Skip to main content

Tower of Hanoi

Tower of Hanoi is a complex tape backup strategy that's useful for archiving data for an extended period of time in an economical manner. The strategy, which is based on a mathematical puzzle invented by the French mathematician Edouard Lucas, uses a cycle of exponential retention periods instead of a large number of tapes.

Lucas, who is well-known for his study of the Fibonacci sequence and his work with prime numbers, loved recreational mathematics. His Tower of Hanoi puzzle, which is still marketed as a toy for children, has a platform with three poles. There is a stack of disks or rings on the first pole. The stack looks like a pyramid; each disk going down the pole is a little larger than the one above it. To solve Lucas' puzzle, the player must move all the discs from the first pole to the third pole in the fewest possible moves. There are two rules: only one disk can be moved at a time and a larger disc cannot be placed on top of a smaller one.

There are several ways to solve the puzzle, but one of the easiest ways is to start with only one ring -- and then figure out how to solve it with two rings -- and then figure out how to solve it with three rings. Once you have solved the puzzle using small numbers, patterns will begin to emerge. This is known as a recursive solution. (See recursion.) A recursive pattern uses the information gained from one step to figure out the next step.


Number of disks
Fewest number of moves
1
1
2
3
3
7
4
15
5
31

Like the puzzle, Towers of Hanoi backup uses a recursive pattern for scheduling tapes. It enables an administrator to restore data from backups that are one, two, four, eight and sixteen days old, yet only use five tapes. This strategy, which requires backup software to support the complex rotation schedule, is good for small businesses that need to be able to do full restores.

Comments

Post a Comment

Popular posts from this blog

Ghosting

Ghosting is to cease communications without notification. The use of the word "ghost" as a verb originated in social media in reference to dating, but the term is now used by employers to describe employees and potential employees who suddenly disappear. Typically, ghosting is used to describe: Job candidates who suddenly stop responding to messages. New hires who fail to show up for their first day of work. Employees who do not show up for a shift. Employees who leave work in the middle of the day and never come back. Some analysts blame ghosting on millennial entitlement. The reasoning is that members of the millennial generation have been brought up to feel they are special -- so special, in fact, that they do not need to follow conventional rules of behavior. Other analysts, however, maintain that ghosting behavior stems from changes in the job market and the phenomenon is simply a reflection of the laws of supply and demand in a healthy jo...
Post a Comment
Read more

Data deduplication

Data deduplication -- often called intelligent compression or single-instance storage -- is a process that eliminates redundant copies of data and reduces storage overhead. Data deduplication techniques ensure that only one unique instance of data is retained on storage media, such as disk, flash or tape. Redundant data blocks are replaced with a pointer to the unique data copy. In that way, data deduplication closely aligns with incremental backup, which copies only the data that has changed since the previous backup. For example, a typical email system might contain 100 instances of the same 1 megabyte (MB) file attachment. If the email platform is backed up or archived, all 100 instances are saved, requiring 100 MB of storage space. With data deduplication, only one instance of the attachment is stored; each subsequent instance is referenced back to the one saved copy. In this example, a 100 MB storage demand drops to 1 MB. Target vs. source deduplication Data deduplica...
Post a Comment
Read more

A Graphics Processing Unit (GPU)

A graphics processing unit (GPU) is a computer chip that performs rapid mathematical calculations, primarily for the purpose of rendering images. A GPU may be found integrated with a central processing unit (CPU) on the same circuit, on a graphics card or in the motherboard of a personal computer or server. In the early days of computing, the CPU performed these calculations. As more graphics-intensive applications such as AutoCAD were developed; however, their demands put strain on the CPU and degraded performance. GPUs came about as a way to offload those tasks from CPUs, freeing up their processing power. NVIDIA, AMD, Intel and ARM are some of the major players in the GPU market. GPU vs. CPU A graphics processing unit is able to render images more quickly than a central processing unit because of its parallel processing architecture, which allows it to perform multiple calculations at the same time. A single CPU does not have this capability, although multi...
Post a Comment
Read more