ln publication-title: J. ACM – volume: 80 start-page: 2549 year: 2018 end-page: 2558 ident: bib0015 article-title: Scalable deletion-robust submodular maximization: data summarization with privacy and fairness constraints publication-title: ICML – volume: 82 start-page: 39 year: 2025 end-page: 75 ident: bib0043 article-title: Practical parallel algorithms for non-monotone submodular maximization publication-title: J. Artif. Intell. Res. – start-page: 1820 year: 2024 end-page: 1831 ident: bib0031 article-title: Constrained submodular maximization via new bounds for DR-submodular functions publication-title: STOC – volume: 134 start-page: 1823 year: 2021 end-page: 1846 ident: bib0040 article-title: Adaptivity in adaptive submodularity publication-title: COLT – start-page: 2049 year: 2013 end-page: 2057 ident: bib0008 article-title: Distributed submodular maximization: identifying representative elements in massive data publication-title: NIPS – year: 2018 ident: bib0037 article-title: A parallel double greedy algorithm for submodular maximization publication-title: CoRR:abs/1812.01591 – volume: 119 start-page: 1134 year: 2020 end-page: 1143 ident: bib0011 article-title: The FAST algorithm for submodular maximization publication-title: ICML – start-page: 303 year: 2019 end-page: 322 ident: bib0022 article-title: Submodular function maximization in parallel via the multilinear relaxation publication-title: SODA – volume: 24 year: 2003 ident: bib0009 article-title: Combinatorial Optimization: Polyhedra and Efficiency – volume: 97 start-page: 1833 year: 2019 end-page: 1842 ident: bib0036 article-title: Non-monotone submodular maximization with nearly optimal adaptivity and query complexity publication-title: ICML – start-page: 1433 year: 2014 end-page: 1452 ident: bib0045 article-title: Submodular maximization with cardinality constraints publication-title: SODA – start-page: 2359 year: 2018 end-page: 2370 ident: bib0017 article-title: Non-monotone submodular maximization in exponentially fewer iterations publication-title: NeurIPS – start-page: 234 year: 1978 end-page: 243 ident: bib0046 article-title: Accelerated greedy algorithms for maximizing submodular set functions publication-title: Optimization Techniques – start-page: 753 year: 2018 end-page: 788 ident: bib0010 article-title: Submodular functions maximization problems publication-title: Handbook of Approximation Algorithms and Metaheuristics (1) – volume: 11 start-page: 105 year: 2015 end-page: 147 ident: bib0002 article-title: Maximizing the spread of influence through a social network publication-title: Theory Comput. – volume: 70 start-page: 2967 year: 2022 end-page: 2981 ident: bib0020 article-title: An optimal approximation for submodular maximization under a matroid constraint in the adaptive complexity model publication-title: Oper. Res. – start-page: 102 year: 2019 end-page: 113 ident: bib0038 article-title: Unconstrained submodular maximization with constant adaptive complexity publication-title: STOC – volume: 48 start-page: 1358 year: 2016 end-page: 1367 ident: bib0004 article-title: Fast constrained submodular maximization: personalized data summarization publication-title: ICML – start-page: 8200 year: 2021 end-page: 8208 ident: bib0025 article-title: Nearly linear-time, parallelizable algorithms for non-monotone submodular maximization publication-title: AAAI – start-page: 1413 year: 2014 end-page: 1421 ident: bib0003 article-title: Learning mixtures of submodular functions for image collection summarization publication-title: NIPS – volume: 40 start-page: 1133 year: 2011 end-page: 1153 ident: bib0044 article-title: Maximizing non-monotone submodular functions publication-title: SIAM J. Comput. – volume: 54 start-page: 1560 year: 2017 end-page: 1568 ident: bib0016 article-title: Scalable greedy feature selection via weak submodularity publication-title: AISTATS – volume: 119 start-page: 6950 year: 2020 end-page: 6960 ident: bib0007 article-title: Coresets for data-efficient training of machine learning models publication-title: ICML – volume: 26 start-page: 1 year: 2025 end-page: 28 ident: bib0047 article-title: Deletion robust non-monotone submodular