Approximation algorithms for the maximum m-peripatetic salesman problem

Edward Kh Gimadi; Oxana Yu Tsidulko

doi:10.1007/978-3-319-73013-4_28

Approximation algorithms for the maximum m-peripatetic salesman problem

Результат исследования: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › рецензирование

Аннотация

We consider the maximum m-Peripatetic Salesman Problem (MAX m-PSP), which is a natural generalization of the classic Traveling Salesman Problem. The problem is strongly NP-hard. In this paper we propose two polynomial approximation algorithms for the MAX m-PSP with different and identical weight functions, correspondingly. We prove that for random inputs uniformly distributed on the interval [a, b] these algorithms are asymptotically optimal for m= o(n). This means that with high probability their relative errors tend to zero as the number n of the vertices of the graph tends to infinity. The results remain true for the distributions of inputs that minorize the uniform distribution.

Язык оригинала	английский
Название основной публикации	Analysis of Images, Social Networks and Texts - 6th International Conference, AIST 2017, Revised Selected Papers
Редакторы	WMP VanDerAalst, DI Ignatov, M Khachay, SO Kuznetsov, Lempitsky, IA Lomazova, N Loukachevitch, A Napoli, A Panchenko, PM Pardalos, AV Savchenko, S Wasserman
Издатель	Springer-Verlag GmbH and Co. KG
Страницы	304-312
Число страниц	9
ISBN (печатное издание)	9783319730127
DOI	https://doi.org/10.1007/978-3-319-73013-4_28
Состояние	Опубликовано - 1 янв 2018
Событие	6th International Conference on Analysis of Images, Social Networks and Texts, AIST 2017 - Moscow, Российская Федерация Продолжительность: 27 июл 2017 → 29 июл 2017

Серия публикаций

Название	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Том	10716 LNCS
ISSN (печатное издание)	0302-9743
ISSN (электронное издание)	1611-3349

Конференция

Конференция	6th International Conference on Analysis of Images, Social Networks and Texts, AIST 2017
Страна	Российская Федерация
Город	Moscow
Период	27.07.2017 → 29.07.2017

Доступ к документу

10.1007/978-3-319-73013-4_28

Link to publication in Scopus

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Цитировать

Gimadi, E. K., & Tsidulko, O. Y. (2018). Approximation algorithms for the maximum m-peripatetic salesman problem. В WMP. VanDerAalst, DI. Ignatov, M. Khachay, SO. Kuznetsov, Lempitsky, IA. Lomazova, N. Loukachevitch, A. Napoli, A. Panchenko, PM. Pardalos, AV. Savchenko, & S. Wasserman (Ред.), Analysis of Images, Social Networks and Texts - 6th International Conference, AIST 2017, Revised Selected Papers (стр. 304-312). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Том 10716 LNCS). Springer-Verlag GmbH and Co. KG. https://doi.org/10.1007/978-3-319-73013-4_28

Gimadi, Edward Kh ; Tsidulko, Oxana Yu. / Approximation algorithms for the maximum m-peripatetic salesman problem. Analysis of Images, Social Networks and Texts - 6th International Conference, AIST 2017, Revised Selected Papers. редактор / WMP VanDerAalst ; DI Ignatov ; M Khachay ; SO Kuznetsov ; Lempitsky ; IA Lomazova ; N Loukachevitch ; A Napoli ; A Panchenko ; PM Pardalos ; AV Savchenko ; S Wasserman. Springer-Verlag GmbH and Co. KG, 2018. стр. 304-312 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We consider the maximum m-Peripatetic Salesman Problem (MAX m-PSP), which is a natural generalization of the classic Traveling Salesman Problem. The problem is strongly NP-hard. In this paper we propose two polynomial approximation algorithms for the MAX m-PSP with different and identical weight functions, correspondingly. We prove that for random inputs uniformly distributed on the interval [a, b] these algorithms are asymptotically optimal for m= o(n). This means that with high probability their relative errors tend to zero as the number n of the vertices of the graph tends to infinity. The results remain true for the distributions of inputs that minorize the uniform distribution.",

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Gimadi, EK & Tsidulko, OY 2018, Approximation algorithms for the maximum m-peripatetic salesman problem. в WMP VanDerAalst, DI Ignatov, M Khachay, SO Kuznetsov, Lempitsky, IA Lomazova, N Loukachevitch, A Napoli, A Panchenko, PM Pardalos, AV Savchenko & S Wasserman (ред.), Analysis of Images, Social Networks and Texts - 6th International Conference, AIST 2017, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), том. 10716 LNCS, Springer-Verlag GmbH and Co. KG, стр. 304-312, 6th International Conference on Analysis of Images, Social Networks and Texts, AIST 2017, Moscow, Российская Федерация, 27.07.2017. https://doi.org/10.1007/978-3-319-73013-4_28

Approximation algorithms for the maximum m-peripatetic salesman problem. / Gimadi, Edward Kh ; Tsidulko, Oxana Yu.

Analysis of Images, Social Networks and Texts - 6th International Conference, AIST 2017, Revised Selected Papers. ред. / WMP VanDerAalst; DI Ignatov; M Khachay; SO Kuznetsov; Lempitsky; IA Lomazova; N Loukachevitch; A Napoli; A Panchenko; PM Pardalos; AV Savchenko; S Wasserman. Springer-Verlag GmbH and Co. KG, 2018. стр. 304-312 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Том 10716 LNCS).

Результат исследования: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › рецензирование

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N2 - We consider the maximum m-Peripatetic Salesman Problem (MAX m-PSP), which is a natural generalization of the classic Traveling Salesman Problem. The problem is strongly NP-hard. In this paper we propose two polynomial approximation algorithms for the MAX m-PSP with different and identical weight functions, correspondingly. We prove that for random inputs uniformly distributed on the interval [a, b] these algorithms are asymptotically optimal for m= o(n). This means that with high probability their relative errors tend to zero as the number n of the vertices of the graph tends to infinity. The results remain true for the distributions of inputs that minorize the uniform distribution.

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Gimadi EK , Tsidulko OY. Approximation algorithms for the maximum m-peripatetic salesman problem. В VanDerAalst WMP, Ignatov DI, Khachay M, Kuznetsov SO, Lempitsky, Lomazova IA, Loukachevitch N, Napoli A, Panchenko A, Pardalos PM, Savchenko AV, Wasserman S, редакторы, Analysis of Images, Social Networks and Texts - 6th International Conference, AIST 2017, Revised Selected Papers. Springer-Verlag GmbH and Co. KG. 2018. стр. 304-312. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-73013-4_28