Streaming submodular maximization

Badanidiyuru, Ashwinkumar; Mirzasoleiman, Baharan; Karbasi, Amin; Krause, Andreas

doi:10.1145/2623330.2623637

Cited by 201 publications

(19 citation statements)

References 28 publications

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“…Here, on the other hand, we present guaranteed approximation results for all monotone and non-monotone submodular functions. In fact, Ashwinkumar and Karbasi [6] observed that if one applies the greedy algorithm without a consistent tie-breaking rule, the approximation factor of the algorithm is not bounded for coverage functions. In this paper, we prove that a class of algorithms including greedy with a consistent tie-breaking rule provide a guaranteed 0.27-approximation algorithm for all monotone submodular functions.…”

Section: Other Related Workmentioning

confidence: 99%

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Randomized Composable Core-sets for Distributed Submodular Maximization

Mirrokni

Zadimoghaddam

2015

Proceedings of the Forty-Seventh Annual ACM Symposium on Theory of Computing

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An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution inside the union of the representative solutions for all pieces. This technique can be captured via the concept of composable core-sets, and has been recently applied to solve diversity maximization problems as well as several clustering problems [7,15,8]. However, for coverage and submodular maximization problems, impossibility bounds are known for this technique [15]. In this paper, we focus on efficient construction of a randomized variant of composable core-sets where the above idea is applied on a random clustering of the data. We employ this technique for the coverage, monotone and non-monotone submodular maximization problems. Our results significantly improve upon the hardness results for nonrandomized core-sets, and imply improved results for submodular maximization in a distributed and streaming settings. The effectiveness of this technique has been confirmed empirically for several machine learning applications [22], and our proof provides a theoretical foundation to this idea.In summary, we show that a simple greedy algorithm results in a 1/3-approximate randomized composable coreset for submodular maximization under a cardinality constraint. Our result also extends to non-monotone submodular functions, and leads to the first 2-round MapReducebased constant-factor approximation algorithm with O(n) total communication complexity for either monotone or nonmonotone functions. Finally, using an improved analysis technique and a new algorithm PseudoGreedy, we present an improved 0.545-approximation algorithm for monotone submodular maximization, which is in turn the first MapReducebased algorithm beating factor 1/2 in a constant number of rounds.

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Section: Other Related Workmentioning

confidence: 99%

“…We can increase the value of a * j by c * j , and then set c * j to zero. This update keeps a * j + c * j intact, and therefore does not change anything in constraints (1), ( 3), ( 5), and (6). It also makes it easier to satisfy constraint (2) since it (possibly) reduces the right hand side, and keeps the left hand side intact.…”

Section: Claim 47mentioning

confidence: 99%

Randomized Composable Core-sets for Distributed Submodular Maximization

Mirrokni

Zadimoghaddam

2015

Proceedings of the Forty-Seventh Annual ACM Symposium on Theory of Computing

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“…Monotone k-submodular Nguyen and Thai (2020) generalize the threshold greedy approach of Badanidiyuru et al (2014) to k-submodular maximization under a common cardinality constraint of size r, that works by guessing the value of the optimum solution. Their method achieves a near-optimal 1 2 − ϵ approximation, but keeps multiple solutions in memory, which requires space O( r log r ϵ ) and is not suited for the online setting.…”

Section: Additional Related Workmentioning

confidence: 99%

Streaming Algorithms for Budgeted k-Submodular Maximization Problem

Pham¹,

Vu²,

Ha³

et al. 2021

Lecture Notes in Computer Science

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Constrained k-submodular maximization is a general framework that captures many discrete optimization problems such as ad allocation, influence maximization, personalized recommendation, and many others. In many of these applications, datasets are large or decisions need to be made in an online manner, which motivates the development of efficient streaming and online algorithms. In this work, we develop single-pass streaming and online algorithms for constrained k-submodular maximization with both monotone and general (possibly non-monotone) objectives subject to cardinality and knapsack constraints. Our algorithms achieve provable constant-factor approximation guarantees which improve upon the state of the art in almost all settings. Moreover, they are combinatorial and very efficient, and have optimal space and running time. We experimentally evaluate our algorithms on instances for ad allocation and other applications, where we observe that our algorithms are efficient and scalable, and construct solutions that are comparable in value to offline greedy algorithms.

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“…[1][2][3][4] The other one is the constraints on the solution. At present, cardinality constraint, [5][6][7] matroid constraint, 8-10 p-system constraint, 11,12 and knapsack constraint [13][14][15] have been widely studied.…”

Section: Introductionmentioning

confidence: 99%

Stochastic greedy algorithms for maximizing constrained submodular + supermodular functions

et al. 2021

Concurrency and Computation

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Summary The problem of maximizing the sum of a constrained submodular and a supermodular function has many applications such as social networks, machine learning, and artificial intelligence. In this article, we study the monotone submodular + supermodular maximization problem under a cardinality constraint and a p‐system constraint, respectively. For each problem, we provide a stochastic algorithm and prove the approximation ratio of each algorithm theoretically. Since the algorithm of the latter problem can also solve the former problem, we do some numerical experiments of the two algorithms to compare the time as well as the quality of the two algorithms in solving the former problem.

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Streaming submodular maximization

Cited by 201 publications

References 28 publications

Randomized Composable Core-sets for Distributed Submodular Maximization

Randomized Composable Core-sets for Distributed Submodular Maximization

Streaming Algorithms for Budgeted k-Submodular Maximization Problem

Stochastic greedy algorithms for maximizing constrained submodular + supermodular functions

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