Causality is expensive (and what to do about it)

05 Feb 2014

In this post, I briefly motivate the use of causality in distributed systems, discuss (likely) fundamental lower bounds on metadata overheads required to capture it, and discuss four strategies for circumventing these overheads.

Why care about causality?

In 1978, Leslie Lamport introduced the important concept of partial ordering in distributed systems: given a partial view over global system state, how can we safely say whether a particular event “happens before” another? Instead of relying on a total order (e.g., using synchronized clocks) to order events, Lamport’s proposed “happens-before” relation captures dependencies between events as a partial order: “happens-before” reflects the order of events within each process as well as the order of events across processes, captured via message channels. This formulation conveniently means that reasoning about “happens-before” does not require synchronous coordination between processes and also captures the possibility that two events may be completely independent of one another (i.e., are concurrent; just like light cones in the real world). Accordingly, “happens-before” is a powerful concept and forms the basis of causality in distributed systems, which is used in many contexts:

  1. Distributed snapshot algorithms (e.g., consistent cuts) and global predicate detection algorithms typically leverage causal ordering for efficient execution (e.g., enable consistent snapshots without forcing processes to pause). This is particularly useful in debugging.

  2. Version vectors are used in databases like Dynamo, Riak, and Voldemort to track concurrent updates to data and manage update conflicts without fast-path synchronization between replicas.

  3. Causal consistency and causal broadcast provide databases and messaging systems with ordering guarantees that respect Lamport’s “happens-before” relation. This means, for example, that replies on Twitter won’t be seen without their parent Tweets. These two use cases in particular have recently seen a resurgence of interest in the research community.

As a theoretical construct and, increasingly, in real-world distributed systems, causality is important. I’ll defer a full description and discussion of causality to the expansive literature (here’s a survey, and here’s my favorite—check out that subtitle!). Instead, I want to ask a specific question: what does causality cost?

Causality is expensive

To use causal ordering, we need some way to capture it via a data structure or other piece of information. There are a variety of techniques for doing so in the literature that you may have heard of, like vector clocks (note that the related Lamport clocks don’t allow us to distinguish between “concurrent” and “earlier” events). If you’re familiar with vector clocks, you’ll know that each process in the system requires a position in the data structure; this means that, with N processes, each vector clock takes up O(N) space.

This leads to a tough question: how much space is required in order to capture causality? This is a difficult question to answer, but it’s fascinating to think about and has serious implications for our above use cases. Fortunately, Bernadette Charron-Bost thought seriously about this problem, and, in 1991, published a surprising result; the actual paper is fairly hairy, but Schwarz and Mattern summarize well:

Is there a way to find a “better” timestamping algorithm based on smaller time vectors which truly characterizes causality? As it seems, the answer is negative. Charron-Bost showed…that causality can be characterized only by vector timestamps of size N.

Wow. Charron-Bost’s result seems to imply that we can’t use less than O(N) metadata! For small numbers of processes, this isn’t so bad, but, if we scale to hundreds or thousands of nodes, each message (or, in a database, operation) is going to require a lot of metadata. Schwarz and Mattern (do you recognize Mattern from earlier?) continue:

It is not immediately evident that — for a more sophisticated type of vector order than < — a smaller vector could not suffice to characterize causality, although the result of Charron-Bost seems to indicate that this is rather unlikely…A definite theorem about the size of vector clocks would require some statement about the minimum amount of information that has to be contained in timestamps in order to define a partial order of dimension N on them. Finding such an information theoretical proof is still an open problem.

So, we don’t have a definitive proof, but, in all likelihood, we’re not going to do better. Moreover, in the now 23 years following this result, we haven’t seen anyone do better.

Intuitively, I think of the lower bound as follows: if I’m a process, and I want to perform an event, I need some way to distinguish my new event from all of the prior events that I’ve performed. This hints that I’ll need some sort of unique marker for my event—as in a vector clock, I can use a local timestamp that I increment on every event (which requires O(log(events)) space). Now, if every other process simultaneously wants to perform a new event, then we’ll collectively need N timestamps. We can’t coalesce these timestamps, since they’re due to unique events, so this puts us at (at least) O(N) metadata! Some recent results from Microsoft Research and the CRDT team show similar bounds for vector-based data structures.

