Reduction from prize-collecting-Φ-TSP to prize-collecting TSP yields (ρ + ε)-approximations for constant prescribed vertices, improving the prize-collecting stroll guarantee to better than 1.6 from 1.6662.
Schrijver.Combinatorial Optimization: Polyhedra and Efficiency
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Reducing Prize-Collecting Stroll and Related Routing Problems to Prize-Collecting TSP
Reduction from prize-collecting-Φ-TSP to prize-collecting TSP yields (ρ + ε)-approximations for constant prescribed vertices, improving the prize-collecting stroll guarantee to better than 1.6 from 1.6662.