Add developer documentation to explain room DAG concepts like `outlie…

…rs` and `state_groups` (#10464)

changelog.d/10464.doc

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+Add some developer docs to explain room DAG concepts like `outliers`, `state_groups`, `depth`, etc.

docs/SUMMARY.md

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     - [Single Sign-On]()
       - [SAML](development/saml.md)
       - [CAS](development/cas.md)
+    - [Room DAG concepts](development/room-dag-concepts.md)
     - [State Resolution]()
       - [The Auth Chain Difference Algorithm](auth_chain_difference_algorithm.md)
     - [Media Repository](media_repository.md)

docs/development/room-dag-concepts.md

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+# Room DAG concepts
+
+## Edges
+
+The word "edge" comes from graph theory lingo. An edge is just a connection
+between two events. In Synapse, we connect events by specifying their
+`prev_events`. A subsequent event points back at a previous event.
+
+```
+A (oldest) <---- B <---- C (most recent)
+```
+
+
+## Depth and stream ordering
+
+Events are normally sorted by `(topological_ordering, stream_ordering)` where
+`topological_ordering` is just `depth`. In other words, we first sort by `depth`
+and then tie-break based on `stream_ordering`. `depth` is incremented as new
+messages are added to the DAG. Normally, `stream_ordering` is an auto
+incrementing integer, but backfilled events start with `stream_ordering=-1` and decrement.
+
+---
+
+ - `/sync` returns things in the order they arrive at the server (`stream_ordering`).
+ - `/messages` (and `/backfill` in the federation API) return them in the order determined by the event graph `(topological_ordering, stream_ordering)`.
+
+The general idea is that, if you're following a room in real-time (i.e.
+`/sync`), you probably want to see the messages as they arrive at your server,
+rather than skipping any that arrived late; whereas if you're looking at a
+historical section of timeline (i.e. `/messages`), you want to see the best
+representation of the state of the room as others were seeing it at the time.
+
+
+## Forward extremity
+
+Most-recent-in-time events in the DAG which are not referenced by any other events' `prev_events` yet.
+
+The forward extremities of a room are used as the `prev_events` when the next event is sent.
+
+
+## Backwards extremity
+
+The current marker of where we have backfilled up to and will generally be the
+oldest-in-time events we know of in the DAG.
+
+This is an event where we haven't fetched all of the `prev_events` for.
+
+Once we have fetched all of its `prev_events`, it's unmarked as a backwards
+extremity (although we may have formed new backwards extremities from the prev
+events during the backfilling process).
+
+
+## Outliers
+
+We mark an event as an `outlier` when we haven't figured out the state for the
+room at that point in the DAG yet.
+
+We won't *necessarily* have the `prev_events` of an `outlier` in the database,
+but it's entirely possible that we *might*. The status of whether we have all of
+the `prev_events` is marked as a [backwards extremity](#backwards-extremity).
+
+For example, when we fetch the event auth chain or state for a given event, we
+mark all of those claimed auth events as outliers because we haven't done the
+state calculation ourself.
+
+
+## State groups
+
+For every non-outlier event we need to know the state at that event. Instead of
+storing the full state for each event in the DB (i.e. a `event_id -> state`
+mapping), which is *very* space inefficient when state doesn't change, we
+instead assign each different set of state a "state group" and then have
+mappings of `event_id -> state_group` and `state_group -> state`.
+
+
+### Stage group edges
+
+TODO: `state_group_edges` is a further optimization...
+      notes from @Azrenbeth, https://pastebin.com/seUGVGeT