On maximizing a monotone <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>k</mml:mi></mml:math>-submodular function subject to a matroid constraint

Sakaue, Shinsaku

doi:10.1016/j.disopt.2017.01.003

Cited by 40 publications

(18 citation statements)

References 10 publications

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“…Ohsaka and Yoshida [17] studied monotone k-submodular maximization under a cardinality constraint. Later, Sakaue [20] generalized it to a matroid constraint.…”

Section: Related Workmentioning

confidence: 99%

No-regret algorithms for online $k$-submodular maximization

Soma¹

2018

Preprint

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We present a polynomial time algorithm for online maximization of k-submodular maximization. For online (nonmonotone) k-submodular maximization, our algorithm achieves a tight approximate factor in an approximate regret. For online monotone k-submodular maximization, our approximate-regret matches to the best-known approximation ratio, which is tight asymptotically as k tends to infinity. Our approach is based on the Blackwell approachability theorem and online linear optimization.

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“…Ohsaka and Yoshida [17] studied monotone k-submodular maximization under a cardinality constraint. Later, Sakaue [20] generalized it to a matroid constraint.…”

Section: Related Workmentioning

confidence: 99%

No-regret algorithms for online $k$-submodular maximization

Soma¹

2018

Preprint

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“…The k-submodular maximization problem appears in a broad range of applications (e.g., influence maximization with k kinds of topics and sensor placement with k kinds of sensors [6]), due to the property of diminishing returns. The k-submodular maximization has been studied in the unconstrained setting [11], under cardinality constraints [6], and under matroid constraints [8]. In this note, we study the maximization problem of a nonnegative monotone k-submodular function under a knapsack constraint.…”

Section: Introductionmentioning

confidence: 99%

“…In the constrained setting, Ohsaka and Yoshida [6] proposed a 1 2 -approximation algorithm for nonnegative monotone k-submodular maximization with a total size constraint (i.e., ∪ i∈[k] |X i | ≤ B for an integer B) and a 1 3 -approximation algorithm for that with individual size constraints (i.e., |X i | ≤ B i ∀i ∈ [k] with integers B i ). Sakaue [8] proposed a 1 2 -approximation algorithm for nonnegative monotone k-submodular maximization with a matroid constraint. Thus, our work completes the picture by studying a knapsack constraint.…”

Section: Introductionmentioning

confidence: 99%

On maximizing a monotone $k$-submodular function under a knapsack constraint

Tang¹,

Wang²,

Chan³

2021

Preprint

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“…Under the size constraint, Oshaka et al [9] first proposed 1/2-approximation algorithm by using a greedy approach for maximizing monotone k-submodular maximization functions. [13] showed a greedy selection that could give an approximation ratio of 1/2 under the matroid constraint. The authors in [11] then further proposed multi-objective evolutionary algorithms that provided 1/2approximation ratio under the size constraint but took O(kn log 2 B) queries in expectation.…”

Section: Introductionmentioning

confidence: 99%

Streaming algorithms for Budgeted $k$-Submodular Maximization problem

Pham¹,

Vu²,

Ha³

et al. 2021

Preprint

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Stimulated by practical applications arising from viral marketing. This paper investigates a novel Budgeted k-Submodular Maximization problem defined as follows: Given a finite set V , a budget B and a k-submodular function f : (k + 1) V → R+, the problem asks to find a solution s = (S1, S2, . . . , S k ), each element e ∈ V has a cost ci(e) to be put into i-th set Si, with the total cost of s does not exceed B so that f (s) is maximized. To address this problem, we propose two streaming algorithms that provide approximation guarantees for the problem. In particular, in the case of each element e has the same cost for all i-th sets, we propose a deterministic streaming algorithm which provides an approximation ratio of 1 4 − ǫ when f is monotone and 1 5 − ǫ when f is non-monotone. For the general case, we propose a random streaming algorithm that provides an approximation ratio of min{ α 2 , (1−α)k (1+β)k−β } − ǫ when f is monotone and min{ α 2 , (1−α)k (1+2β)k−2β }−ǫ when f is non-monotone in expectation, where β = max e∈V,i,j∈[k],i =j c i (e) c j (e) and ǫ, α are fixed inputs.

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On maximizing a monotone k-submodular function subject to a matroid constraint

Cited by 40 publications

References 10 publications

No-regret algorithms for online $k$-submodular maximization

No-regret algorithms for online $k$-submodular maximization

On maximizing a monotone $k$-submodular function under a knapsack constraint

Streaming algorithms for Budgeted $k$-Submodular Maximization problem

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