Concurrent Computing and Shellable Complexes

  • Maurice Herlihy
  • Sergio Rajsbaum
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6343)


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 studied in the combinatorial topology literature because they have many nice properties.

It turns out that many standard models of concurrent computation can be captured either as shellable complexes, or as the simple union of shellable complexes. We consider general adversaries in the synchronous, asynchronous, and semi-synchronous message-passing models, as well as asynchronous shared memory augmented by consensus and set agreement objects.

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.


Simplicial Complex Protocol Complex Shellability Condition General Adversary Canonical Order 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Maurice Herlihy
    • 1
  • Sergio Rajsbaum
    • 2
  1. 1.Computer Science DepartmentBrown UniversityProvidence
  2. 2.Instituto de MatemáticasUniversidad Nacional Autónoma de México, Ciudad UniversitariaMexico

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