当前位置: X-MOL 学术J. Comb. Optim. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Maximizing k-submodular functions under budget constraint: applications and streaming algorithms
Journal of Combinatorial Optimization ( IF 1 ) Pub Date : 2022-04-18 , DOI: 10.1007/s10878-022-00858-x
Canh V. Pham , Quang C. Vu , Dung K. T. Ha , Tai T. Nguyen , Nguyen D. Le

Motivated by the practical applications in solving plenty of important combinatorial optimization problems, this paper investigates the Budgeted k-Submodular Maximization problem defined as follows: Given a finite set V, a budget B and a k-submodular function \(f: (k+1)^V \mapsto \mathbb {R}_+\), the problem asks to find a solution \(\mathbf{s }=(S_1, S_2, \ldots , S_k) \in (k+1)^V \), in which an element \(e \in V\) has a cost \(c_i(e)\) when added into the i-th set \(S_i\), with the total cost of \(\mathbf{s }\) that does not exceed B so that \(f(\mathbf{s })\) is maximized. To address this problem, we propose two single pass streaming algorithms with approximation guarantees: one for the case that an element e has only one cost value when added to all i-th sets and one for the general case with different values of \(c_i(e)\). We further investigate the performance of our algorithms in two applications of the problem, Influence Maximization with k topics and sensor placement of k types of measures. The experiment results indicate that our algorithms can return competitive results but require fewer the number of queries and running time than the state-of-the-art methods.



中文翻译:

在预算约束下最大化 k-submodular 函数:应用程序和流算法

受解决大量重要组合优化问题的实际应用启发,本文研究了如下定义的 Budgeted k -Submodular Maximization 问题:给定有限集V,预算Bk -submodular 函数\(f: (k+ 1)^V \mapsto \mathbb {R}_+\),问题要求找到一个解决方案\(\mathbf{s }=(S_1, S_2, \ldots , S_k) \in (k+1)^V \),其中元素\(e \in V\ )在添加到第i个集合\(S_i\ ) 时具有成本\(c_i(e)\),总成本为\(\mathbf{ s }\)不超过B使\(f(\mathbf{s })\)最大化。为了解决这个问题,我们提出了两种具有近似保证的单通道流算法:一种用于元素e在添加到所有第i个集合时只有一个成本值的情况,另一种用于具有不同\(c_i (e)\)。我们进一步研究了我们的算法在该问题的两个应用中的性能,即具有k个主题的影响最大化和k种测量类型的传感器放置。实验结果表明,与最先进的方法相比,我们的算法可以返回有竞争力的结果,但需要的查询次数和运行时间更少。

更新日期:2022-04-18
down
wechat
bug