On Asymptotically Optimal Solvability of Max m-k-Cycles Cover Problem in a Normed Space

On Asymptotically Optimal Solvability of Euclidean Max m-k-Cycles Cover Problem

“…A polynomial-time approximation algorithm A with parameters t * = m n m d+1 d−1 and k ≤ min n 8m , o(n) gives asymptotically optimal solutions for the Max m-k-CsCP in the Euclidean space with a fixed dimension d and m = o(n).Proof. Setting the given value of the parameter t = t * in the condition of Theorem, we obtainε A (n) ≤2k The specificity of the Euclidean space made it possible to obtain a solution of the Max m-k-CsCP with better accuracy in comparison with the solution in a Normed space in[9].Indeed, it follows directly from the estimations of the relative error ε A (n) in Theorems 3…”

“…Our goal is to explore a more general problem with both m and k being given as a part of input. Note that, using properties of the remote angle between two vectors in the normed space, introduced in [17], an asymptotically optimal approach was realized for the Normed Max m-PSP [8], and then for the Normed Max m-k-CsCP [9].…”