maximization over matroids publication-title: J. Mac. Learn. Res. – start-page: 283 year: 2019 end-page: 302 ident: bib0019 article-title: An exponential speedup in parallel running time for submodular maximization without loss in approximation publication-title: Soda – start-page: 7261 year: 2023 end-page: 7269 ident: bib0023 article-title: Practical parallel algorithms for submodular maximization subject to a knapsack constraint with nearly optimal adaptivity publication-title: AAAI – start-page: 25528 year: 2021 end-page: 25539 ident: bib0035 article-title: Best of both worlds: practical and theoretically optimal submodular maximization in parallel publication-title: NeurIPS – volume: 119 start-page: 2902 year: 2020 end-page: 2911 ident: bib0024 article-title: Parallel algorithm for non-monotone DR-submodular maximization publication-title: ICML – volume: 139 start-page: 231 year: 2021 end-page: 242 ident: bib0042 article-title: Submodular maximization subject to a knapsack constraint: combinatorial algorithms with near-optimal adaptive complexity publication-title: ICML – volume: 74 start-page: 661 year: 2022 end-page: 690 ident: bib0012 article-title: Fast adaptive non-Monotone submodular maximization subject to a knapsack constraint publication-title: J. Artif. Intell. Res. – volume: 14 start-page: 265 year: 1978 end-page: 294 ident: bib0013 article-title: An analysis of approximations for maximizing submodular set functions - i publication-title: Math. Program. – start-page: 1 year: 2007 end-page: 8 ident: bib0014 article-title: Non-metric affinity propagation for unsupervised image categorization publication-title: ICCV – start-page: 255 year: 2019 end-page: 273 ident: bib0034 article-title: Submodular maximization with nearly optimal approximation, adaptivity and query complexity publication-title: SODA – year: 2020 ident: bib0041 article-title: Fully dynamic algorithm for constrained submodular optimization publication-title: NeurIPS – start-page: 1406 year: 2025 end-page: 1417 ident: bib0049 article-title: The cost of consistency: submodular maximization with constant recourse publication-title: STOC – start-page: 45 year: 2008 end-page: 54 ident: bib0005 article-title: Algorithms for subset selection in linear regression publication-title: STOC – start-page: 274 year: 2019 end-page: 282 ident: bib0033 article-title: Submodular maximization with nearly-optimal approximation and adaptivity in nearly-linear time publication-title: SODA – volume: 32 start-page: 41 year: 2004 end-page: 43 ident: bib0026 article-title: A note on maximizing a submodular set function subject to a knapsack constraint publication-title: Oper. Res. Lett. – volume: 21 start-page: 11:1 year: 2025 end-page: 11:23 ident: bib0048 article-title: Fully dynamic submodular maximization over matroids publication-title: ACM Trans. Algor. – start-page: 1138 year: 2018 end-page: 1151 ident: bib0018 article-title: The adaptive complexity of maximizing a submodular function publication-title: STOC – volume: 43 start-page: 1831 year: 2014 end-page: 1879 ident: bib0030 article-title: Submodular function maximization via the multilinear relaxation and contention resolution schemes publication-title: SIAM J. Comput. – volume: 38 start-page: 729 year: 2013 end-page: 739 ident: bib0029 article-title: Approximations for monotone and nonmonotone submodular maximization with knapsack constraints publication-title: Math. Oper. Res. – volume: 6484 start-page: 246 year: 2010 end-page: 257 ident: bib0032 article-title: Constrained non-monotone submodular maximization: offline and secretary algorithms publication-title: WINE – start-page: 90 year: 2019 end-page: 101 ident: bib0021 article-title: Submodular maximization with matroid and packing constraints in parallel publication-title: STOC – volume: 11 start-page: 105 year: 2015 ident: 10.1016/j.tcs.2025.115629_bib0002 article-title: Maximizing the spread of influence through a social network publication-title: Theory Comput. doi: 10.4086/toc.2015.v011a004 – year: 2020 ident: 10.1016/j.tcs.2025.115629_bib0041 article-title: Fully dynamic algorithm for constrained submodular optimization – start-page: 1433 year: 2014 ident: 