距离约束标号和均匀信道分配问题的固定参数复杂性
Fixed parameter complexity of distance constrained labeling and uniform channel assignment problems
摘要：
从固定参数易处理性的角度研究了一类距离约束图标号问题的计算复杂性。研究的参数是邻域多样性和团宽度。我们重新措辞的距离约束图标记问题的信道分配问题的一个特定的统一的变种，并表明，这个问题是固定参数听话时，参数化的邻域多样性与最大的权重。因此，每个$L(p_1, p_2, \dots, p_k)$ -标记问题是FPT时，参数化的邻域多样性，最大$p_i$和$k.$我们的结果也产生FPT算法的所有$L(p_1, p_2, \dots, p_k)$ -标记问题时，参数化的最小顶点覆盖的大小，回答一个开放的问题Fiala等人：着色问题的参数化复杂性：树宽与顶点覆盖。当最大权重附加地包括在参数中时，相同的结果适用于信道分配。最后，我们表明，统一的信道分配问题的变种成为NP-完全时，推广到有界集团宽度的图形。
英文摘要：
We study computational complexity of the class of distance-constrained graph labeling problems from the fixed parameter tractability point of view. The parameters studied are neighborhood diversity and clique width. We rephrase the distance constrained graph labeling problem as a specific uniform variant of the Channel Assignment problem and show that this problem is fixed parameter tractable when parameterized by the neighborhood diversity together with the largest weight. Consequently, every $L(p_1, p_2, \dots, p_k)$-labeling problem is FPT when parameterized by the neighborhood diversity, the maximum $p_i$ and $k.$ Our results yield also FPT algorithms for all $L(p_1, p_2, \dots, p_k)$-labeling problems when parameterized by the size of a minimum vertex cover, answering an open question of Fiala et al.: Parameterized complexity of coloring problems: Treewidth versus vertex cover. The same consequence applies on Channel Assignment when the maximum weight is additionally included among the parameters. Finally, we show that the uniform variant of the Channel Assignment problem becomes NP-complete when generalized to graphs of bounded clique width.
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