Sheaf cohomology on network codings: maxflow-mincut theorem

Miradain Atontsa Nguemo; Calvin Tcheka

doi:10.4995/agt.2017.3371

Authors

Miradain Atontsa Nguemo University of Yaoundé 1
Calvin Tcheka University of Dschang

DOI:

https://doi.org/10.4995/agt.2017.3371

Keywords:

network information flow, network coding sheaves, topological cut, relative sheaf cohomology.

Abstract

Surveying briefly a novel algebraic topological application sheaf theory into directed network coding
problems, we obtain the weak duality in multiple source scenario by
using the idea of modified graph. Furthermore,we establish the
maxflow-mincut theorem with network coding sheaves in the case of multiple source.

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References

J. M. Curry, Sheaves, cosheaves and applications, arXiv:1303.3255 [math.AT] (2013).

Y. Felix, S. Halperin and J-C. Thomas, Rational homotopy theory, volume 205 of Graduate Texts in Mathematics. Springer-Verlag, New York, 2001. E. Gasparim, A first lecture on sheaf cohomology, Universidade Federal de Pernambuco, Cidade Universitária, Recife, PE, BRAZIL, 50670-901.

https://doi.org/10.1007/978-1-4613-0105-9

R. Ghrist and Y. Hiraoka, Applications of sheaf cohomology and exact sequences to network coding, NOLTA, 2011.

R. Ghrist and S. Krishnan, A topological max-flow-min-cut theorem, in Proc. Global Sig. Inf. Proc, Aug. 2013.

R. Hartshorne, Algebraic geometry, Springer, 1997.

R. Koetter and M. Médard, An algebraic approach to network coding, IEEE Trans. on Networking 11 (2003), 782--795.

https://doi.org/10.1109/TNET.2003.818197

L. I. Nicolaescu, The derived category of sheaves and the Poincaré-Verdier duality, April, 2005 (www3.nd.edu/~lnicolae/Verdier-ams.pdf).