As we know if you are using dump as a backup system. Then modified tower of hanoi algorithm is suitable. But why?
The idea is is to make the numbers rise and fall to minimise the number of backups needed to do a full restore. Write yourself some sequences and figure out for yourself which ones you would need for a full backup. Try to figure out for each backup whether the same files will be dumped by a later backup. They will, if a later backup number is lower. The agorithm your aiming to create is Start with a level 0 and ignore everything before. from end of list, find the lowest number before you reach the starting dump. You'll need this backup. Make it the new start of list. from end of list, find the lowest number before you reach the starting dump. You'll need this backup. Make it the new start of list. etc. E.g. Given 0 3 2 5 4 7 6 9 To restore everything you need the 0, 2, 4 and 6. I.e. every second dump. You'll see that wherever you stop in that sequence, no more than 3 backups are required to recover everything.
Nice.Using the algorithm above I get the following:Sequence
Sequence Dumps needed
0 3 0 3
0 3 2 0 2
0 3 2 5 0 2 5
0 3 2 5 4 0 2 4
0 3 2 5 4 7 0 2 4 7
0 3 2 5 4 7 6 0 2 4 6
0 3 2 5 4 7 6 9 0 2 4 6 9
Every time a dump of level N is, eh, taken,earlier tapes of level N become obsolete and are free to go(*). In thiscase, that happens every other time.
The idea is is to make the numbers rise and fall to minimise the number of backups needed to do a full restore. Write yourself some sequences and figure out for yourself which ones you would need for a full backup. Try to figure out for each backup whether the same files will be dumped by a later backup. They will, if a later backup number is lower. The agorithm your aiming to create is Start with a level 0 and ignore everything before. from end of list, find the lowest number before you reach the starting dump. You'll need this backup. Make it the new start of list. from end of list, find the lowest number before you reach the starting dump. You'll need this backup. Make it the new start of list. etc. E.g. Given 0 3 2 5 4 7 6 9 To restore everything you need the 0, 2, 4 and 6. I.e. every second dump. You'll see that wherever you stop in that sequence, no more than 3 backups are required to recover everything.
Nice.Using the algorithm above I get the following:Sequence
Sequence Dumps needed
0 3 0 3
0 3 2 0 2
0 3 2 5 0 2 5
0 3 2 5 4 0 2 4
0 3 2 5 4 7 0 2 4 7
0 3 2 5 4 7 6 0 2 4 6
0 3 2 5 4 7 6 9 0 2 4 6 9
Every time a dump of level N is, eh, taken,earlier tapes of level N become obsolete and are free to go(*). In thiscase, that happens every other time.
