Abstract
Roughly speaking, a simplicial complex is shellable if it can be constructed by gluing a sequence of n-simplexes to one another along $$(n-1)$$ -faces only. Shellable complexes have been widely studied because they have nice combinatorial properties. It turns out that several standard models of concurrent computation can be constructed from shellable complexes. We consider adversarial schedulers in the synchronous, asynchronous, and semi-synchronous message-passing models, as well as asynchronous shared memory. We show how to exploit their common shellability structure to derive new and remarkably succinct tight (or nearly so) lower bounds on connectivity of protocol complexes and hence on solutions to the $$k$$ -set agreement task in these models. Earlier versions of material in this article appeared in the 2010 ACM Symposium on Principles of Distributed Computing (Herlihy and Rajsbaum 2010), and the International Conference on Distributed Computing (Herlihy and Rajsbaum 2010, doi: 10.1145/1835698.1835724 ).
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
