Abstract
In this paper we study a natural special case of the Traveling Salesman Problem (TSP) with pointlocationaluncertainty which we will call the adversarial TSP problem (ATSP). Given a metric space (X, d) and a set of subsets R = {R_1, R_2, ... , R_n} : R_i subseteq X, the goal is to devise an ordering of the regions, sigma_R, that the tour will visit such that when a single point is chosen from each region, the induced tour over those points in the ordering prescribed by sigma_R is as short as possible. Unlike the classical locationaluncertaintyTSP problem, which focuses on minimizing the expected length of such a tour when the point within each region is chosen according to some probability distribution, here, we focus on the adversarial model in which once the choice of sigma_R is announced, an adversary selects a point from each region in order to make the resulting tour as long as possible. In other words, we consider an offline problem in which the goal is to determine an ordering of the regions R that is optimal with respect to the ``worst'' point possible within each region being chosen by an adversary, who knows the chosen ordering. We give a 3approximation when R is a set of arbitrary regions/sets of points in a metric space. We show how geometry leads to improved constant factor approximations when regions are parallel line segments of the same lengths, and a polynomialtime approximation scheme (PTAS) for the important special case in which R is a set of disjoint unit disks in the plane.
BibTeX  Entry
@InProceedings{citovsky_et_al:LIPIcs:2017:7233,
author = {Gui Citovsky and Tyler Mayer and Joseph S. B. Mitchell},
title = {{TSP With Locational Uncertainty: The Adversarial Model}},
booktitle = {33rd International Symposium on Computational Geometry (SoCG 2017)},
pages = {32:132:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959770385},
ISSN = {18688969},
year = {2017},
volume = {77},
editor = {Boris Aronov and Matthew J. Katz},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/7233},
URN = {urn:nbn:de:0030drops72334},
doi = {10.4230/LIPIcs.SoCG.2017.32},
annote = {Keywords: traveling salesperson problem, TSP with neighborhoods, approximation algorithms, uncertainty}
}
Keywords: 

traveling salesperson problem, TSP with neighborhoods, approximation algorithms, uncertainty 
Seminar: 

33rd International Symposium on Computational Geometry (SoCG 2017) 
Issue Date: 

2017 
Date of publication: 

08.06.2017 