The minimal set of Ingleton inequalities
Laurent Guille, Terence Chan, Alex Grant
TL;DR
This paper identifies the minimal set of Ingleton inequalities needed to compute the Ingleton-LP bound, simplifying the process and reducing computational effort for determining multicast capacity regions with linear network codes.
Contribution
It provides a unique minimal set of Ingleton inequalities, streamlining the calculation of the Ingleton-LP bound for multicast capacity analysis.
Findings
Reduced number of inequalities needed for bound computation
Simplified characterization of the polyhedral cone
Enhanced efficiency in multicast capacity analysis
Abstract
The Ingleton-LP bound is an outer bound for the multicast capacity region, assuming the use of linear network codes. Computation of the bound is performed on a polyhedral cone obtained by taking the intersection of half-spaces induced by the basic (Shannon-type) inequalities and Ingleton inequalities. This paper simplifies the characterization of this cone, by obtaining the unique minimal set of Ingleton inequalities. As a result, the effort required for computation of the Ingleton-LP bound can be greatly reduced.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · Complexity and Algorithms in Graphs