A new algorithm approximates the prize-collecting rural postman problem within a factor strictly less than 1.6 and proves a 2-approximation barrier for PCTSP reductions.
Combining Approximation Algorithms for the Prize-Collecting TSP
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We present a 1.91457-approximation algorithm for the prize-collecting travelling salesman problem. This is obtained by combining a randomized variant of a rounding algorithm of Bienstock et al. and a primal-dual algorithm of Goemans and Williamson.
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Approximation algorithms for the prize-collecting rural postman problem
A new algorithm approximates the prize-collecting rural postman problem within a factor strictly less than 1.6 and proves a 2-approximation barrier for PCTSP reductions.