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Submodular Maximization Beyond Non-negativity: Guarantees, Fast Algorithms, and Applications [article]

Christopher Harshaw and Moran Feldman and Justin Ward and Amin Karbasi
<span title="2019-04-19">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper, we show that once the function is expressed as the difference f = g - c, where g is monotone, non-negative, and γ-weakly submodular and c is non-negative modular, then strong approximation  ...  It is generally believed that submodular functions -- and the more general class of γ-weakly submodular functions -- may only be optimized under the non-negativity assumption f(S) ≥ 0.  ...  Conclusion We presented a suite of fast algorithms for maximizing the difference between a nonnegative monotone γ-weakly submodular g and a non-negative modular c in both the cardinality constrained and  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1904.09354v1">arXiv:1904.09354v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qa7wpf264ve4zf5pbt3tzihvqa">fatcat:qa7wpf264ve4zf5pbt3tzihvqa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200831070856/https://arxiv.org/pdf/1904.09354v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/43/57/4357cb6e7b0c73a975c555e84017415a538ca054.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1904.09354v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Continuous Submodular Maximization: Beyond DR-Submodularity [article]

Moran Feldman, Amin Karbasi
<span title="2020-06-21">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper, we propose the first continuous optimization algorithms that achieve a constant factor approximation guarantee for the problem of monotone continuous submodular maximization subject to a  ...  We first prove that a simple variant of the vanilla coordinate ascent, called Coordinate-Ascent+, achieves a (e-1/2e-1-ε)-approximation guarantee while performing O(n/ε) iterations, where the computational  ...  (namely, maximizing a non-negative monontone discrete submodular function subject to a knapsack constraint) using O(n 4 ) function evaluations.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2006.11726v1">arXiv:2006.11726v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lybjh5up3rgjpnokxqfctdpqzq">fatcat:lybjh5up3rgjpnokxqfctdpqzq</a> </span>
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Nearly Linear Time Deterministic Algorithms for Submodular Maximization Under Knapsack Constraint and Beyond [article]

Wenxin Li
<span title="2020-12-21">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this work, we study the classic submodular maximization problem under knapsack constraints and beyond.  ...  Lastly we present nearly linear time algorithms for the intersection of p-system and d knapsack constraint, we achieve approximation ratio of (1/(p+7/4d+1)-ε) for monotone objective and (p/(p+1)(2p+7/4d  ...  There is an (1/(p + 7 4 d+ 1)− ε)-approximate algorithm for maximizing a non-negative monotone submodular function subject to a p-system and d knapsack constraints, which performs nearly linear number  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1804.08178v6">arXiv:1804.08178v6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/47tudonhwzghpahwwx3h4lzraq">fatcat:47tudonhwzghpahwwx3h4lzraq</a> </span>
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Beyond 1/2-Approximation for Submodular Maximization on Massive Data Streams

Ashkan Norouzi-Fard, Jakub Tarnawski, Slobodan Mitrović, Amir Zandieh, Aida Mousavifar, Ola Svensson
<span title="2018-08-06">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We answer this question affirmatively by designing a new algorithm SALSA for streaming submodular maximization.  ...  We consider this question in the streaming setting, where elements arrive over time at a fast pace and thus we need to design an efficient, low-memory algorithm.  ...  Ola Svensson and Jakub Tarnawski were supported by ERC Starting Grant 335288-OptApprox. References  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1808.01842v1">arXiv:1808.01842v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5tulhiyu35fp7hh5rdacpn26rq">fatcat:5tulhiyu35fp7hh5rdacpn26rq</a> </span>
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Weakly Submodular Function Maximization Using Local Submodularity Ratio [article]

Richard Santiago, Yuichi Yoshida
<span title="2020-09-23">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This leads to improved approximation guarantees in some settings. We provide applications of our results for monotone and non-monotone maximization problems.  ...  We show that an efficient randomized greedy algorithm has provable approximation guarantees for maximizing these functions subject to a cardinality constraint.  ...  Submodular maximization beyond non-negativity: Guarantees, fast algorithms, and applications.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2004.14650v2">arXiv:2004.14650v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ym3qnirktbdnvaap34g4iq2egm">fatcat:ym3qnirktbdnvaap34g4iq2egm</a> </span>
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Streaming Non-monotone Submodular Maximization: Personalized Video Summarization on the Fly [article]

