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Minor paper tweaks

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Andrew Noyes
2024-03-16 12:45:36 -07:00
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@@ -42,13 +42,13 @@ We can also consider any other ordered data structure to augment, such as any va
Let's compare the relevant properties of our candidate data structures for insertion/update and read operations. Let's compare the relevant properties of our candidate data structures for insertion/update and read operations.
After insertion, the max version along the search path must reflect the update. After insertion, the max version along the search path must reflect the update.
For comparison-based trees, updating max version along the search path cannot be done during top-down search, because \emph{insertion will change the search path}, and we do not know whether or not this is an insert or an update until we complete the top-down search. For self-balancing comparison-based trees, updating max version along the search path cannot be done during top-down search, because \emph{insertion will change the search path}, and we do not know whether or not this is an insert or an update until we complete the top-down search.
We have no choice but to do a second, bottom-up pass to propagate max version changes. We have no choice but to do a second, bottom-up pass to propagate max version changes.
Furthermore, the change will always propagate all the way to the root, since inserts always use the highest-yet version. Furthermore, the change will always propagate all the way to the root, since inserts always use the highest-yet version.
For a radix tree, insertion does not affect the search path, and so max version can be updated on the top-down pass. For a radix tree, insertion does not affect the search path, and so max version can be updated on the top-down pass.
There's minimal overhead compared to the radix tree unaugmented. There's minimal overhead compared to the radix tree unaugmented.
For ``last less than or equal to'' queries (which comprise the core of our read workload), skip lists have the convenient property that no backtracking is necessary, since the bottommost level is a sorted linked list. For ``last less than or equal to'' queries (which make up the core of our read workload), skip lists have the convenient property that no backtracking is necessary, since the bottommost level is a sorted linked list.
Binary search trees and radix trees both require backtracking up the search path when an equal element is not found. Binary search trees and radix trees both require backtracking up the search path when an equal element is not found.
It's possible to trade off the backtracking for the increased overhead of maintaining the elements in an auxiliary sorted linked list during insertion. It's possible to trade off the backtracking for the increased overhead of maintaining the elements in an auxiliary sorted linked list during insertion.