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Persistent Data Structures (Version Control ). Partial persistence. Full persistence. Confluently persistence. Purely functional. Ephemeral. version list. version DAG. version tree. v 0. v 0. v 0. v 0. car cdr. update. never modify only create new pairs only DAGs. v 1.

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  1. Persistent Data Structures (Version Control) Partialpersistence Full persistence Confluently persistence Purelyfunctional Ephemeral version list version DAG version tree v0 v0 v0 v0 carcdr update nevermodify onlycreate new pairs onlyDAGs v1 v1 v1 v2 v1 v2 v2 v2 v3 v6 v3 queryonly v3 v3 v4 v5 v5 update/merge/queryall versions updates at leaves any version canbecopiedquery all versions v4 v4 v5 v5 Retroactive v0 v1 v2 v3 v4 v6 v6 update & query all versions updates in the pastpropragate update& query query

  2. Retroactive Data Structures r v0 v1 v2 v3 v4 m m Total number of updates/versions r Distance from current time nMaximal data structuresize at any time PartialretroactiveUpdate all versions & querycurrent FullretroactiveUpdate & query all versions [E.D. Demaine, J. Iacono, S. Langerman, Retroactive Data Structures, Proc. 15thAnnual ACM-SIAM Symposium on Discrete Algorithms, 274-283, 2004]

  3. Rollback FullRetroactivity current v0 v1 v2 v3 v4 Update u1 u2 u3 u4 Change 1  2  3  4 + Generic, canalwaysbeapplied, spaceefficient- Slowretroactive operations

  4. Lowerbounds for Retroactivity a0 + a1x + a2x2 + ∙∙∙ + anxn ( requiresΩ(n) multiplicationsgiven x by Motzkin’stheorem ) * ( prefix sum queriesrequireΩ(log n) ) *[M. Patrascu, E.D. Demaine, Logarithmic Lower Bounds in the Cell-Probe Model, SIAM J. of Computing 35(4): 932-963, 2006]

  5. Partial FullRetroactivity (m) current ½ v0 v1 v2 v3 v4 v5 v6 v7 v8 v9 u1 u6 u8 u9 u2 u4 u7 u5 u3 v4 v5 partialretroactivestructures (rememberusingfullpersistence) temporaryduringqueries to V5 (rollback)

  6. PartialRetroactiveCommutative Data Structures

  7. DecomposableSearch Problems T(2n)≥(1+)T(n) n C A CD AD D B B D A B C insert(D) delete(D) time

  8. SpecificRetroactive Data Structures ? * *[D.D. Sleator, R.E. Tarjan, A Data Structure for Dynamic Trees, Proc. 13th Annual ACM Symposium on Theory of Computing, 114-122, 1981]

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