…and what to do about it

There are many optimizations that reduce the overhead of causal tracking in the best case, but these worst-case overheads are too costly for many modern services running at scale. (Perhaps surprisingly, many modern implementations are even more expensive, with worst-case metadata overheads that are linear in the number of events or the number of keys in a database.) If you’re interested, we wrote a paper a while ago about how bad this overhead can become (voiceover) for causally consistent databases backing modern internet services.

Can we do anything to avoid these overheads?

  1. Restrict the set of participants: To reduce the O(N) factor, we can reduce N, or the number of processes across which we track causal information. For example, if we’re building a distributed database, we can simply track causality across replicas of a each data item instead of causality across all servers. This sacrifices causal guarantees across data items but allows us to detect update conflicts for a single data item and is exactly the strategy adopted by version vectors. In most systems, the number of replicas for an item is much smaller than the number of servers in the system (e.g., 3 vs. 100), so this is a substantial reduction in practice. (Carlos Baquero has a good post on this distinction.)

  2. Explicitly specify relevant relationships: The above discussion assumes that all events matter equally; in practice, this isn’t necessarily the case. On Twitter, when a user posts a reply to a Tweet, the causal relationship between the reply and the parent Tweet is—from a UX perspective—more important than the relationship between all of the Tweets the user read at login and her new reply. Effectively, if traditional forms of causality (i.e., potential causality) treat all possible (transitive) influences equally, what if we could explicitly specify which partial orders matter? In our Twitter example, tracking this explicit causality would only require a metadata overhead of O(1) for the “reply-to” relationship. The trade-off is that (like foreign key dependencies in database systems), the user now has to specify her causal dependencies manually at write time; our paper I mentioned earlier describes this strategy in greater detail.

  3. Reduce availability: The problem with reducing the set of participants or using explicit causality is that we will necessarily throw away some causal dependencies. The upshot is that we were able to to reduce metadata while preserving availability. An alternative strategy is to attempt to compress causality by restricting availability: if we bound the number of processes that can simultaneously perform operations to a constant factor K, we only need K entries in our vector at any given time (i.e., to perform an operation, a process must “reserve” a spot in the vector, then “catch up” to the current vector position in the causal history—by, say, processing the events created and received by the prior occupant of the position). Under this strategy, metadata size determines maximum concurrency; in the limit, with K=1, we have a total order on events (close—if not identical to—linearizability). With this strategy, we’ve traded metadata by sacrificing availability and forcing some processes to effectively “share” causal dependencies.

  4. Drop happens-before entirely: If we don’t want to suffer metadata overheads, require programmer intervention, or sacrifice availability, we can always use a weaker partial order (i.e., weaker but still available model). For example, if, in a database, we simply want each user to read her writes, we don’t (necessarily) need any metadata and can simply use sticky routing policies. Vanilla eventual consistency is even cheaper. Of course, this strategy can clearly compromise application consistency because we lose the ability to distinguish between concurrent writes and overwrites to the same item, but, on the plus side, it doesn’t get much cheaper!

It’s also important to remember that, regardless of the model we choose, if we want true “availability”, we necessarily lose the ability to make many useful guarantees, like preventing concurrent updates. There’s no free lunch, but, given that not all “weak” models are created equal (at least in terms of metadata cost), sometimes it makes sense to drop full causal ordering across all events and all processes and settle for enforcing a less costly alternative.

Takeaways

Causality is an immensely powerful concept in distributed systems, but it’s unlikely that we’ll discover a more compact, sub-linear representation that is sufficient to characterize it. I have no doubt that causality will remain important for debugging and reasoning about global states of distributed computations and am excited by the recent work in causally consistent distributed systems (full disclosure: I spent some time on this earlier in my Ph.D.). As researchers, it’s our job to push the envelope, and understanding the compromises required in light of the (likely) fundamental trade-offs I’ve described is a worthwhile exercise. However, given the worst-case overheads of causality tracking—at least in real-world deployments—and lack of a more compact counterexample, I’m more bullish on the four alternatives I’ve outlined.

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