Baharan Mirzasoleiman, Stefanie Jegelka, Andreas Krause
<span title="2017-12-26">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We develop the first efficient single pass streaming algorithm, Streaming Local Search, that for any streaming monotone submodular maximization algorithm with approximation guarantee α under a collection  ...  of independence systems I, provides a constant 1/(1+2/√(α)+1/α +2d(1+√(α))) approximation guarantee for maximizing a non-monotone submodular function under the intersection of I and d knapsack constraints  ...  This research was partially supported by ERC StG 307036, and NSF CAREER 1553284.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1706.03583v3">arXiv:1706.03583v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/j3d5wz7m6vdkfjvdzeyahgv3u4">fatcat:j3d5wz7m6vdkfjvdzeyahgv3u4</a> </span>
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Very Fast Streaming Submodular Function Maximization [article]

Sebastian Buschjäger, Philipp-Jan Honysz, Lukas Pfahler, Katharina Morik
<span title="2021-05-08">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
These algorithms offer worst-case approximations guarantees to the expense of higher computation and memory requirements.  ...  In this paper, we propose a new submodular function maximization algorithm called ThreeSieves, which ignores the worst-case, but delivers a good solution in high probability.  ...  Algorithms for non-negative, monotone submodular maximization with cardinality constraint K.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2010.10059v5">arXiv:2010.10059v5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wixhwc2tbbaulewnhdq4j664wm">fatcat:wixhwc2tbbaulewnhdq4j664wm</a> </span>
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Optimal Streaming Algorithms for Submodular Maximization with Cardinality Constraints [article]

Naor Alaluf, Alina Ene, Moran Feldman, Huy L. Nguyen, Andrew Suh
<span title="2020-08-10">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
It is also worth mentioning that our algorithm is combinatorial and deterministic, which is rare for an algorithm for non-monotone submodular maximization, and enjoys a fast update time of O(log k + log  ...  At the end of the stream, our algorithm post-processes its data structure using any offline algorithm for submodular maximization, and obtains a solution whose approximation guarantee is α/1+α-ε, where  ...  Note now that the submodularity and non-negativity of f guarantee together f (O) + f (OPT\ O) ≥ f (OPT) ≥ τ .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1911.12959v3">arXiv:1911.12959v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rci55cucxbgudoi4asppuqieji">fatcat:rci55cucxbgudoi4asppuqieji</a> </span>
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Non-monotone Submodular Maximization in Exponentially Fewer Iterations [article]

Eric Balkanski, Adam Breuer, Yaron Singer
<span title="2018-07-30">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Beyond its provable guarantees, the algorithm performs well in practice.  ...  In this paper we consider parallelization for applications whose objective can be expressed as maximizing a non-monotone submodular function under a cardinality constraint.  ...  Is it possible to design fast parallel algorithms for non-monotone submodular maximization?  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1807.11462v1">arXiv:1807.11462v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lev3n53fvbdkznnhq4q2hbu3t4">fatcat:lev3n53fvbdkznnhq4q2hbu3t4</a> </span>
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Submodularity in Action: From Machine Learning to Signal Processing Applications [article]

Ehsan Tohidi, Rouhollah Amiri, Mario Coutino, David Gesbert, Geert Leus, Amin Karbasi
<span title="2020-06-17">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We introduce a variety of submodular-friendly applications, and elucidate the relation of submodularity to convexity and concavity which enables efficient optimization.  ...  Submodular functions exhibit strong structure that lead to efficient optimization algorithms with provable near-optimality guarantees.  ...  If all of the involved functions in the multiway-partitioning problem are non-negative, monotone, and submodular, then the greedy algorithm provides a 1 2approximation guarantee [12] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2006.09905v1">arXiv:2006.09905v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ksn2bqbdczechktpa6ivcpwcau">fatcat:ksn2bqbdczechktpa6ivcpwcau</a> </span>
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Continuous Submodular Function Maximization [article]

Yatao Bian, Joachim M. Buhmann, Andreas Krause
<span title="2020-06-24">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We present inapproximability results and provable algorithms for two problem settings: constrained monotone DR-submodular maximization and constrained non-monotone DR-submodular maximization.  ...  In this paper, we systematically study continuous submodularity and a class of non-convex optimization problems: continuous submodular function maximization.  ...  D.2 Proof of Lemma 24 Proof First of all, we prove that g(x) := s:xs=0 R s (x) is a non-negative submodular function. It is easy to see that g(x) is non-negative.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2006.13474v1">arXiv:2006.13474v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/aqlqnvv4qzfyxiydpficoeu55q">fatcat:aqlqnvv4qzfyxiydpficoeu55q</a> </span>
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Guaranteed Non-convex Optimization: Submodular Maximization over Continuous Domains [article]

