电视频道中选择$k$最佳节目时隙的调度算法：一种图论方法
Scheduling algorithm to select $k$ optimal programme slots in television channels: A graph theoretic approach
摘要：
在本文中，它表明，所有电视频道的所有节目可以建模为一个区间图。将节目槽作为图的顶点，如果两个{节目槽}的持续时间有非空相交，则认为对应的顶点由边连接。将节目的观众数量作为顶点的权重。在时间安排方面相互排斥的一组节目称为一个会话。我们假设一间公司的目的，是在不同信道的$k$平行时段中，选择受欢迎的节目，使其商业广告能达到最多观众，即公司同时选择$k$合适的节目时段作广告宣传。因此，本文的目的是帮助公司选择节目时段，这些节目时段相对于广播时间的时间表是互斥的，以这样的方式，使得在$k$并行时段中所选节目的观众总数上升到最佳水平。证明了该问题的解是通过求解区间{图}上的最大权$k$ -着色问题得到的。利用$O(kMn^2)$时间设计了一种算法来求解该准时制优化问题，其中$n$和$M$分别表示所有频道的节目总数和所有频道的所有节目的观众上限。本文考虑的问题是一个日常生活问题，它是由区间图上的$k$ -着色问题建模的。
英文摘要：
In this paper, it is shown that all programmes of all television channels can be modelled as an interval graph. The programme slots are taken as the vertices of the graph and if the time duration of two {programme slots} have non-empty intersection, the corresponding vertices are considered to be connected by an edge. The number of viewers of a programme is taken as the weight of the vertex. A set of programmes that are mutually exclusive in respect of time scheduling is called a session. We assume that a company sets the objective of selecting the popular programmes in $k$ parallel sessions among different channels so as to make its commercial advertisement reach the maximum number of viewers, that is, a company selects $k$ suitable programme slots simultaneously for advertisement. The aim of the paper is, therefore, to {help} the companies to select the programme slots, which are mutually exclusive with respect to the time schedule of telecasting time, in such a way that the total number of viewers of the selected programme in $k$ parallel slots rises to the optimum level. It is shown that the solution of this problem is obtained by solving the maximum weight $k$-colouring problem on an interval {graph}. An algorithm is designed to solve this just-in-time optimization problem using $O(kMn^2)$ time, where $n$ and $M$ represent the total number of programmes of all channels and the upper bound of the viewers of all programmes of all channels respectively. The problem considered in this paper is a daily life problem which is modeled by $k$-colouring problem on interval graph.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
