Fast Streaming Algorithms for k-Submodular Maximization under a Knapsack Constraint

Pham, Canh V.; Ha, Dung K. T.; Hoang, Huan X.; Tran, Duc–Tan

doi:10.1109/dsaa54385.2022.10032383

Cited by 6 publications

(4 citation statements)

References 21 publications

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“…Pham et al [12] proposed streaming algorithms with approximation ratios 1 4 − and 1 5 − for the monotone and non-monotone cases, respectively, which requires O( n log n) queries of the k-submodular function. Other works related to kSKM include [11,16,22,23,24]. While all the above mentioned are combinatorial algorithms, the best known result for kSKM comes from extension-based methods.…”

Section: Related Workmentioning

confidence: 99%

Improved Analysis of Greedy Algorithm on k-Submodular Knapsack

Tang,

Wang

2023

Frontiers in Artificial Intelligence and Applications

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A k-submodular function is a generalization of submodular functions that takes k disjoint subsets as input and outputs a real value. It captures many problems in combinatorial optimization and machine leaning such as influence maximization, sensor placement, feature selection, etc. In this paper, we consider the monotone k-submodular maximization problem under a knapsack constraint, and explore the performance guarantee of a greedy-based algorithm: enumerating all size-2 solutions and extending every singleton solution greedily; the best outcome is returned. We provide a novel analysis framework and prove that this algorithm achieves an approximation ratio of at least 0.328. This is the best-known result of combinatorial algorithms on k-submodular knapsack maximization. In addition, within the framework, we can further improve the approximation ratio to a value approaching 1/3 with any desirable accuracy, by enumerating sufficiently large base solutions. The results can even be extended to non-monotone k-submodular functions.

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Section: Related Workmentioning

confidence: 99%

Improved Analysis of Greedy Algorithm on k-Submodular Knapsack

Tang,

Wang

2023

Frontiers in Artificial Intelligence and Applications

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“…Personalized movie recommendation (Mirzasoleiman, Badanidiyuru, and Karbasi 2016;Feldman, Harshaw, and Karbasi 2017;Haba et al 2020;Amanatidis et al 2020Amanatidis et al , 2021 aims to recommend a list of high-quality and diverse movies to a user according to the ratings from similar users. We use the popular MovieLens dataset containing 1,793 movies with adventure, animation and fantasy genres (Haba et al 2020). Given a set of N movies, each movie u ∈ N is associated with a 25 dimensional feature vector q u calculated from user ratings.…”

Section: Performance Evaluationmentioning

confidence: 99%

“…Given a set of N movies, each movie u ∈ N is associated with a 25 dimensional feature vector q u calculated from user ratings. Following (Mirzasoleiman, Badanidiyuru, and Karbasi 2016;Haba et al 2020), the utility of any S ⊆ N is defined as f (S) = u∈S v∈N s u,v − u∈S v∈S s u,v , where we use s u,v = e −λdist (qu,qv) to measure the similarity between movies u and v; dist(q u , q v ) is the euclidean distance between q u and q v ; and λ is set to 2. Following (Haba et al 2020), we also define the cost c(u) of any movie u to be proportional to 10 − r u , where r u denotes the rating of movie u (ranging from 0 to 10), and the costs of all movies are normalized such that the average movie cost is 1.…”

Section: Performance Evaluationmentioning

confidence: 99%

Practical Parallel Algorithms for Submodular Maximization Subject to a Knapsack Constraint with Nearly Optimal Adaptivity

Cui

Han

Tang

et al. 2023

AAAI

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Submodular maximization has wide applications in machine learning and data mining, where massive datasets have brought the great need for designing efficient and parallelizable algorithms. One measure of the parallelizability of a submodular maximization algorithm is its adaptivity complexity, which indicates the number of sequential rounds where a polynomial number of queries to the objective function can be executed in parallel. In this paper, we study the problem of non-monotone submodular maximization subject to a knapsack constraint, and propose the first combinatorial algorithm achieving an (8+epsilon)-approximation under O(log n) adaptive complexity, which is optimal up to a factor of O(loglog n). Moreover, under slightly larger adaptivity, we also propose approximation algorithms with nearly optimal query complexity of O(n), while achieving better approximation ratios. We show that our algorithms can also be applied to the special case of submodular maximization subject to a cardinality constraint, and achieve performance bounds comparable with those of state-of-the-art algorithms. Finally, the effectiveness of our approach is demonstrated by extensive experiments on real-world applications.

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“…As a result, the SK problem has attracted tremendous attention since the 1980s (Wolsey 1982). In recent years, with the increase in the amount of data, there has been a growing focus on the design of low-memory streaming algorithms for submodular maximization problems (Kazemi et al 2019;Mitrovic et al 2017;Mirzasoleiman, Jegelka, and Krause 2018;Haba et al 2020;El Halabi et al 2020;Chekuri, Gupta, and Quanrud 2015), which is one of the primary focuses of our paper.…”

Section: Introductionmentioning

confidence: 99%

Deletion-Robust Submodular Maximization with Knapsack Constraints

Cui,

Han,

Huang

2024

AAAI

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Submodular maximization algorithms have found wide applications in various fields such as data summarization, recommendation systems, and active learning. In recent years, deletion-robust submodular maximization algorithms have garnered attention due to their significant implications in scenarios where some data points may be removed due to user preferences or privacy concerns, such as in recommendation systems and influence maximization. In this paper, we study the fundamental problem of submodular maximization with knapsack constraints and propose a robust streaming algorithm for it. To the best of our knowledge, our algorithm is the first to solve this problem for non-monotone submodular functions and can achieve an approximation ratio of 1/(6.82+2.63d)-ϵ under a near-optimal summary size of O(k+r), where k denotes the maximum cardinality of any feasible solution, d denotes the number of the knapsack constraints and r is the robustness parameter. For monotone submodular functions, our algorithm can achieve an approximation ratio of 1/(2+2d)-ϵ under a near-optimal summary size of O(k+r), significantly improving upon the best-known ratio of Ω((1/d-ϵ)^2). The empirical performance of our algorithm is extensively evaluated in several applications including influence maximization and recommendation systems, and the experimental results demonstrate the effectiveness of our algorithm.

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Fast Streaming Algorithms for k-Submodular Maximization under a Knapsack Constraint

Cited by 6 publications

References 21 publications

Improved Analysis of Greedy Algorithm on k-Submodular Knapsack

Improved Analysis of Greedy Algorithm on k-Submodular Knapsack

Practical Parallel Algorithms for Submodular Maximization Subject to a Knapsack Constraint with Nearly Optimal Adaptivity

Deletion-Robust Submodular Maximization with Knapsack Constraints

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