不一致的派系问题

K. Jansen, Petra Scheffler, G. Woeginger
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引用次数: 21

摘要

给定一个图G = (V, E),我们考虑在图中寻找顶点总数最大的D对不相交团的问题。我们确定了这个问题的计算复杂度限制在各种不同的图类。我们给出了区间图、图、有向路径图和部分k树问题的多项式时间算法。相反,我们展示了这个问题对于无向路径图的np完备性。此外,我们还研究了一个密切相关的调度问题。给定D乘以单位,我们寻找工人序列w 1,…,w K和分区J 1,…,作业集的J k,使得J i可以在D个时间单位内被wi执行。目标是找到一个工人总工资最低的序列。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Disjoint Cliques Problem
Given a graph G = (V, E), we consider the problem of finding a set of D pairwise disjoint cliques in the graph with maximum overall number of vertices. We determine the computational complexity of this problem restricted to a variety of different graph classes. We give polynomial time algorithms for the problem restricted to interval graphs, cographs, directed path graphs and partial k-trees. In contrast, we show the NP-completeness of this problem for undirected path graphs. Moreover, we investigate a closely related scheduling problem. Given D times units, we look for a sequence of workers w 1 ,...,w K and a partition J 1 ,..., J k of the job set such that J i can be executed by w i within D time units. The goal is to find a sequence with minimum total wage of the workers.
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