Map segmentation: Difference between revisions

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In [[mathematics]], the '''map segmentation''' problem is a kind of [[optimization problem]]. It involves a certain geographic region that has to be partitioned into smaller sub-regions in order to achieve a certain goal. Typical optimization objectives include:<ref name=rag14>{{cite book | url=http://search.proquest.com/docview/1614472017 | title=Geometric Partitioning Algorithms for Fair Division of Geographic Resources | publisher=A Ph.D. thesis submitted to the faculty of university of Minnesota | author=Raghuveer Devulapalli (|others=Advisor: John Gunnar Carlsson) | year=2014|id = {{ProQuest|1614472017}}}}</ref>

* Minimizing the workload of a fleet of vehicles assigned to the sub-regions;

* Balancing the consumption of a resource, as in [[fair cake-cutting]].

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* Maximizing the surveillance coverage.

Fair division of land has been an important issue since ancient times, e.g. in [[ancient Greece]].<ref>{{Cite journal|doi=10.2307/147876|jstor=147876|title=Urban and Rural Land Division in Ancient Greece|journal=Hesperia|volume=50|issue=4|pages=327|year=1981|last1=Boyd|first1=Thomas D.|last2=Jameson|first2=Michael H.}}</ref>

== Notation ==