3 ms·

I really wish the applications section had more detail or perhaps an "editorial". I don't really follow the consequence of a frequency map being associative.

noelwelsh 10y ago
Yeah, the application section is pretty poor. The number one large-scale practical application of semigroups (and, more often, their extension the monoid) is in parallel and concurrent systems. Associativity says that order of operations doesn't matter, which in turn implies you can distribute computations however you like across multiple machines and still get the correct result. This is the big idea leveraged in systems like Summingbird and other big data frameworks (e.g. https://arxiv.org/abs/1304.7544 https://arxiv.org/abs/1304.7544) and in CRDTs.
- vit_tucek 10y ago
  Associativity says that the order of __evaluation__ of operations doesn't matter. You are talking about commutativity.
  - noelwelsh 10y ago
    I meant associativity, but was not precise in my description. Commutativity is also useful.
- deepnet 10y ago
  And yet the article concludes : "The form of parallelism induced by the associativity of the semigroup operation is heavily relied upon in the Map-Reduce programming model. We’ll expound on this in more detail in a later article, as this is more easily developed algebraically after defining the concept of a Monoid."
  - noelwelsh 10y ago
    Right. So my HN comment has more information on this than the entire blog post, which is kinda the point.
    - deepnet 10y ago
      Absolutely fair point and Jeremy Lin's Monoidify paper is intruiging, many thanks. Although OP, philipnilsson is taking it step by step which I greatly appreciate as well
  - Ixiaus 10y ago
    noelwalsh also included a bit about CRDTs, which he didn't expand upon, but is pretty different from "the Map-Reduce programming model" in a few ways. I expanded on the CRDT comment above.
- Ixiaus 10y ago
  This is a good reply and I'll add to it. Note that CRDT stands for Conflict free Replicated Datatype and there are a few sub-acronym expansions: Convergent Replicated Datatype and Commutative Replicated Datatype. [EDIT] I wanted to add that CRDTs were mentioned here because in order for them to provide the kind of guarantees they do they must satisfy the law of associativity (or, be a semigroup), commutativity, and idempotency. So, technically, you have to go further than semigroups with commutative semigroups. [/EDIT] At Plum we made heavy use of CRDT's on-top of an eventually consistent whole-state replication technology called Plumtree, no relation to the company's name, just coincidence, within the internet-connected dimmer we built called the Lightpad. The primary design goal was to enable advanced configurations: Arbitrary groups of Lightpads could be controlled from any other one on the same network by binding it to a specific finger gesture. We also did not want this configuration to be dependent upon any single master, they had to be truly master-less. In-general, Eventual Consistency is pretty scary when you're deploying it to embedded internet-connected devices where you can't immediately shell onto the device like you can with a server in a data center. I have lots of stories here I'll write about sometime of the pains I encountered while developing this solution and how I ended up on CRDTs. Strong Eventual Consistency (typically, CRDTs deployed on-top of an eventually consistent substrate), though, is very safe and provides a lot of guarantees about the concurrent behavior of the algorithm as it acts upon your data. Using a CRDT (specifically the ORSWOT - Observed Removal Set Without Tombstones) eliminated the majority of our pains and concerns with data-loss, conflicting concurrent writes, and integrity in the face of flaky consumer-grade home networks (Plumtree is highly-available and partition tolerant - perfect for our needs where we have to be able to continue moving forward even if a majority or more of the Lightpads go offline and never come back up).
  - ergl 10y ago
    It's always good to hear about IOT companies using CRDTs because it seems like the perfect fit for it, yet you don't hear very much about it. Also interesting hearing you mention you were using plumtree for your replication backend. To elaborate more on your point, CRDTs are super helpful while trying to distribute a lot of devices, but they only get you so far. While building Lasp[0][1], a distributed data-flow language using CRDTs, we found out a lot of scalability problems with naive usage of CRDTs. We are aiming to reach 10k-20k nodes in the near future, so we are focusing a lot on reducing network usage. State-based CRDTs send their full state to all their peers, which works ok when your states are small, but they introduce lots of overhead in any other case. Operation-based CRDTs only send the actions performed on it (add 1, or rmv 2, for example), but these are not idempotent and require a lot of guarantees from the underlying distribution backend. We are focusing on using Delta CRDTs, that combine the low network usage of operation-based structures, with the idempotence of state-based approaches. Using plumtree for your backend makes it resilient to network failures, but using the default full membership protocol makes it almost unusable when you're dealing with a big number of nodes. Using alternative protocols like Hyparview greatly reduces the number of protocol messages in your network. Finally, since Lasp is a data-flow language, we are applying control-flow analysis to select and remove unused or intermediate values in the program, thus also reducing network usage. [0]: http://lasp-lang.org/ http://lasp-lang.org/ [1]: https://github.com/lasp-lang/lasp https://github.com/lasp-lang/lasp
- vikiomega9 10y ago
  I think summingbird and scalding introduced, for me, the notion of having functional types that make it easier to combine things together for distributed computing/big data. I've never read that paper before, it's really good. I like how the author's objective is to formalize map-side aggregations. But I'm wondering if that's a natural extension of map-reduce itself? ie. don't move data if it's not required given that's the constraint? Do you have more of such papers handy?
deleted 10y ago
[deleted]

noelwelsh 10y ago

Yeah, the application section is pretty poor. The number one large-scale practical application of semigroups (and, more often, their extension the monoid) is in parallel and concurrent systems. Associativity says that order of operations doesn't matter, which in turn implies you can distribute computations however you like across multiple machines and still get the correct result. This is the big idea leveraged in systems like Summingbird and other big data frameworks (e.g. https://arxiv.org/abs/1304.7544 https://arxiv.org/abs/1304.7544) and in CRDTs.

