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The Minimum Manhattan Network Problem: Approximations and Exact SolutionsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2006 (English)In: Computational geometry, ISSN 0925-7721, E-ISSN 1879-081X, Vol. 35, no 3, p. 188-208Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Elsevier, 2006. Vol. 35, no 3, p. 188-208
##### Keywords [en]

Spanners, Minimum Manhattan networks, Approximation algorithm, Mixed-integer programming
##### National Category

Computer Sciences
##### Identifiers

URN: urn:nbn:se:kth:diva-66463DOI: 10.1016/j.comgeo.2005.09.004ISI: 000240795500004Scopus ID: 2-s2.0-84867954426OAI: oai:DiVA.org:kth-66463DiVA, id: diva2:484115
#####

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##### Note

Given a set of points in the plane and a constant *t*⩾1, a Euclidean *t*-*spanner* is a network in which, for any pair of points, the ratio of the network distance and the Euclidean distance of the two points is at most *t*. Such networks have applications in transportation or communication network design and have been studied extensively.

In this paper we study 1-spanners under the Manhattan (or *L*_{1}-) metric. Such networks are called *Manhattan networks*. A Manhattan network for a set of points is a set of axis-parallel line segments whose union contains an *x*- and *y*-monotone path for each pair of points. It is not known whether it is NP-hard to compute minimum Manhattan networks (MMN), i.e., Manhattan networks of minimum total length. In this paper we present an approximation algorithm for this problem. Given a set *P* of *n* points, our algorithm computes in O(*n*log*n*) time and linear space a Manhattan network for *P* whose length is at most 3 times the length of an MMN of *P*.

We also establish a mixed-integer programming formulation for the MMN problem. With its help we extensively investigate the performance of our factor-3 approximation algorithm on random point sets.

QC 20120126

Available from: 2012-01-26 Created: 2012-01-26 Last updated: 2018-01-12Bibliographically approved
doi
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