The top-nodes algorithm is an algorithm for managing a resource reservation calendar. The algorithm has been first published in 2003,[1] and has been improved in 2009.[2] 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.
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.
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 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 M is the number of reservations that are active during the added calendar periods.
(M = 0 if reservations are not allowed after the end of the calendar.)
References
- ^ Related US patent (the algorithm is in the public domain since 2008)
- ^ Improved top-nodes algorithm
External links
- (in French) C source code
This page was last edited on 5 October 2022, at 13:34