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Applications of Shellable Complexes to Distributed Computing

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CONCUR 2010 - Concurrency Theory (CONCUR 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6269))

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Abstract

This talk describes recent Joint work with Sergio Rajsbaum [3].

For models of concurrent computation in which processes may fail by crashing, each possible computation can be characterized as a simplicial complex, a geometric structure constructed by “gluing together” simplexes in a regular manner [6]. Informally, a complex is k-connected if it has no “holes” in dimension k or lower. It is known that if the complex corresponding to every such computation is k-connected, then one cannot solve (k + 1)-set agreement [4,5,6].

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References

  1. Björner, A.: Shellable and Cohen-Macaulay partially ordered sets. Transactions of the American Mathematical Society (1), 159–183 (July 1980)

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  2. Bruggesser, H., Mani, P.: Shellable decompositions of cells and spheres. Math. Scand. 29, 197–205 (1971)

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  3. Herlihy, M., Rajsbaum, S.: Concurrent computing and shellable complexes (submitted for Publication)

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  4. Herlihy, M., Rajsbaum, S.: Set consensus using arbitrary objects (preliminary version). In: PODC 1994: Proceedings of the thirteenth annual ACM symposium on Principles of distributed computing, pp. 324–333. ACM, New York (1994)

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  5. Herlihy, M., Rajsbaum, S.: Algebraic spans. Mathematical Structures in Computer Science 10(4), 549–573 (2000)

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  6. Herlihy, M., Shavit, N.: The topological structure of asynchronous computability. J. ACM 46(6), 858–923 (1999)

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  7. Kozlov, D.: Combinatorial Algebraic Topology. Springer, Heidelberg (2007)

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Author information

Authors and Affiliations

  1. Computer Science Department, Brown University,  

    Maurice Herlihy

Authors
  1. Maurice Herlihy
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Editor information

Editors and Affiliations

  1. Laboratoire Spécification et Vérification (LSV), ENS de Cachan & CNRS, 94235, Cachan cedex, France

    Paul Gastin

  2. LIAFA, Université Paris Diderot, 75205, Paris cedex, France

    François Laroussinie

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Herlihy, M. (2010). Applications of Shellable Complexes to Distributed Computing. In: Gastin, P., Laroussinie, F. (eds) CONCUR 2010 - Concurrency Theory. CONCUR 2010. Lecture Notes in Computer Science, vol 6269. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15375-4_2

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  • DOI: https://doi.org/10.1007/978-3-642-15375-4_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15374-7

  • Online ISBN: 978-3-642-15375-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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