772 research outputs found
A note on hierarchical hubbing for a generalization of the VPN problem
Robust network design refers to a class of optimization problems that occur
when designing networks to efficiently handle variable demands. The notion of
"hierarchical hubbing" was introduced (in the narrow context of a specific
robust network design question), by Olver and Shepherd [2010]. Hierarchical
hubbing allows for routings with a multiplicity of "hubs" which are connected
to the terminals and to each other in a treelike fashion. Recently, Fr\'echette
et al. [2013] explored this notion much more generally, focusing on its
applicability to an extension of the well-studied hose model that allows for
upper bounds on individual point-to-point demands. In this paper, we consider
hierarchical hubbing in the context of a previously studied (and extremely
natural) generalization of the hose model, and prove that the optimal
hierarchical hubbing solution can be found efficiently. This result is relevant
to a recently proposed generalization of the "VPN Conjecture".Comment: 14 pages, 1 figur
Galois module structure of Galois cohomology for embeddable cyclic extensions of degree p^n
Let p>2 be prime, and let n,m be positive integers. For cyclic field
extensions E/F of degree p^n that contain a primitive pth root of unity, we
show that the associated F_p[Gal(E/F)]-modules H^m(G_E,mu_p) have a sparse
decomposition. When E/F is additionally a subextension of a cyclic, degree
p^{n+1} extension E'/F, we give a more refined F_p[Gal(E/F)]-decomposition of
H^m(G_E,mu_p)
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