Persistent Data Structures Version Control v 0 v 1 v 2 v 3 v 4 v 5 v 6 Ephemeral query v 0 v 1 v 2 v 3 v 4 v 5 v 6 Partial persistence query only update ID: 389805
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Slide1
update
Persistent
Data
Structures
(Version
Control)
v0
v1
v2
v3
v4
v5
v
6
Ephemeral
query
v
0
v
1
v
2
v
3
v
4
v
5
v
6
Partial
persistence
query
only
update
& query
v
0
v1
v2
v3
v4
v6
Full
persistence
updates
at leavesany version can be copiedquery all versions
v
5
v
0
v
1
v
2
v
3
Confluently
persistence
update/merge/query
all versions
v
5
Purely
functional
car cdr
never
modify
only create new pairsonly DAGs
version DAG
version
tree
version list
1
Retroactive
v
0
v
1
v
2
v3
v4
update
&
query
all versions
updates in the past propragateSlide2
Retroactive Data Structures
2
v0
v
1
v2v3v
4
m
Total
number
of
updates/versions
r Distance from current time
n Maximal data structure size
at any timePartial
retroactive Update all versions & query
currentFull retroactive
Update & query all versions
r
m
[E.D
.
Demaine, J. Iacono, S.
Langerman, Retroactive Data Structures, Proc. 15th Annual ACM-SIAM Symposium on Discrete Algorithms, 274-283, 2004]Slide3
Rollback Full
Retroactivity3
v
0
v
1v2v3
v4
Update
u
1u
2u3
u4
Change
1
2
3
4
current
+ Generic
, can
always be applied
, space efficient
- Slow retroactive operationsSlide4
Lower bounds for
Retroactivity4
a
0
+
a1x + a2x2 + ∙∙∙ + anxn ( requires
Ω(n) multiplications given x by Motzkin’s
theorem )
x0
x1
x
2
∙∙∙
x
i
∙
∙∙
x
n
*
[M. Patrascu, E.D
. Demaine, Logarithmic Lower Bounds in the Cell-Probe Model, SIAM J. of Computing 35(4): 932-963, 2006]
( prefix sum queries
require Ω(log n) )
*Slide5
Partial Full
Retroactivity5
v
5
v
7v8
v
1
v
2
v4
(
m
)
u
1
u
2
u
3
partial
retroactive structures
(remember using full
persistence)
v
0
v
9
current
u7
u8
u9
½
v
3
v6
u4
u5u6
v
5
v4
temporary
during queries to V5 (rollback
)Slide6
Partial Retroactive
Commutative Data Structures
6Slide7
Decomposable
Search
Problems
7
n
T
(2
n
)≥(1+
)T(
n
)
A
B
C
A
D
A
B
B
C
C
D
D
D
time
delete
(D)
insert
(D)Slide8
Specific Retroactive Data
Structures8
*
[D.D. Sleator
, R.E. Tarjan, A Data Structure for Dynamic Trees,
Proc. 13th Annual ACM Symposium on Theory of Computing, 114-122, 1981]*?