In Part 1 of TerminusDB internals we looked at how to construct a graph using succinct data structures. Succinct data structures are nice and compact, but they are not intrinsically dynamic. That is, you can’t mutate them directly.
To see why it would be hard to mutate, imagine we have a dictionary:
And we want to add
Jack Jim Joan
This entry shifts all of the indexes of everything by one. Every entry in all of our arrays which represent our graph is now wrong. Directly mutating the data structures is clearly not the easiest way to proceed.
There is another strategy however. Instead of mutating, we can build up a delta. This delta is actually two new graphs. One which adds some number of edges, and another which deletes them.
The engineering team calls these positive and negative planes, since it’s easy to imagine them layering over the previous database. And the original plane is called the base plane, since it is only ever positive.
This trick is actually quite similar to the way that Multi-Version Concurrency Control works, and can be used to implement not only immutable updates, and versioning, but also concurrency control.
However, now, when a query comes in, we need to do something a bit more elaborate to resolve it. And what precisely we do depends on the mode.
If we are searching for a triple, with some aspects unknown, for instance the mode
(+,-,-), we need to cascade downwards through our planes searching for it.
For instance, the search for a triple:
let v = Vars("p","x"); triple("joe", v.p, v.x)
In a database which has experienced two updates
| Plane 1 | Plane 2 | Plane 3 | | +(joe,name,"Joe") | +(joe,dob,"1978-01-01") | +(joe,name,"Joe Bob") | | +(joe,dob,"1979-01-01") | -(joe,dob,"1979-01-01") | -(joe,name,"Joe") |
Here we will start at plane 3, fall back to plane 2, then the base plane, and then bubble back up.
| Plane 1 | Plane 2 | Plane 3 | | +(joe,name,"Joe") | +(joe,dob,"1978-01-01") | +(joe,name,"Joe Bob") | | +(joe,dob,"1979-01-01") | -(joe,dob,"1979-01-01") | -(joe,name,"Joe") | || || || || || \/ || || (joe,name,"Joe Bob") =>Answer || \/ || (joe,dob,"1978-01-01") ======================>Answer \/ (joe,name,"Joe") ======================================> X (joe,dob,"1979-01-01") ==========> X
The two elements in the base plan get cancelled by deletions on the way up. They can’t be answers since they aren’t there anymore. This approach works for arbitrary modes, however, as the stack of planes gets large, it starts to get slow. The performance degrades linearly as a function of the number of transactions which have been performed on the database. In practice you can often start to feel things slowing down when the stack is on the order of 10 transactions.
Hence we need to rollup some of these deltas. Essentially we need to do a delta compression, create a new plane which represents some number of intermediate planes, but in which we’ve cancelled everything which was ephemeral (such as the two triples in the base plan).
This delta rollup, sits along side our previous planes, as an equivalence layer. All of the deltas are kept, as this allows us to time-travel, and to push or pull commits to other servers, but we introduce a pointer from our layer saying we have a faster way to query. Should any query come in, they should preferentially take the delta rollup layer instead.
However, we don’t need to always roll-up everything all of the time. In addition, since the operation takes some time there is a danger that rollups might occur too late to matter if expect to have a rollup at every layer.
Instead we want to try to make sure that our rollups are log-like, in their occurance. Basically we want to merge more things deeper into the past, as these will be stable, and progressively fewer as we get closer to the present.
For instance, we might have the following rollups for some sequence of commits:
_____c1-4______ __c4-6_ / \/ \ c1 - c2 - c3 - c4 - c5 - c6 - c7 | main
Here we keep a rollup for the orders 4, then 2, then 1. As we go back into the past the number of rollups gets smaller, and the total number of rollups we expect to see, and hence have to traverse is now log-like as the number of commits grows. For instance, as we increase the number of commits we get:
_______c1-8__________________ / \ _____c1-4______ __c4-6_ \ ____c8-c11__ / \/ \ \ / \ c1 - c2 - c3 - c4 - c5 - c6 - c7 - c8 - c9 -c10 -c11 -c12 | main
In addition, because of our log-based approach, when rolling up the c1-8 commits we are only have to look at 4 layers, rather than 8. This speeds up the merge operation on a running basis, and we will have a relatively small number of layers to query, in fact in both cases we have 3.
If you’re paying close attention you might see there are potential optimisations in the representation of negatives. You could tomb-stone a particular SP pair for instance, if there is cardinality zero, and save some traversals. We have not implemented this yet in TerminusDB, but we would like to do some experiments with it in the future.
Even the Graphs have Graphs
Since we have this commit structure to our graph, access to a graph comes in through the head of the graph. We need to know what is the most recent current graph.
In TerminusDB, our graphs are schema checked, and our schemata themselves are stored in a graph. So a typical data product is actually a number of graphs:
- A Schema Graph
- An Instance Graph
- A Commit Graph
- A Repo Graph
In addition we have a central graph, the System Graph which stores which data products exist and some properties about them that are external to the data product.
The combination of schema and instance graph are stored in the commit graph. This associates a commit with both its current instance graph and its current schema graph. The head of a given branch points to the most recent commit.
When we open a data product for reading or writing, we look up the branch in the commit graph, get the latest head, and then open the associated layers for querying.
The Repo graph stores information about local and remote repositories, and which commit graphs are associated with them. This is used for the push/pull type repository collaboration features.
In order to orchaestrate all of these graphs we need to be a bit careful about the order in which we perform operations in order to make sure that everything is properly atomic.
The operation order is something like this:
- We perform a query, and if there are any mutations we create a builder recording all insertions and deletions.
- We update the commit graph, advancing the branch head, and update the repo graph, advancing the repo head to point to the commit graph id, creating builders for them as well.
- Once the query has completed successfully, we transform each of these builders into a validation object. A validation object checks any outstanding schema checks which could not be quickly performed during the query. For instance referential integrity checking which requires that we have everything completed before we can check that it holds.
- We write all of the validated objects to disk, synchronising on completion of all layers.
- We set the label file of the database to point at the most advanced repository identifier.
If someone has gotten in and changed the label file before us, we use optimistic concurrency and re-execute the query. This gives us our acid properties.
The Journey Forward
One might notice however that this is a bit too strict. It would be nice if we could check to see if some weaker form of isolation could be maintained so we don’t have to re-run the query. Instead we might be able to simply place our current transaction on top of the previous one without running anything again.
In order to do this we need a concept of an isolation level, for instance snap-shot isolation were we could maintain a read-set which specifies which things must be stable based on what we read during the query.
We could also be a bit more clever about the way we deal with garbage created during transactions. Currently we leave around layers that we’ve written even when the transaction fails. This can be cleaned up with a garbage collection process, but it’s probably better if we don’t write it in the first place.
We are keen to get these improvements into a future release of TerminusDB.
In the next blog on TerminusDB internals, we’ll look at data layout, search and compression. If you’ve made it to the bottom of this post, then you’re probably waiting for this next one with bated breath.