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Polynomial-time $(k+\epsilon)$-approximation for $k$-coloured Non-crossing Euclidean TSP
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abstract
Given a $k$-coloured point set $P\subseteq \mathbb{R}^2$, the $k$-coloured Non-crossing Euclidean Travelling Salesperson Problem (short $k$-ETSP) asks for $k$ non-crossing closed curves, where one curve spans one corresponding colour class, such that the curves are pairwise non-crossing and the sum of their Euclidean lengths is minimised. This problem is NP-hard as $1$-ETSP is the standard Euclidean Travelling Salesperson Problem. We present a polynomial-time $(k+\epsilon)$-approximation for $k$-ETSP.
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