Randomized approximation scheme for Steiner Multi Cycle in the Euclidean plane

We propose a randomized approximation scheme for the Euclidean Steiner Multi Cycle problem which runs in quasilinear time. In this problem, we are given a set ofnpairs of points (terminals) T = {t(i), t(i)'}(i=1)(n) in the Euclidean plane, and the objective is to find a collection of cycles of minimum cost such that t(i) and t(i)' belong to a same cycle, for each i is an element of {1, ... ,n}. This problem extends the Steiner Cycle problem in the same way the Steiner Forest extends the Steiner Tree problem. Additionally, it has applications on routing problems with pickup and delivery locations. (c) 2020 Elsevier B.V. All rights reserved.