Geodesic
An asymptotically optimal algorithm for the $m$-peripatetic salesman problem on random inputs with discrete distribution
Diskretnyj analiz i issledovanie operacij, Tome 24 (2017) no. 3, pp. 5-19

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We consider the $m$-Peripatetic Salesman Problem ($m$-PSP) on random inputs with discrete distribution function. In this paper we present a polynomial approximation algorithm which, under certain conditions, with high probability (w.h.p.) gives optimal solution for both the $m$-PSP on random inputs with identical weight functions and the $m$-PSP with different weight functions. Illustr. 1, bibliogr. 27.
Keywords: $m$-Peripatetic Salesman Problem, asymptotically optimal algorithm, random inputs, discrete distribution. 
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     author = {E. Kh. Gimadi and O. Yu. Tsidulko},
     title = {An asymptotically optimal algorithm for the $m$-peripatetic salesman problem on random inputs with discrete distribution},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {5--19},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2017_24_3_a0/}
}
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E. Kh. Gimadi; O. Yu. Tsidulko. An asymptotically optimal algorithm for the $m$-peripatetic salesman problem on random inputs with discrete distribution. Diskretnyj analiz i issledovanie operacij, Tome 24 (2017) no. 3, pp. 5-19. http://geodesic.mathdoc.fr/item/DA_2017_24_3_a0/