Polynomial Time Approximation Scheme for the Minimum-weight k-Size Cycle Cover Problem in Euclidean space of an arbitrary fixed dimension

Michael Khachay, Katherine Neznakhina
2016 IFAC-PapersOnLine  
We study the Min-k-SCCP on the partition of a complete weighted digraph by k vertex-disjoint cycles of minimum total weight. This problem is the generalization of the wellknown traveling salesman problem (TSP) and the special case of the classical vehicle routing problem (VRP). It is known that the problem Min-k-SCCP is strongly NP-hard and remains intractable even in the geometric statement. For the Euclidean Min-k-SCCP in R d , we construct a polynomial-time approximation scheme, which
more » ... izes the approach proposed earlier for the planar Min-2-SCCP. For any fixed c > 1, the scheme finds Keywords: cycle cover of size k, traveling salesman problem (TSP), NP-hard problem, polynomial-time approximation scheme (PTAS). Abstract: We study the Min-k-SCCP on the partition of a complete weighted digraph by k vertex-disjoint cycles of minimum total weight. This problem is the generalization of the wellknown traveling salesman problem (TSP) and the special case of the classical vehicle routing problem (VRP). It is known that the problem Min-k-SCCP is strongly NP-hard and remains intractable even in the geometric statement. For the Euclidean Min-k-SCCP in R d , we construct a polynomial-time approximation scheme, which generalizes the approach proposed earlier for the planar Min-2-SCCP. For any fixed c > 1, the scheme finds a (1 + 1/c)-approximate solution Keywords: cycle cover of size k, traveling salesman problem (TSP), NP-hard problem, polynomial-time approximation scheme (PTAS).
doi:10.1016/j.ifacol.2016.07.541 fatcat:jzsopddbcfb4zjne2ij4lnpsha