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Architectural Considerations for a Self-Configuring Routing Scheme for Spontaneous Networks
Decoupling the permanent identifier of a node from the node's
topology-dependent address is a promising approach toward completely scalable
self-organizing networks. A group of proposals that have adopted such an
approach use the same structure to: address nodes, perform routing, and
implement location service. In this way, the consistency of the routing
protocol relies on the coherent sharing of the addressing space among all nodes
in the network. Such proposals use a logical tree-like structure where routes
in this space correspond to routes in the physical level. The advantage of
tree-like spaces is that it allows for simple address assignment and
management. Nevertheless, it has low route selection flexibility, which results
in low routing performance and poor resilience to failures. In this paper, we
propose to increase the number of paths using incomplete hypercubes. The design
of more complex structures, like multi-dimensional Cartesian spaces, improves
the resilience and routing performance due to the flexibility in route
selection. We present a framework for using hypercubes to implement indirect
routing. This framework allows to give a solution adapted to the dynamics of
the network, providing a proactive and reactive routing protocols, our major
contributions. We show that, contrary to traditional approaches, our proposal
supports more dynamic networks and is more robust to node failures
Primes represented by incomplete norm forms
Let with the root of a degree monic
irreducible polynomial . We show the degree polynomial
in variables formed by setting the
final coefficients to 0 takes the expected asymptotic number of prime
values if . In the special case , we
show takes infinitely many prime
values provided .
Our proof relies on using suitable `Type I' and `Type II' estimates in
Harman's sieve, which are established in a similar overall manner to the
previous work of Friedlander and Iwaniec on prime values of and of
Heath-Brown on . Our proof ultimately relies on employing explicit
elementary estimates from the geometry of numbers and algebraic geometry to
control the number of highly skewed lattices appearing in our final estimates.Comment: 103 pages; v2 is significant rewrite of v1, main results unchange
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