In “An Improved Approximation Algorithm for TSP,” Karlin, Klein, and Oveis Gharan design the first improvement over classical 1.5 approximation algorithm of Christofides-Serdyukov after more than 40 years. Their chooses a random spanning tree from maximum entropy distribution trees with marginals equal to optimum LP solution TSP, then, similar Christofides’ algorithm, it adds minimum cost match...

An approximation algorithm is an efficient algorithm that finds an approximate solution with a provable approximation guarantee. The standard measure of the quality of an approximation algorithm is its approximation factor. The approximation factor of an algorithm is the worst case ratio between the value (cost) of the solution the algorithm finds and the value (cost) of the optimal solution. T...

in this paper, we introduce an efficient method for solving the quadratic riccati differential equation. in this technique, combination of laplace transform and new homotopy perturbation methods (ltnhpm) are considered as an algorithm to the exact solution of the nonlinear riccati equation. unlike the previous approach for this problem, so-called nhpm, the present method, does not need the init...