Andrew An Bian, Baharan Mirzasoleiman, Joachim M. Buhmann, Andreas Krause
<span title="2019-05-06">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We characterize these functions and demonstrate that they can be maximized efficiently with approximation guarantees.  ...  Submodular continuous functions naturally find applications in various real-world settings, including influence and revenue maximization with continuous assignments, sensor energy management, multi-resolution  ...  This research was partially supported by ERC StG 307036 and the Max Planck ETH Center for Learning Systems. 9. http://snap.stanford.edu/data/com-Youtube.html  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1606.05615v5">arXiv:1606.05615v5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/meh4cdyikfgxzgbuvpdh2eckri">fatcat:meh4cdyikfgxzgbuvpdh2eckri</a> </span>
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A Parallel Double Greedy Algorithm for Submodular Maximization [article]

Alina Ene, Huy L. Nguyen, Adrian Vladu
<span title="2018-12-04">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We study parallel algorithms for the problem of maximizing a non-negative submodular function.  ...  Our algorithm applies more generally to the problem of maximizing a continuous diminishing-returns (DR) function.  ...  Recent work has shown that DR-submodular optimization problems have applications beyond submodular maximization [7, 6, 20, 5] , including several of the applications mentioned above. Theorem 1.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1812.01591v1">arXiv:1812.01591v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qjgbyzcmezhztjsvkkeovvw2eq">fatcat:qjgbyzcmezhztjsvkkeovvw2eq</a> </span>
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Submodular Combinatorial Information Measures with Applications in Machine Learning [article]

Rishabh Iyer and Ninad Khargonkar and Jeff Bilmes and Himanshu Asnani
<span title="2021-03-02">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
functions whose third-order partial derivatives satisfy a non-negativity property.  ...  Regarding applications, we connect the maximization of submodular (conditional) mutual information to problems such as mutual-information-based, query-based, and privacy-preserving summarization -- and  ...  Kai Wei, Rishabh K Iyer, Shengjie Wang, Wenruo Bai, and Jeff A Bilmes. Mixed Robust/Average Submodular Partitioning: Fast Algorithms, Guarantees, and Applications.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2006.15412v6">arXiv:2006.15412v6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ns3ctxnkovdgbo66awqimjzjuy">fatcat:ns3ctxnkovdgbo66awqimjzjuy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210313020636/https://arxiv.org/pdf/2006.15412v6.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/cc/c7/ccc762cb40cb9221dba45a2ec3bae1f56896beaf.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2006.15412v6" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Optimal Streaming Algorithms for Submodular Maximization with Cardinality Constraints

Naor Alaluf, Alina Ene, Moran Feldman, Huy L. Nguyen, Andrew Suh, Emanuela Merelli, Artur Czumaj, Anuj Dawar
<span title="2020-06-29">2020</span> <i title="Schloss Dagstuhl - Leibniz-Zentrum für Informatik"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/pf6v2q6ji5h7birkbrtpdc2uhy" style="color: black;">International Colloquium on Automata, Languages and Programming</a> </i> &nbsp;
At the end of the stream, both our algorithms post-process their data structures using any offline algorithm for submodular maximization, and obtain a solution whose approximation guarantee is α/(1+α)-  ...  One of our algorithms is combinatorial and enjoys fast update and overall running times.  ...  for the problem of maximizing a non-negative submodular function subject to cardinality constraint.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.icalp.2020.6">doi:10.4230/lipics.icalp.2020.6</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/icalp/AlalufEFNS20.html">dblp:conf/icalp/AlalufEFNS20</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/stfimivg4rhrtoktgfn5viwcsy">fatcat:stfimivg4rhrtoktgfn5viwcsy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201210190218/https://drops.dagstuhl.de/opus/volltexte/2020/12413/pdf/LIPIcs-ICALP-2020-6.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/29/fc/29fcb37490db7b3558e9739a8bb9592e9424e98c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.icalp.2020.6"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>
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