A fast approximation algorithm for TSP with neighborhoods and red-blue separation
Author
Editor
- Takano Asano
Summary, in English
In TSP with neighborhoods (TSPN) we are given a collec-tion X of k polygonal regions, called neighborhoods, with totally n ver-tices, and we seek the shortest tour that visits each neighborhood. TheEuclidean TSP is a special case of the TSPN problem, so TSPN is alsoNP-hard. In this paper we present a simple and fast algorithm that, givena start point, computes a TSPN tour of length O(log k) times the opti-mum in time O(n+k log k). When no start point is given we show howto compute a good start point in time O(n2 log n), hence we obtain alogarithmic approximation algorithm that runs in time O(n2 log n). Wealso present an algorithm which performs at least one of the followingtwo tasks (which of these tasks is performed depends on the given input):(1) It outputs in time O(n log n) a TSPN tour of length O(log k) timesthe optimum. (2) It outputs a TSPN tour of length less than (1+) timesthe optimum in cubic time, where is an arbitrary real constant givenas an optional parameter.The results above are signicant improvements, since the best previouslyknown logarithmic approximation algorithm runs in (n5) time in theworst case.
Department/s
- Computer Science
Publishing year
1999
Language
English
Pages
473-482
Publication/Series
Computing and combinatorics / Lecture notes in computer science
Volume
1627
Full text
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Document type
Conference paper
Publisher
Springer
Topic
- Computer Science
Conference name
5th annual international conference, COCOON '99
Conference date
1999-07-26 - 1999-07-28
Conference place
Tokyo, Japan
Status
Published