We study a generalization of the vertex cover problem. For a given graph with weights on the vertices and an integer k, we aim to find a subset of the vertices with minimum total weight, so that at least k edges in th...We study a generalization of the vertex cover problem. For a given graph with weights on the vertices and an integer k, we aim to find a subset of the vertices with minimum total weight, so that at least k edges in the graph are covered. The problem is called the k-partial vertex cover problem. There are some 2-approximation algorithms for the problem. In the paper we do not improve on the approximation ratios of the previous algorithms, but we derive an iterative rounding algorithm. We present our technique in two algorithms. The first is an iterative rounding algorithm and gives a （2 ＋ Q/OPT ）-approximation for the k-partial vertex cover problem where Q is the largest finite weight in the problem definition and OPT is the optimal value for the instance. The second algorithm uses the first as a subroutine and achieves an approximation ratio of 2.展开更多
通过总结2004/2005～2006/2007年3个年度在长江流域冬油菜主产区10个省（市）的72个田间试验数据,以产量、增产率、偏生产力、农学效率、生理利用率及表观利用率等指标分析了长江流域施钾增产效果及钾肥利用率,以期为油菜进一步增产提...通过总结2004/2005～2006/2007年3个年度在长江流域冬油菜主产区10个省（市）的72个田间试验数据,以产量、增产率、偏生产力、农学效率、生理利用率及表观利用率等指标分析了长江流域施钾增产效果及钾肥利用率,以期为油菜进一步增产提供依据.分析结果表明,长江流域冬油菜施钾效果显著,与对照不施钾处理相比,施用钾肥油菜籽平均增产量为349 kg hm-2,平均增产率为19.8％,其中增产率小于5％的试验数占总数的20.8％,另外,油菜籽增产率随着土壤速效钾含量的升高而明显下降;施钾处理油菜地上部钾素积累量比不施钾处理显著增加38.1％;钾肥的平均偏生产力、农学效率、生理利用率和表观利用率分别为21.1、2.9、8.5 kg·kg-1和46.7％.综合结果表明,在施用氮、磷及硼肥基础上增施钾肥能够明显提高油菜地上部的生物量及钾素的累积,从而增加油菜籽产量,且根据基础地力及油菜对钾的需求规律而合理施肥极为重要.展开更多
基金Supported by the National Natural Science Foundation of China(No.11201021)
文摘We study a generalization of the vertex cover problem. For a given graph with weights on the vertices and an integer k, we aim to find a subset of the vertices with minimum total weight, so that at least k edges in the graph are covered. The problem is called the k-partial vertex cover problem. There are some 2-approximation algorithms for the problem. In the paper we do not improve on the approximation ratios of the previous algorithms, but we derive an iterative rounding algorithm. We present our technique in two algorithms. The first is an iterative rounding algorithm and gives a （2 ＋ Q/OPT ）-approximation for the k-partial vertex cover problem where Q is the largest finite weight in the problem definition and OPT is the optimal value for the instance. The second algorithm uses the first as a subroutine and achieves an approximation ratio of 2.
文摘通过总结2004/2005～2006/2007年3个年度在长江流域冬油菜主产区10个省（市）的72个田间试验数据,以产量、增产率、偏生产力、农学效率、生理利用率及表观利用率等指标分析了长江流域施钾增产效果及钾肥利用率,以期为油菜进一步增产提供依据.分析结果表明,长江流域冬油菜施钾效果显著,与对照不施钾处理相比,施用钾肥油菜籽平均增产量为349 kg hm-2,平均增产率为19.8％,其中增产率小于5％的试验数占总数的20.8％,另外,油菜籽增产率随着土壤速效钾含量的升高而明显下降;施钾处理油菜地上部钾素积累量比不施钾处理显著增加38.1％;钾肥的平均偏生产力、农学效率、生理利用率和表观利用率分别为21.1、2.9、8.5 kg·kg-1和46.7％.综合结果表明,在施用氮、磷及硼肥基础上增施钾肥能够明显提高油菜地上部的生物量及钾素的累积,从而增加油菜籽产量,且根据基础地力及油菜对钾的需求规律而合理施肥极为重要.
