Edge-Cut Bounds on Network Coding Rates
Gerhard Kramer,Serap A. Savari +1 more
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TLDR
A new bound on communication rates is developed that applies to network coding, which is a promising active network application that has processors transmit packets that are general functions, for example a bit-wise XOR of selected received packets.Abstract:
Active networks are network architectures with processors that are capable of executing code carried by the packets passing through them. A critical network management concern is the optimization of such networks and tight bounds on their performance serve as useful design benchmarks. A new bound on communication rates is developed that applies to network coding, which is a promising active network application that has processors transmit packets that are general functions, for example a bit-wise XOR, of selected received packets. The bound generalizes an edge-cut bound on routing rates by progressively removing edges from the network graph and checking whether certain strengthened d-separation conditions are satisfied. The bound improves on the cut-set bound and its efficacy is demonstrated by showing that routing is rate-optimal for some commonly cited examples in the networking literature.read more
Citations
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Dissertation
Guessing Games on Undirected Graphs
TL;DR: A new result of the thesis is that Shannon’s information inequalities, which work particularly well for a wide range of graph classes, are not sufficient for computing the guessing number.
Network coding for line networks with broadcast channels
TL;DR: In this paper, an achievable rate region for line networks with edge and node capacity constraints and broadcast channels (BCs) is derived, where the BCs are orthogonal, deterministic, physically degraded, or packet erasure with one-bit feedback.
Proceedings ArticleDOI
Undirected Unicast Network Capacity: A Partition Bound
TL;DR: In this paper, an upper bound on the symmetric rate of information flow in undirected unicast networks is derived and an algorithm to compute it is presented. But the upper bound is tight and the capacity is achievable by routing.
Journal Article
When the vertex coloring of a graph is an edge coloring of its line graph - a rare coincidence.
TL;DR: For graphs G of minimum degree at least 2, denoting by L(G) the line graph of G, it is proved that there is a bijection between the 3-consecutive vertex colorings of G and the3- Consecutive edge coloring of L, which keeps the number of colors unchanged, too.
References
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