vit_tucek 10y ago
Associativity says that the order of __evaluation__ of operations doesn't matter. You are talking about commutativity.
- noelwelsh 10y ago
  I meant associativity, but was not precise in my description. Commutativity is also useful.
deepnet 10y ago
And yet the article concludes : "The form of parallelism induced by the associativity of the semigroup operation is heavily relied upon in the Map-Reduce programming model. We’ll expound on this in more detail in a later article, as this is more easily developed algebraically after defining the concept of a Monoid."
- noelwelsh 10y ago
  Right. So my HN comment has more information on this than the entire blog post, which is kinda the point.
  - deepnet 10y ago
    Absolutely fair point and Jeremy Lin's Monoidify paper is intruiging, many thanks. Although OP, philipnilsson is taking it step by step which I greatly appreciate as well
- Ixiaus 10y ago
  noelwalsh also included a bit about CRDTs, which he didn't expand upon, but is pretty different from "the Map-Reduce programming model" in a few ways. I expanded on the CRDT comment above.
Ixiaus 10y ago
This is a good reply and I'll add to it. Note that CRDT stands for Conflict free Replicated Datatype and there are a few sub-acronym expansions: Convergent Replicated Datatype and Commutative Replicated Datatype. [EDIT] I wanted to add that CRDTs were mentioned here because in order for them to provide the kind of guarantees they do they must satisfy the law of associativity (or, be a semigroup), commutativity, and idempotency. So, technically, you have to go further than semigroups with commutative semigroups. [/EDIT] At Plum we made heavy use of CRDT's on-top of an eventually consistent whole-state replication technology called Plumtree, no relation to the company's name, just coincidence, within the internet-connected dimmer we built called the Lightpad. The primary design goal was to enable advanced configurations: Arbitrary groups of Lightpads could be controlled from any other one on the same network by binding it to a specific finger gesture. We also did not want this configuration to be dependent upon any single master, they had to be truly master-less. In-general, Eventual Consistency is pretty scary when you're deploying it to embedded internet-connected devices where you can't immediately shell onto the device like you can with a server in a data center. I have lots of stories here I'll write about sometime of the pains I encountered while developing this solution and how I ended up on CRDTs. Strong Eventual Consistency (typically, CRDTs deployed on-top of an eventually consistent substrate), though, is very safe and provides a lot of guarantees about the concurrent behavior of the algorithm as it acts upon your data. Using a CRDT (specifically the ORSWOT - Observed Removal Set Without Tombstones) eliminated the majority of our pains and concerns with data-loss, conflicting concurrent writes, and integrity in the face of flaky consumer-grade home networks (Plumtree is highly-available and partition tolerant - perfect for our needs where we have to be able to continue moving forward even if a majority or more of the Lightpads go offline and never come back up).
- ergl 10y ago
  It's always good to hear about IOT companies using CRDTs because it seems like the perfect fit for it, yet you don't hear very much about it. Also interesting hearing you mention you were using plumtree for your replication backend. To elaborate more on your point, CRDTs are super helpful while trying to distribute a lot of devices, but they only get you so far. While building Lasp[0][1], a distributed data-flow language using CRDTs, we found out a lot of scalability problems with naive usage of CRDTs. We are aiming to reach 10k-20k nodes in the near future, so we are focusing a lot on reducing network usage. State-based CRDTs send their full state to all their peers, which works ok when your states are small, but they introduce lots of overhead in any other case. Operation-based CRDTs only send the actions performed on it (add 1, or rmv 2, for example), but these are not idempotent and require a lot of guarantees from the underlying distribution backend. We are focusing on using Delta CRDTs, that combine the low network usage of operation-based structures, with the idempotence of state-based approaches. Using plumtree for your backend makes it resilient to network failures, but using the default full membership protocol makes it almost unusable when you're dealing with a big number of nodes. Using alternative protocols like Hyparview greatly reduces the number of protocol messages in your network. Finally, since Lasp is a data-flow language, we are applying control-flow analysis to select and remove unused or intermediate values in the program, thus also reducing network usage. [0]: http://lasp-lang.org/ http://lasp-lang.org/ [1]: https://github.com/lasp-lang/lasp https://github.com/lasp-lang/lasp
vikiomega9 10y ago
I think summingbird and scalding introduced, for me, the notion of having functional types that make it easier to combine things together for distributed computing/big data. I've never read that paper before, it's really good. I like how the author's objective is to formalize map-side aggregations. But I'm wondering if that's a natural extension of map-reduce itself? ie. don't move data if it's not required given that's the constraint? Do you have more of such papers handy?

deleted 10y ago

[deleted]