[en] We investigate the algorithmic complexity of several geometric problems of the following type: given a "feasible" box and a collection of balls in Euclidean space, find a feasible point which is covered by as few or, respectively, by as many balls as possible. We establish that all these problems are NP-hard in their most general version. We derive tight lower and upper bounds on the complexity of their one-dimensional versions. Finally, we show that all these problems can be solved in polynomial time when the dimension of the space is fixed.
Disciplines :
Mathematics Quantitative methods in economics & management
Author, co-author :
Crama, Yves ; Université de Liège > HEC-Ecole de gestion : UER > Recherche opérationnelle et gestion de la production
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Bibliography
F. Aurenhammer, Power diagrams: Properties, algorithms and applications, SIAM Journal on Computing 16(1987)78-96.
S. Albers and K. Brockhoff, A procedure for new product positioning in an attribute space, European Journal of Operational Research 1(1977)230-238.
C.H. Coombs, A Theory of Data, Wiley, New York, 1964.
Y. Crama, P. Hansen and B. Jaumard, Complexity of product positioning and ball intersection problems, Mathematics of Operations Research 20(1995)885-894.
Z. Drezner, On a modified one-center model, Management Science 27(1981)848-851.
H. Edelsbrunner, Algorithms in Combinatorial Geometry, Springer, New York/Berlin/Heidelberg/Tokyo, 1987.
M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freeman, New York, 1979.
B. Gavish, D. Horsky and K. Srikanth, An approach to the optimal positioning of a new product, Management Science 29(1983)1277-1297.
P.E. Green and A.M. Krieger, Recent contributions to optimal product positioning and buyer segmentation, European Journal of Operational Research 41(1989)127-141.
Similar publications
Sorry the service is unavailable at the moment. Please try again later.
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.
