Locating a median line with partial coverage distance

Jack Brimberg, Robert Schieweck () and Anita Schöbel

Journal of Global Optimization, 2015, vol. 62, issue 2, 389 pages

Abstract: We generalize the classical median line location problem, where the sum of distances from a line to some given demand points is to be minimized, to a setting with partial coverage distance. In this setting, a demand point within a certain specified threshold distance $$r$$ r of the line is considered covered and its partial coverage distance is considered to be zero, while non-covered demand points are penalized an amount proportional to their distance to the coverage region. The sum of partial coverage distances is to be minimized. We consider general norm distances as well as the vertical distance and extend classical properties of the median line location problem to the partial coverage case. We are finally able to derive a finite dominating set. While a simple enumeration of the finite dominating set takes $$O(m^3)$$ O ( m 3 ) time, $$m$$ m being the number of demand points, we show that this can be reduced to $$O(m^2\log m)$$ O ( m 2 log m ) in the general case by plane sweeping techniques and even to $$O(m)$$ O ( m ) for the vertical distance and block norm distances by linear programming. Copyright Springer Science+Business Media New York 2015

Keywords: Median line location; Partial coverage; Finite dominating set; Plane sweeping; Block norm (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10898-014-0239-2 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jglopt:v:62:y:2015:i:2:p:371-389

Ordering information: This journal article can be ordered from
http://www.springer. ... search/journal/10898

DOI: 10.1007/s10898-014-0239-2

Access Statistics for this article

Journal of Global Optimization is currently edited by Sergiy Butenko

More articles in Journal of Global Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().