10.1016/j.tcs.2025.115629_bib0045 article-title: Submodular maximization with cardinality constraints – volume: 119 start-page: 1134 year: 2020 ident: 10.1016/j.tcs.2025.115629_bib0011 article-title: The FAST algorithm for submodular maximization – start-page: 2359 year: 2018 ident: 10.1016/j.tcs.2025.115629_bib0017 article-title: Non-monotone submodular maximization in exponentially fewer iterations – start-page: 255 year: 2019 ident: 10.1016/j.tcs.2025.115629_bib0034 article-title: Submodular maximization with nearly optimal approximation, adaptivity and query complexity – volume: 119 start-page: 2902 year: 2020 ident: 10.1016/j.tcs.2025.115629_bib0024 article-title: Parallel algorithm for non-monotone DR-submodular maximization – start-page: 78 year: 2019 ident: 10.1016/j.tcs.2025.115629_bib0039 article-title: Parallelizing greedy for submodular set function maximization in matroids and beyond – start-page: 283 year: 2019 ident: 10.1016/j.tcs.2025.115629_bib0019 article-title: An exponential speedup in parallel running time for submodular maximization without loss in approximation – start-page: 8200 year: 2021 ident: 10.1016/j.tcs.2025.115629_bib0025 article-title: Nearly linear-time, parallelizable algorithms for non-monotone submodular maximization – volume: 54 start-page: 1560 year: 2017 ident: 10.1016/j.tcs.2025.115629_bib0016 article-title: Scalable greedy feature selection via weak submodularity – start-page: 1138 year: 2018 ident: 10.1016/j.tcs.2025.115629_bib0018 article-title: The adaptive complexity of maximizing a submodular function – start-page: 7261 year: 2023 ident: 10.1016/j.tcs.2025.115629_bib0023 article-title: Practical parallel algorithms for submodular maximization subject to a knapsack constraint with nearly optimal adaptivity – start-page: 1820 year: 2024 ident: 10.1016/j.tcs.2025.115629_bib0031 article-title: Constrained submodular maximization via new bounds for DR-submodular functions – start-page: 1413 year: 2014 ident: 10.1016/j.tcs.2025.115629_bib0003 article-title: Learning mixtures of submodular functions for image collection summarization – start-page: 570 year: 2011 ident: 10.1016/j.tcs.2025.115629_bib0028 article-title: A unified continuous greedy algorithm for submodular maximization – volume: 24 year: 2003 ident: 10.1016/j.tcs.2025.115629_bib0009 – start-page: 102 year: 2019 ident: 10.1016/j.tcs.2025.115629_bib0038 article-title: Unconstrained submodular maximization with constant adaptive complexity – start-page: 303 year: 2019 ident: 10.1016/j.tcs.2025.115629_bib0022 article-title: Submodular function maximization in parallel via the multilinear relaxation – volume: 139 start-page: 231 year: 2021 ident: 10.1016/j.tcs.2025.115629_bib0042 article-title: Submodular maximization subject to a knapsack constraint: combinatorial algorithms with near-optimal adaptive complexity – volume: 14 start-page: 265 issue: 1 year: 1978 ident: 10.1016/j.tcs.2025.115629_bib0013 article-title: An analysis of approximations for maximizing submodular set functions - i publication-title: Math. Program. doi: 10.1007/BF01588971 – start-page: 189 year: 2008 ident: 10.1016/j.tcs.2025.115629_bib0001 article-title: Optimal marketing strategies over social networks – volume: 48 start-page: 1358 year: 2016 ident: 10.1016/j.tcs.2025.115629_bib0004 article-title: Fast constrained submodular maximization: personalized data summarization – start-page: 25528 year: 2021 ident: 10.1016/j.tcs.2025.115629_bib0035 article-title: Best of both worlds: practical and theoretically optimal submodular maximization in parallel – volume: 74 start-page: 661 year: 2022 ident: 10.1016/j.tcs.2025.115629_bib0012 article-title: Fast adaptive non-Monotone submodular maximization subject to a knapsack constraint publication-title: J. Artif. Intell. Res. doi: 10.1613/jair.1.13472 – start-page: 234 year: 1978 ident: 10.1016/j.tcs.2025.115629_bib0046 article-title: Accelerated greedy algorithms for maximizing submodular set functions – volume: 19 start-page: 3:1 year: 2018 ident: 10.1016/j.tcs.2025.115629_bib0006 article-title: Approximate submodularity and its applications: subset selection, sparse approximation and dictionary selection