The Communication Complexity of Approximate Set Packing and Covering
The Communication Complexity of Approximate Set Packing and Covering
复制标题
近似集打包和覆盖的通信复杂度
DOI：
10.1007/3-540-45465-9_74
复制
发表时间：
2002
影响因子：
8.2
通讯作者：
N. Nisan
中科院分区：
文献类型：
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作者：
N. Nisan
我们考虑一个设置，k播放器是{1..n}子集的每个集合集合。我们考虑了大约解决问题的通信复杂性：封面编号：集合的最小数量（在其集合的结合中），其联合为{1 ... n}和包装编号：最大集合数（在他们的集合的结合）是配对的脱节。我们证明，封面的计算（ln n） - 封面和最小值（k，o（o（？n） - 包装umber）可以使用polynomial来完成（在n）通信量中，获得封面号的（1/2 - ？）log n近似值，或者比最小的（k，n1/2 - ？）更好（the packingn umber的近似值）需要指数式的通信复杂性。
We consider a settingwhere k players are each holdingsome collection of subsets of {1..n}. We consider the communication complexity of approximately solvingt wo problems: The cover number: the minimal number of sets (in the union of their collections) whose union is {1...n} and the packing number: the maximum number of sets (in the union of their collections) that are pair-wise disjoint.We prove that while computinga (ln n)-approximation for the cover number and an min(k,O(?n)-approximation for the packingn umber can be done with polynomial (in n) amount of communication, getting a (1/2 - ?) log n approximation for the cover number or a better than min(k, n1/2-?)-approximation for the packingn umber requires exponential communication complexity.