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 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, * 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 leaves represent elementary time periods. Other nodes represent the period of time covered by all their descendants. center|Example of a seven-hour calendar (with elementary periods of one hour) {{center|''Example of a seven-hour calendar (with elementary periods of one hour)''}}
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|Top-nodes for a reservation from 1:00 to 5:59 {{center|''Top-nodes for a reservation from 1:00 to 5:59''}}
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]
Category:Scheduling algorithms