Summary
2011 International Symposium on Nonlinear Theory and Its Applications
2011
Session Number:A4L-C
Session:
Number:A4L-C3
Network Codings and Sheaf Cohomology
Robert Ghrist, Yasuaki Hiraoka,
pp.266-269
Publication Date:2011/9/4
Online ISSN:2188-5079
Summary:
This paper introduces a novel application of sheaf cohomology to network coding problems. After recalling the definition of sheaves, we introduce NETWORK CODING SHEAVES for a general multi-source network coding scenario, and consider various forms of sheaf cohomologies. The main theorem states that 0-th network coding sheaf cohomology is equivalent to information flows for the network coding. This theorem is then applied to several practical problems in network codings such as maxflow bounds, global extendability, network robustness, and data merging; these applications all follow from exact sequences of sheaf cohomology.