publication-title: J. Mach. Learn. Res. – start-page: 2049 year: 2013 ident: 10.1016/j.tcs.2025.115629_bib0008 article-title: Distributed submodular maximization: identifying representative elements in massive data – volume: 82 start-page: 39 year: 2025 ident: 10.1016/j.tcs.2025.115629_bib0043 article-title: Practical parallel algorithms for non-monotone submodular maximization publication-title: J. Artif. Intell. Res. doi: 10.1613/jair.1.16801 – volume: 43 start-page: 1831 issue: 6 year: 2014 ident: 10.1016/j.tcs.2025.115629_bib0030 article-title: Submodular function maximization via the multilinear relaxation and contention resolution schemes publication-title: SIAM J. Comput. doi: 10.1137/110839655 – start-page: 1 year: 2007 ident: 10.1016/j.tcs.2025.115629_bib0014 article-title: Non-metric affinity propagation for unsupervised image categorization – volume: 6484 start-page: 246 year: 2010 ident: 10.1016/j.tcs.2025.115629_bib0032 article-title: Constrained non-monotone submodular maximization: offline and secretary algorithms – start-page: 274 year: 2019 ident: 10.1016/j.tcs.2025.115629_bib0033 article-title: Submodular maximization with nearly-optimal approximation and adaptivity in nearly-linear time – volume: 97 start-page: 1833 year: 2019 ident: 10.1016/j.tcs.2025.115629_bib0036 article-title: Non-monotone submodular maximization with nearly optimal adaptivity and query complexity – volume: 26 start-page: 1 issue: 66 year: 2025 ident: 10.1016/j.tcs.2025.115629_bib0047 article-title: Deletion robust non-monotone submodular maximization over matroids publication-title: J. Mac. Learn. Res. – volume: 80 start-page: 2549 year: 2018 ident: 10.1016/j.tcs.2025.115629_bib0015 article-title: Scalable deletion-robust submodular maximization: data summarization with privacy and fairness constraints – year: 2018 ident: 10.1016/j.tcs.2025.115629_bib0037 article-title: A parallel double greedy algorithm for submodular maximization publication-title: CoRR:abs/1812.01591 – volume: 38 start-page: 729 issue: 4 year: 2013 ident: 10.1016/j.tcs.2025.115629_bib0029 article-title: Approximations for monotone and nonmonotone submodular maximization with knapsack constraints publication-title: Math. Oper. Res. doi: 10.1287/moor.2013.0592 – volume: 21 start-page: 11:1 issue: 1 year: 2025 ident: 10.1016/j.tcs.2025.115629_bib0048 article-title: Fully dynamic submodular maximization over matroids publication-title: ACM Trans. Algor. – volume: 119 start-page: 6950 year: 2020 ident: 10.1016/j.tcs.2025.115629_bib0007 article-title: Coresets for data-efficient training of machine learning models – volume: 45 start-page: 634 issue: 4 year: 1998 ident: 10.1016/j.tcs.2025.115629_bib0027 article-title: A threshold of ln n for approximating set cover publication-title: J. ACM doi: 10.1145/285055.285059 – start-page: 90 year: 2019 ident: 10.1016/j.tcs.2025.115629_bib0021 article-title: Submodular maximization with matroid and packing constraints in parallel – volume: 70 start-page: 2967 issue: 5 year: 2022 ident: 10.1016/j.tcs.2025.115629_bib0020 article-title: An optimal approximation for submodular maximization under a matroid constraint in the adaptive complexity model publication-title: Oper. Res. doi: 10.1287/opre.2021.2170 – volume: 40 start-page: 1133 issue: 4 year: 2011 ident: 10.1016/j.tcs.2025.115629_bib0044 article-title: Maximizing non-monotone submodular functions publication-title: SIAM J. Comput. doi: 10.1137/090779346 – start-page: 1406 year: 2025 ident: 10.1016/j.tcs.2025.115629_bib0049 article-title: The cost of consistency: submodular maximization with constant recourse – start-page: 45 year: 2008 ident: 10.1016/j.tcs.2025.115629_bib0005 article-title: Algorithms for subset selection in linear regression – volume: 32 start-page: 41 issue: 1 year: 2004 ident: 10.1016/j.tcs.2025.115629_bib0026 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: 134 start-page: 1823 year: 2021 ident: 10.1016/j.tcs.2025.115629_bib0040 article-title: Adaptivity in adaptive submodularity – start-page: 753 year: 2018 ident: 10.1016/j.tcs.2025.115629_bib0010 article-title: Submodular functions maximization problems |
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