Content deleted Content added
Reword, fix a link's apperance |
Added a covering problem image and description. |
||
Line 26:
==Kinds of covering problems==
There are various kinds of covering problems in [[graph theory]], [[computational geometry]] and more; see [[:Category:Covering problems]]. Other stochastic related versions of the problem can be found.<ref>{{cite web|author = Douek-Pinkovich, Y., Ben-Gal, I., & Raviv, T. (2022)|title = The Stochastic Test Collection Problem: Models, Exact and Heuristic Solution Approaches |url = http://www.eng.tau.ac.il/~bengal/STCP.pdf|publisher = European Journal of Operational Research, 299 (2022), 945–959} }}</ref>
[[File:Covering problem of Rado.gif|thumb|500px|The [[covering problem of Rado]], where a series of squares with parallel edges needs to cover an area of 1. For any set meeting these conditions, a subset of these squares is selected (indicated by the red coloring) in which no two squares overlap, and the total area is maximized. The goal is to make an arrangement of squares so that the total area of the optimal subset is ''minimized''. The examples each have maximal areas of 1/4, but there are some which have slightly lower.
<ref>{{citation
| last = Ajtai | first = Miklós | author-link = Miklós Ajtai
| journal = Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Mathématiques, Astronomiques et Physiques
| mr = 319053
| pages = 61–63
| title = The solution of a problem of T. Radó
| volume = 21
| year = 1973}}</ref>
<ref>{{citation
| last1 = Bereg | first1 = Sergey
| last2 = Dumitrescu | first2 = Adrian
| last3 = Jiang | first3 = Minghui
| doi = 10.1007/s00453-009-9298-z
| issue = 3
| journal = Algorithmica
| mr = 2609053
| pages = 538–561
| title = On covering problems of Rado
| volume = 57
| year = 2010}}; preliminary announcement in [[SWAT and WADS conferences|SWAT 2008]], {{doi|10.1007/978-3-540-69903-3_27}}</ref>]]
=== Covering in Petri nets ===
| |||