We show that the STEINER TREE problem and TRAVELING SALESMAN problem for points in the plane are NP-complete when distances are measured either by the rectilinear (Manhattan) metric or by a natural discretized version of the Euclidean metric. Our proofs also indicate that the problems are NP-hard if the distance measure is the (unmodified) Euclidean metric. However, for reasons we discuss, there is some question as to whether these problems, or even the well-solved MINIMUM SPANNING TREE problem, are in NP when the distance measure is the Euclidean metric.
我们表明,当通过直线(曼哈顿)度量或自然离散形式的欧几里得度量来测量距离时,平面上点的Steiner Tree问题和TRAVELING SALESMAN问题都是NP完全的。我们的证据还表明,如果距离度量是(未修改的)欧几里德度量,则问题是NP难的。但是,由于我们讨论的原因,当距离度量是欧几里德度量时,这些问题,或者甚至是解决得很好的MINIMUM SPANNING TREE问题,是否都存在于NP中。 P>
机译:医学诊断和治疗是NP-Complete
机译:测试间隙K平面性是NP-Treminess
机译:如果空时间是离散的,则可以解决多项式时间中的NP完整问题
机译:决定连接保存融合语法生成的超空白的非空虚是NP-Complete
机译:探索所选NP完全问题的近似算法及其经验分析。
机译:更正了必须提供的东西:通过生物代理探索编码NP完全问题的物理网络来扩展组合计算
机译:基于几何相位的量子计算在Np-Complete中的应用 问题