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Multicast Triangular Semilattice Network [article]

Angelina Grosso, Felice Manganiello, Shiwani Varal, Emily Zhu
2018 arXiv   pre-print
We investigate the structure of the code graph of a multicast network that has a characteristic shape of an inverted equilateral triangle.  ...  ' receivers and required field sizes up to a network of 4 sources.  ...  A k-triangle in a triangular semilattice network ▽ n is a subgraph isomorphic as a directed graph to a triangular semilattice network ▽ k . We call k the length of a k-triangle.  ... 
arXiv:1808.04512v1 fatcat:2oeod2vptfdarivu4ggoecpgpi

Cantor meets Scott: Semantic Foundations for Probabilistic Networks [article]

Steffen Smolka, Praveen Kumar, Nate Foster, Dexter Kozen, Alexandra Silva
2016 arXiv   pre-print
implementation and show how to use it to solve a variety of problems including characterizing the expected congestion induced by different routing schemes and reasoning probabilistically about reachability in a network  ...  (M, ) is not a Semilattice Despite the fact that (M, ) is a directed set (Lemma 12), it is not a semilattice. Here is a counterexample. Let b = {π, σ, τ }, where π, σ, τ are distinct packets.  ...  Consider the infinite triangular matrix E and its inverse E −1 with rows and columns indexed by the finite subsets of H, where Eac = [a ⊆ c] E −1 ac = (−1) |c−a| [a ⊆ c] .  ... 
arXiv:1607.05830v5 fatcat:dktiz7otdzfflnw2lsctab2ife

Cantor meets Scott: semantic foundations for probabilistic networks

Steffen Smolka, Praveen Kumar, Nate Foster, Dexter Kozen, Alexandra Silva
2017 SIGPLAN notices  
implementation and show how to use it to solve a variety of problems including characterizing the expected congestion induced by different routing schemes and reasoning probabilistically about reachability in a network  ...  Surprisingly, despite Lemma 12, the probability measures do not form an upper semilattice under , although counterexamples are somewhat difficult to construct.  ...  Consider the infinite triangular matrix E and its inverse E −1 with rows and columns indexed by the finite subsets of H, where Eac = [a ⊆ c] E −1 ac = (−1) |c−a| [a ⊆ c].  ... 
doi:10.1145/3093333.3009843 fatcat:mdvrhemsxnblpoxseuh6nkjvc4