Sparsest Cut

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. That is, an algorithm has approximation factor (at most) α = α(n) if for every instance of the problem of size n the algorithm finds a feasible solution of value at most αOPT, if the problem is a minimization problem, and of value at least αOPT if the problem is a maximization problem, where OPT is the value of the optimal solution. An algorithm is an α-approximation algorithm if it gives α-approximation.