Maximizing k-submodular functions under budget constraint: applications and streaming algorithms

Pham, Canh V.; Vu, Quang C.; Ha, Dung K. T.; Nguyen, Tai T.; Le, Nguyen D.

doi:10.1007/s10878-022-00858-x

Cited by 17 publications

(4 citation statements)

References 27 publications

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“…This algorithm has been well studied in knapsack problems with linear and submodular objective functions due to its simplicity and efficiency, and Chen et al proved an approximation ratio 1 4 (1 − 1 e ) for the kSKM. 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].…”

Section: Related Workmentioning

confidence: 99%

“…Since Huber and Kolmogorov [5] proposed the notion of ksubmodularity one decade ago, there have been increased theoretical and algorithmic interests in the study of k-submodular functions, as various problems in combinatorial optimization and machine learning can be formulated as k-submodular function maximization. The application scenarios include influence maximization [12,18], sensor placement [9,25], document summarization [7] and feature selection [25], etc.…”

Section: Introductionmentioning

confidence: 99%

“…The problem of maximizing a k-submodular function is known to be NP-hard, since it is a generalization of the NP-hard submodular maximization problem. Extensive research has been dedicated to developing efficient algorithms with desirable approximation ratios for the problem under different constraints, for example, cardinality constraints [2,9,18], matroid constraints [13,15], knapsack constraints [17,12], and the unconstrained setting [19,6,14].…”

Section: Introductionmentioning

confidence: 99%

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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%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Improved Analysis of Greedy Algorithm on k-Submodular Knapsack

Tang,

Wang

2023

Frontiers in Artificial Intelligence and Applications

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“…Those studies have shown the advantages of the streaming method compared to the greedy method. Some prominent studies include using the streaming algorithm for maximizing k-submodular functions under budget constraints [26], optimizing a submodular function under noise by streaming algorithms [27], maximizing a monotone submodular function by multi-pass streaming algorithms [20], and using fast streaming for the problem of submodular maximization [22].…”

Section: Introductionmentioning

confidence: 99%

Efficient Streaming Algorithms for Maximizing Monotone DR-Submodular Function on the Integer Lattice

Nguyen

Phạm

et al. 2022

Mathematics

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In recent years, the issue of maximizing submodular functions has attracted much interest from research communities. However, most submodular functions are specified in a set function. Meanwhile, recent advancements have been studied for maximizing a diminishing return submodular (DR-submodular) function on the integer lattice. Because plenty of publications show that the DR-submodular function has wide applications in optimization problems such as sensor placement impose problems, optimal budget allocation, social network, and especially machine learning. In this research, we propose two main streaming algorithms for the problem of maximizing a monotone DR-submodular function under cardinality constraints. Our two algorithms, which are called StrDRS1 and StrDRS2, have (1/2−ϵ), (1−1/e−ϵ) of approximation ratios and O(nϵlog(logBϵ)logk), O(nϵlogB), respectively. We conducted several experiments to investigate the performance of our algorithms based on the budget allocation problem over the bipartite influence model, an instance of the monotone submodular function maximization problem over the integer lattice. The experimental results indicate that our proposed algorithms not only provide solutions with a high value of the objective function, but also outperform the state-of-the-art algorithms in terms of both the number of queries and the running time.

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