Dear list, Thanks a lot for the many replies to my query on how to distribute points in a complex area in an optimal way.
A few of you gave me a list of papers on network optimization that do not reply to my question as these take into account the spatial correlation of the monitored phenomenon. My question was about the location of points independently of any variable and was thus somehow geometrical question. To reuse Gerards' words, I want to minimise the maximum distance from any point in the area to the nearest sampling point, not minimize the kriging variance. An impressive review on the last topic (sampling design + matlab codes for network optimization) can be found in Gunter Spoeck's PhD, see http://www.math.uni-klu.ac.at/~guspoeck/book.pdf , (22 MB pdf). Chapter 9 in Okabe et al. is a good reference and discusses as a case study the optimal distribution of mailboxes in Tokyo. However, the borders of the monitored area are defined as a rectangle, which simplifies greatly the problem. Another reference (see end of mail) given to me seems to be more appropriate for what I am looking for. Still have to read it properly but it is very much related to what I am looking for (here, its is about the distrubution of siren locations). Thanks Morton ! SOFTWARE: >From Jeffrey W. Lively, I received the following suggestions: - Visual Sample Plan (VSP). It is maintained by Battelle for the DOE's Pacific Northwest National Laboratory in Washington State. It has an algorithm that they call adaptive fill which is designed to suggest to you the optimal spatial location to place additional samples. - SADA. It has comparable adaptive fill algorithms and can suggest sample placement based on reducing the amount of uncertainty in addition to simple geometric considerations. It is developed and maintained by the University of Tennessee and is available for download from the web. Very useful (thanks to [EMAIL PROTECTED] for that!) is the following resource: http://www.faqs.org/faqs/graphics/algorithms-faq/ PAPERS In addition to Roderick's reference "Spatial tessellations: Concepts and applications of Voronoi diagrams", by Atsuyuki Okabe and Barry Boots and Kokichi Sugihara and Sung Nok Chiu. Published by Wiley, NYC (2000), worth to mention are: Papers in Regional Science Volume 83 Page 565 - July 2004 doi:10.1111/j.1435-5597.2004.tb01925.x Volume 83 Issue 3 A lattice covering model for evaluating existing service facilities Morton E. O'Kelly, Alan T. Murray Abstract. This article presents the following location problem: align a regularly spaced grid of new facilities as well as possible with a set of existing centres. The problem has some similarity to a problem in classical central place theory, namely the spatial arrangement of services with a particular range of coverage. The article poses the problem, gives a non-linear formulation, and details solution approaches. A robust heuristic, based on geometric insights, is also devised: if the basis for the new grid is centred on at least one fixed centre, an enumeration of various rotation angles will be effective for finding local minima (and maxima). As a practical application of this problem, a region may wish to supplement an existing system of fixed siren locations with additional facilities in such a way as to fill in, or complete, the partial coverage pattern. An evaluation of the siren system in Dublin, OH, USA, is utilised to demonstrate the effectiveness of the technique. 2 other references provided by Dan Bebber are: Button J et al. 1996. Mobile network design and optimisation. British Telecom Technology Journal 14:29-46 G. W. Wiskin, R. G. Manton and J. H. Causebrook 1992. Masts, Antennas and Service Planning, Focal Press. I did not list other references I received on monitoring network optimization for groundwater, rainfall, etc. modelling as these are not directly linked to my question. Thanks to all for the replies and discussions ! Gregoire __________________________________________ Gregoire Dubois (Ph.D.) European Commission (EC) Joint Research Centre (JRC) Institute for Environment and Sustainability (IES) TP 441, Via Fermi 1 21020 Ispra (VA) ITALY Tel. +39 (0)332 78 6360 Fax. +39 (0)332 78 5466 Email: [EMAIL PROTECTED] WWW: http://www.ai-geostats.org WWW: http://rem.jrc.cec.eu.int "The views expressed are purely those of the writer and may not in any circumstances be regarded as stating an official position of the European Commission."
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