<p>Maurice Herlihy, Dmitry Kozlov and Sergio Rajsbaum, &quot;<a href="https://www.sciencedirect.com/book/9780124045781/distributed-computing-through-combinatorial-topology" rel="nofollow noreferrer">Distributed Computing Through Combinatorial Topology</a>&quot;, 2014</p>

CC BY-SA 4.0
2024-05-17T05:00:51.230Z
2024-05-17T05:00:51.230Z
Kaveh
<p>I have just discovered the <a href="https://cs.brown.edu/%7Emph/HerlihyS99/p858-herlihy.pdf" rel="noreferrer">paper of M. Herlihy and N. Shavit</a> on the use of algebraic topology methods in TCS and distributed computing in particular.</p>
<p>Now I am wondering if there is any further work being done in this area and if there are any current interesting follow up papers. Does anyone know anything about the state of the art?</p>
<p>Thank you!</p>

CC BY-SA 4.0
2024-05-14T12:55:45.893Z
Check out [Eric Goubault's work](https://scholar.google.fr/citations?user=pCksTpcAAAAJ&hl=en) on algebraic topology and parallelism, e.g. [this book](https://link.springer.com/book/10.1007/978-3-319-15398-8)
Martin Berger
CC BY-SA 4.0
2024-05-14T14:33:16.447Z
Bounds on Betty numbers of the set of zeros of polynomials (such as those given by Milnor and Thom) are used to prove bounds on the number of certain structures (such as order types) in discrete and computational geometry. The works of Ben-or, Yao, etc., giving lower bounds for the complexity of algebraic decision trees also comes to mind (a lot of work on algebraic decision/computation trees in general could fit).
Tassle
CC BY-SA 4.0
2024-05-15T02:22:12.043Z
When you say "further work in this area" are you asking specifically about applying algebraic topology to distributed computing? Or more generally applications of algebraic topology in TCS?
Joshua Grochow
CC BY-SA 4.0
2024-05-15T02:24:48.740Z
Related (but, AFAICT, not duplicate Qs): https://cstheory.stackexchange.com/q/7958/129, https://cstheory.stackexchange.com/q/41296/129, https://cstheory.stackexchange.com/q/53512/129,
Joshua Grochow
CC BY-SA 4.0
2024-05-15T07:44:17.773Z
Maybe the title of the question is missleading. I was asking for further work specifically applying algebraic topology to distributed computing, but anyway thanks for linking the other questions. I will give them a look.
timtombobjohn
CC BY-SA 4.0
2024-05-15T08:21:25.373Z
@timtombobjohn then change the title of your post...
mathworker21
CC BY-SA 4.0
2024-05-17T14:44:25.657Z
There is a conference which is purely devoted to the applications of algebraic topology in TCS, and in particular in distributed computing. https://getco-conf.github.io/2024/ I suggest you look at the program of the recent editions (in the "history" tab of the website) to check the latest developement in the field.
Louis Esperet
CC BY-SA 4.0
2024-05-17T17:16:33.927Z
some of these comments should be answers really.
Kaveh
<soft-question><dc.distributed-comp><concurrency><topology><algebraic-topology>
algebraic topology in distributed computing
timtombobjohn
# algebraic topology in distributed computing

(Asked by: username_0 on 2024-05-14)

I have just discovered the [paper of M. Herlihy and N. Shavit](https://cs.brown.edu/%7Emph/HerlihyS99/p858-herlihy.pdf) on the use of algebraic topology methods in TCS and distributed computing in particular.

Now I am wondering if there is any further work being done in this area and if there are any current interesting follow up papers. Does anyone know anything about the state of the art?

Thank you!

**Tags:** soft-question, dc.distributed-comp, concurrency, topology, algebraic-topology

> **Comments:**
> **username_1**: Check out [Eric Goubault's work](https://scholar.google.fr/citations?user=pCksTpcAAAAJ&hl=en) on algebraic topology and parallelism, e.g. [this book](https://link.springer.com/book/10.1007/978-3-319-15398-8)  
> **username_2**: Bounds on Betty numbers of the set of zeros of polynomials (such as those given by Milnor and Thom) are used to prove bounds on the number of certain structures (such as order types) in discrete and computational geometry. The works of Ben-or, Yao, etc., giving lower bounds for the complexity of algebraic decision trees also comes to mind (a lot of work on algebraic decision/computation trees in general could fit).  
> **username_3**: When you say "further work in this area" are you asking specifically about applying algebraic topology to distributed computing? Or more generally applications of algebraic topology in TCS?  
> **username_3**: Related (but, AFAICT, not duplicate Qs): https://cstheory.stackexchange.com/q/7958/129, https://cstheory.stackexchange.com/q/41296/129, https://cstheory.stackexchange.com/q/53512/129,  
> **username_0**: Maybe the title of the question is missleading. I was asking for further work specifically applying algebraic topology to distributed computing, but anyway thanks for linking the other questions. I will give them a look.  
> **username_4**: @username_0 then change the title of your post...  
> **username_5**: There is a conference which is purely devoted to the applications of algebraic topology in TCS, and in particular in distributed computing. https://getco-conf.github.io/2024/ I suggest you look at the program of the recent editions (in the "history" tab of the website) to check the latest developement in the field.  
> **username_6**: some of these comments should be answers really.  

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## 1 answers

### Answer by username_6 on 2024-05-17. Score: 1

Maurice Herlihy, Dmitry Kozlov and Sergio Rajsbaum, "[Distributed Computing Through Combinatorial Topology](https://www.sciencedirect.com/book/9780124045781/distributed-computing-through-combinatorial-topology)", 2014


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