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.
翻译:在本文中,我们研究了Knapsack问题的一些多试剂变体。Fluschnik等人[AAI 2019]审议了每个代理商对每个项目给予某种效用的模式,他们研究了为寻找一个子集(knapsack)物品而提出的三种偏好汇总规则:个人最佳、多样和以Nash-welfar(knapsack)为基础的;非正式地说,通过满足尽可能多的选民而实现多样性;在多赢者选举中采用集合操作员的动力下,我们把研究范围从多样化的集合规则扩大到中型和最佳评分功能;我们研究了关于某些自然参数的问题的计算和参数复杂性,即选民人数、项目数量和与简单实例的距离;我们还研究了在域限制下问题的复杂性;此外,我们提出了关于多样性集合规则的选民人数的参数化算法,我们提出了大大加快。