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Concurrent Computing and Shellable Complexes

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Distributed Computing (DISC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6343))

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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 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.

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Author information

Authors and Affiliations

  1. Computer Science Department, Brown University, Providence, RI, 02912

    Maurice Herlihy

  2. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, D.F., 04510, Mexico

    Sergio Rajsbaum

Authors
  1. Maurice Herlihy
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  2. Sergio Rajsbaum
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Editor information

Editors and Affiliations

  1. Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 02139-4307, Cambridge, MA, USA

    Nancy A. Lynch

  2. Computer Science and Engineering, University of Connecticut, 371 Fairfield Way, Unit 2155, 06269, Storrs, CT, USA

    Alexander A. Shvartsman

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Herlihy, M., Rajsbaum, S. (2010). Concurrent Computing and Shellable Complexes. In: Lynch, N.A., Shvartsman, A.A. (eds) Distributed Computing. DISC 2010. Lecture Notes in Computer Science, vol 6343. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15763-9_10

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  • DOI: https://doi.org/10.1007/978-3-642-15763-9_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15762-2

  • Online ISBN: 978-3-642-15763-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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