Acronis backup recovery 10 workstation Manuale Utente
Copyright © Acronis, Inc., 2000-2009
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2.6. Tower of Hanoi backup scheme
The need to have frequent backups always conflicts with the cost of keeping such backups for a long
time. The Tower of Hanoi (ToH) backup scheme is a useful compromise.
time. The Tower of Hanoi (ToH) backup scheme is a useful compromise.
Tower of Hanoi overview
The Tower of Hanoi scheme is based on a mathematical puzzle of the same name. In the puzzle a
series of rings are stacked in size order, the largest on the bottom, on one of three pegs. The goal is to
move the ring series to the third peg. You are only allowed to move one ring at a time, and are
prohibited from placing a larger ring above a smaller ring. The solution is to shift the first ring every
other move (moves 1, 3, 5, 7, 9, 11...), the second ring at intervals of four moves (moves 2, 6, 10...),
the third ring at intervals of eight moves (moves 4, 12...), and so on.
series of rings are stacked in size order, the largest on the bottom, on one of three pegs. The goal is to
move the ring series to the third peg. You are only allowed to move one ring at a time, and are
prohibited from placing a larger ring above a smaller ring. The solution is to shift the first ring every
other move (moves 1, 3, 5, 7, 9, 11...), the second ring at intervals of four moves (moves 2, 6, 10...),
the third ring at intervals of eight moves (moves 4, 12...), and so on.
For example, if there are five rings labeled A, B, C, D, and E in the puzzle, the solution gives the
following order of moves:
following order of moves:
The Tower of Hanoi backup scheme is based on the same patterns. It operates with Sessions instead
of Moves and with Backup levels instead of Rings. Commonly an N-level scheme pattern contains (N-
th power of two) sessions.
of Moves and with Backup levels instead of Rings. Commonly an N-level scheme pattern contains (N-
th power of two) sessions.
So, the five-level Tower of Hanoi backup scheme cycles the pattern that consists of 16 sessions
(moves from 1 to 16 in the above figure).
(moves from 1 to 16 in the above figure).
The table shows the pattern for the five-level backup scheme. The pattern consists of 16 sessions.
The Tower of Hanoi backup scheme implies keeping only one backup per level. All the outdated
backups have to be deleted. So the scheme allows for efficient data storage: more backups
accumulate toward the present time. Having four backups, you can recover data as of today,
yesterday, half a week ago, or a week ago. For the five-level scheme you can also recover data backed
up two weeks ago. So every additional backup level doubles the maximal roll-back period for your
data.
backups have to be deleted. So the scheme allows for efficient data storage: more backups
accumulate toward the present time. Having four backups, you can recover data as of today,
yesterday, half a week ago, or a week ago. For the five-level scheme you can also recover data backed
up two weeks ago. So every additional backup level doubles the maximal roll-back period for your
data.