Main Article Content
This paper introduces a relationship between the independence of polynomials associated with the links of the network, and the Jacobian determinant of these polynomials. Also, it presents a way to simplify a given communication network through an algorithm that splits the network into subnets and reintegrates them into a network that is a general representation or model of the studied network. This model is also represented through a combination of polynomial equations and uses Groebner bases to reach a new simplified network equivalent to the given network, which may make studying the ability to solve the problem of network coding less expensive and much easier.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Ahlswede R, Cai N, Robert Li. Network Information Flow: IEEE Trans Inf Theory. 2000 July; 46(4):1204 -1216.
Robert Li, Yeung RW, Cai, N. Linear Network Coding: IEEE Trans Inf Theory. 2003 Feb; 49(2):371-381.
Dougherty R, Freiling C, Zeger K. Insufficiency of Linear Coding in Network Information Flow: IEEE Trans Inf Theory. 2005 Aug; 51(8):2745-2759
Mosaarab M, Barekatain B, Raahemifar K, Movahednejad H. An enhanced heuristic XoR network coding-based method for high quality video streaming over VANETs: Computer Science, Medicine. PLoS one; 2019 June. Available from: https://doi.org/10.1371/journal.pone.0218647.
Cai H, Etzion T, Schwartz M, Wachter A. Network Coding Solutions for the Combination Network and its Subgraphs: IEEE Trans Inf Theory. 2019 September, Available from: https://doi.org/10.1109/ISIT.2019.8849620
Celebiler M, Stette G. On Increasing the Down-Link Capacity of a Regenerative Satellite Repeater in Point-to-Point Communications: IEEE Trans Inf Theory. 1978 Jan;66 (1): 98–100.
Médini L, Mrissa M, Khalfi El, Terdjimi M, Sommer NL, Capdepuy P, Jamont JP, Occello M, Touseau L. Managing the Web of Things Linking the Real World to the Web 1st ed: Morgan Kaufmann; 2017.p151-180 Available from: https://doi.org/10.1016/B978-0-12-809764-9.00007-X
Hansen J, Krigslund J, Lucani DE , Pahlevani P, Fitzek FH. Bridging inter-flow and intra-flow network coding in wireless mesh networks: Comput. Netw. 2018 Nov;145:1-12. Available from: https://doi.org/10.1016/j.comnet.2018.07.014.
Cox D, Little J, O’Shea, D. Using Algebraic Geometry. 2nd ed. New York-Berlin-Heidelberg Springer; 1998. 572 p.
Perry J. A dynamic F4 algorithm to compute Grobner bases: Appl. Algebra Eng. Commun. Comput. Springer; 2020 July; 31(5-6):411-434.
Bhayani S, Kukelova Z, Heikkil J. A sparse resultant based method for efficient minimal solvers: IEEE/CVF Conf Comput Vis Pattern Recognit Workshops. 2020: 1770-1779.
Fragouli Ch, Soljanin E, (Secure) Linear network coding multicast: Designs, Des Codes Cryptogr. Springer; 2016 Jan; 78: 269-310. Available from: https://doi.org/10.1007/s10623-015-0155-6.