Computing bounds on network capacity regions as a polytope reconstruction problem
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Medard_Computing bounds.pdf
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238.22 KB
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Author(s)
Kim, Anthony
Medard, Muriel
Date Issued
October 2011
Journal
Proceedings on the IEEE International Symposium on Information Theory Proceedings (ISIT), 2011
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Kim, Anthony, and Muriel Medard. “Computing Bounds on Network Capacity Regions as a Polytope Reconstruction Problem.” IEEE International Symposium on Information Theory Proceedings (ISIT), 2011. 588–592.
Version
Author's final manuscript
Abstract
We define a notion of network capacity region of networks that generalizes the notion of network capacity defined by Cannons et al. and prove its notable properties such as closedness, boundedness and convexity when the finite field is fixed. We show that the network routing capacity region is a computable rational polytope and provide exact algorithms and approximation heuristics for computing the region. We define the semi-network linear coding capacity region, with respect to a fixed finite field, that inner bounds the corresponding network linear coding capacity region, show that it is a computable rational polytope, and provide exact algorithms and approximation heuristics. We show connections between computing these regions and a polytope reconstruction problem and some combinatorial optimization problems, such as the minimum cost directed Steiner tree problem. We provide an example to illustrate our results. The algorithms are not necessarily polynomial-time.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Research Laboratory of Electronics
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1109/ISIT.2011.6034197
