From 1f5fd56ebc3e751183e92fe20f852d03f641dbfc Mon Sep 17 00:00:00 2001 From: Ivan Shvedunov Date: Mon, 28 Oct 2024 23:21:47 +0400 Subject: [PATCH] sync2: add fptree description to dev-docs --- dev-docs/fptree-agg-from-root.png | Bin 0 -> 583603 bytes dev-docs/fptree-agg-lca.png | Bin 0 -> 492928 bytes dev-docs/fptree-agg-limit-wraparound.png | Bin 0 -> 489952 bytes dev-docs/fptree-agg-limit.png | Bin 0 -> 439457 bytes dev-docs/fptree-agg-wraparound.png | Bin 0 -> 598164 bytes dev-docs/fptree-with-values.png | Bin 0 -> 371555 bytes dev-docs/fptree.excalidraw.gz | Bin 0 -> 59202 bytes dev-docs/fptree.png | Bin 0 -> 829707 bytes dev-docs/sync2-set-reconciliation.md | 294 ++++++++++++++++++++++- 9 files changed, 291 insertions(+), 3 deletions(-) create mode 100644 dev-docs/fptree-agg-from-root.png create mode 100644 dev-docs/fptree-agg-lca.png create mode 100644 dev-docs/fptree-agg-limit-wraparound.png create mode 100644 dev-docs/fptree-agg-limit.png create mode 100644 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zta$t8Swt+>uv3gNE}V<@M3HbZGFpJ}4Db)>fC8KZb{t`OW5Ty3#+AjhST?T~@ZV%4 zwsHCAC!v4M+&cek{Z1e*Vugcq3y6#Y4e8(i(m$qqbd{c(!dm`~VEUJ-w#cz_y1_)e z*XwoYg~dO1=#c#=MNlcSVJ;rV6Cgr6Xus|`;4cGY@Huvu?7WUEJ}mF8q9Noz`fMpQ zhzkcRzd%w5*$n{CC;jO(|NUj!Ia{@{E6XPh)0D0((-2L%XoV|>XcI5_+Y z_N>IbqQ)V=R}o@l9ZvPNy6+)gCna-S z-v+v?kNq+`jj91G04J~D-G7WR?ui78<6lVsKAXRj{&Qryo^hglERX7gkf0I`2vLhhmT^)yae$0Cp97a{uc{CCkY7Y{uJ8sugCV&Q2%@>fqBKr!b{co y` ranges and full set range + `[x,x)` (see [Range representation](#range-representation)). +1. Each FPTree node has corresponding bit prefix by which it can be + reached. + +The tree structure is shown on the diagram below. The leaf nodes +correspond to the rows in database table with IDs having the bit prefix +corresponding to the leaf node. + +![FPTree structure](fptree.png) + +As it is mentioned above, FPTree itself can also store the actual IDs, +without using an underlying database table. + +![FPTree with values](fptree-with-values.png) + +## Aggregation + +Aggregation means calculation of fingerprint and item count for a +range. The aggregation is done using different methods depending on +whether the `[x,y)` range is normal (`xy`) or +indicates the whole set (`x=y`). Aggregation may also be bounded by +the maximum number of items to include. The easiest case is full set +aggregation, in which we just take the fingerprint and count values +from the root node of the FPTree. + +### Aggregation of normal ranges + +In case of a normal range `[x,y)` with `xy`, `aggregateLeft` and +`aggregateRight` are used, too. Somewhat unintuitively, in this case +`aggregateLeft` is used on the right side of the tree, b/c that's +where the beginning ("left side") of the wrapped-around `[x,y)` range +lies, whereas `aggregateRight` is applied to the left side of the tree +corresponding to the end ("right side") of the range. + +The subtree on which `aggregateLeft` is done is rooted at the node +reachable by following the longest prefix of `x` consisting entirely +of `1`s. Conversely, the subtree on which `aggregateRight` is done is +rooted at the node reachable by following the longest prefix of `y` +consisting entirely of `0`s. + +The figure below shows aggregation of the `[x,y)` range with +`x=0xD1..` and `y=0x29`. + +![Aggregation of a wrapped-around range](fptree-agg-wraparound.png) + +## Splitting ranges and limited aggregation + +During recursive set reconciliation, range split operation often needs +to be performed. This involves partitioning the range roughly in half +with respect to the number of items in each new subrange, and +calculating item count and fingerprint for each part resulting from +the split. FPTree will try to perform such an operation on node +boundary, but if the range is to small or not aligned to the node +boundary, the following is done: + +1. The number of items in the range obtained (`N`). +2. The items in the range are aggregated with the cap on maximum + aggregated count equal to `N/2`, and the non-inclusive upper bound + of the aggregated subrange is noted (`m`). The aggregated items + can be said to lie in range `[x,m)` +3. The second half of the range is aggregated starting with `m`. This + part of the range is `[m,y)`. + +In both cases, the operation is based upon imposing the limit on +number of items aggregated. In the easy, node-aligned case, the +aggregation continues after exhausting the limit on the total item +count, but using separate places for accumulation of remaining nodes' +fingerprints and counts. The initial accumulated fingerprint and count +are returned for the first resulting subrange, and the second +accumulated fingerprint and count are returned for the second subrange +resulting from the partition. In case if node-aligned "easy split" +cannot be done, aggregation stops after exhausting the limit. + +When limited aggregation is done, instead of including full right +subtrees during `aggregateLeft`, including full left subtrees during +`aggregateRight`, and including the whole tree during `[x,x)` (full +set) range aggregation, when subtree count exceeds the remaining limit +after processing all the nodes visited so far, the corresponding +subtrees are descended into to find the cutoff point. + +Below limited aggregation is shown for a normal `x= ? AND + "rowid" <= ? ORDER BY "id" LIMIT ? +``` + +Select number of recently received items items for recent sync +(which is not done using FPTree): +```sql +SELECT count("id") FROM "atxs" WHERE "epoch" = ? AND + "rowid" <= ? AND "received" >= ? +``` + +Select recently received IDs: +```sql +SELECT "id" FROM "atxs" WHERE "epoch" = ? AND "id" >= ? AND + "rowid" <= ? AND "received" >= ? ORDER BY "id" LIMIT ? +``` + # Multi-peer Reconciliation -The multi-peer reconciliation approach is loosely based on -[SREP: Out-Of-Band Sync of Transaction Pools for Large-Scale Blockchains](https://people.bu.edu/staro/2023-ICBC-Novak.pdf) -paper by Novak Boškov, Sevval Simsek, Ari Trachtenberg, and David Starobinski. +The multi-peer reconciliation approach is loosely based on [SREP: +Out-Of-Band Sync of Transaction Pools for Large-Scale +Blockchains](https://people.bu.edu/staro/2023-ICBC-Novak.pdf) paper by +Novak Boškov, Sevval Simsek, Ari Trachtenberg, and David Starobinski. ![Multi-peer set reconciliation](multipeer.png)

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