Top-nodes algorithm: Difference between revisions

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The '''top-nodes algorithm''' is an [[algorithm]] for managing a resource reservation calendar. The algorithm has been first published in 2003,<ref>[https://archive.today/20120215024923/http://www.wikipatents.com/apps/20040204978.html Related US patent] (the algorithm is in the public ___domain since 2008)</ref> and has been improved in 2009.<ref>[https://www.researchgate.net/publication/311582722_Method_of_Managing_Resources_in_a_Telecommunication_Network_or_a_Computing_System Improved top-nodes algorithm]</ref> It is used when a resource is shared among many users (for example [[Bandwidth (signal processing)|bandwidth]] in a [[telecommunication]] link, or [[disk capacity]] in a large [[data center]]).
{{Underlinked|date=December 2012}}
 
The algorithm allows users to:
The '''top-nodes algorithm''' is an [[algorithm]] for managing a resource reservation calendar.<ref>[http://www.wikipatents.com/apps/20040204978.html Related US patent]</ref>
* to check if an amount of [[resource]] is available during a specific period of time,
 
* to reserve an amount of resource for a specific period of time,
It is used when a resource is shared among lots of users (for example [[Bandwidth (signal processing)|bandwidth]] in a [[telecommunication]] link, or [[disk capacity]] in a large [[data center]]).
* to delete a previous reservation,
 
* to move the calendar forward (the calendar covers a defined duration, and it must be moved forward as time goes by).
The algorithm allows
* to check if an amount of resource is available during a specific period of time,
* to reserve an amount of resource for a specific period of time,
* to delete a previous reservation,
* to move the calendar forward (the calendar covers a defined duration, and it must be moved forward as time goes by).
 
==Principle==
The calendar is stored as a [[binary tree]] where leafsleaves represent elementary time periods. Other nodes represent the period of time covered by all their descendants.
<center>[[File:AlgoRayroleArbre.svg|center|Example of a 7seven-hour calendar (with elementary periods of one hour)]]</center>
<{{center>|''Example of a 7seven-hour calendar (with elementary periods of one hour)''</center>}}
 
The period of time covered by a reservation is represented by a set of "top-nodes". This set is the minimal set of nodes that exactly cover the reservation period of time.
 
A node of the [[binary tree]] is a "top-node" for a given reservation if
* all its descendants are inside the reservation period of time, and
and
* it is the root node, or at least one descendant of the parent node is outside of the reservation period of time.
<center>[[File:AlgoRayroleResa.svg|center|Top-nodes for a reservation from 1:00 to 5:59]]</center>
<{{center>|''Top-nodes for a reservation from 1:00 to 5:59''</center>}}
 
The following value is stored in each node:
q(node) = max(q(left child), q(right child))
+ total amount of reserved resource for all reservations having this node as a "top-node"
(for [[code optimization]], the two parts of this sum are usually stored separately.)
 
==Performance==
The advantage of this algorithm is that the time to register a new resource reservation depends only on the calendar size (it does not depend on the total number of reservations).
 
Let "{{var|n"}} be the number of elementary periods in the calendar.
 
The maximal number of "top-nodes" for a given reservation is 2.log n.
* to check if an amount of resource is available during a specific period of time : ''O''(log ''n'')
* to reserve an amount of resource for a specific period of time : ''O''(log ''n'')
* to delete a previous reservation : ''O''(log ''n'')
* to move the calendar forward : ''O''(log ''n'' + M.log n)
where {{var|M}} is the number of reservations that are active during the added calendar periods.
 
({{var|M}} = 0 if reservations are not allowed after the end of the calendar.)
 
==References==
{{Reflist}}
 
==External links==
* {{in lang|fr}} [http://www.developpez.net/forums/showthread.php?p=3078887 C source code]
 
==References==
<references/>
 
[[Category:Scheduling algorithms]]
[[Category:Calendar algorithms]]