论文标题
为多方面背包做更多的努力
More Effort Towards Multiagent Knapsack
论文作者
论文摘要
在本文中，我们研究了背包问题的一些多重变体。 Fluschnik等。 [AAAI 2019]考虑了每个代理商为每个项目分配一些实用程序的模型。他们研究了三个偏好聚合规则，以查找项目的子集（背包）：单独，多样和基于NASH福利。从非正式的角度来看，通过满足尽可能多的选民来实现多样性。由于聚合操作员在多翼纳选举中的应用，我们将研究从不同的聚合规则扩展到中位数和最佳评分功能。我们研究问题的计算和参数化复杂性，即某些自然参数，即选民的数量，项目数量以及与简单案件的距离。我们还研究了域限制下问题的复杂性。此外，我们相对于不同的聚合规则的选民数量，我们提出了更快的参数化算法。
In this paper, we study some multiagent variants of the knapsack problem. Fluschnik et al. [AAAI 2019] considered the model in which every agent assigns some utility to every item. They studied three preference aggregation rules for finding a subset (knapsack) of items: individually best, diverse, and Nash-welfare-based. Informally, diversity is achieved by satisfying as many voters as possible. Motivated by the application of aggregation operators in multiwinner elections, we extend the study from diverse aggregation rule to Median and Best scoring functions. We study the computational and parameterized complexity of the problem with respect to some natural parameters, namely, the number of voters, the number of items, and the distance from an easy instance. We also study the complexity of the problem under domain restrictions. Furthermore, we present significantly faster parameterized algorithms with respect to the number of voters for the diverse aggregation rule.
