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.istoday/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 '''top-nodes algorithm''' is an [[algorithm]] for managing a resource reservation calendar. The algorithm has been first published in 2003,<ref>[https://archive.is/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]]).

The algorithm allows users to:

* check if an amount of [[resource]] is available during a specific period of time,

* reserve an amount of resource for a specific period of time,

* delete a previous reservation,

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==Principle==

The calendar is stored as a [[binary tree]] where leaves represent elementary time periods. Other nodes represent the period of time covered by all their descendants.

<center>[[File:AlgoRayroleArbre.svg|center|Example of a seven-hour calendar (with elementary periods of one hour)]]</center>

<{{center>|''Example of a seven-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

* 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==