The general asymmetric TSP with triangle inequality is known to be approximable only to within an O(log n) factor, and is also known to be approximable within a constant factor as soon as the metric is bounded. In this paper we study the asymmetric and symmetric TSP problems with bounded metrics and prove approximation lower bounds of 131=130 and 174=173, respectively, for these problems, impro...

Abstract By means of the weight functions, Hermite–Hadamard’s inequality, and techniques real analysis, a new more accurate reverse half-discrete Mulholland-type inequality involving one higher-order derivative function is given. The equivalent statements best possible constant factor related to few parameters, forms, several particular inequalities are provided. Another kind reverses also cons...