CSE 489/589Homework Assignment 3
Due at the end of class on Mon, Nov 16.
*
October 30, 2009
Problem 1
(Virtual Circuit)
.
In a virtual circuit network, a new connection establishes a path from the
source to the destination of the connection. Edges on the same connection path are allowed to have
different VCI (virtual circuit identifier). Suppose the VCIfield is
k
bit long, then there can be up to
2
k
paths containing a particular edge on the network. (Think of the network as a graph, an edge is a link
between two vertices of the graph.)
Now, suppose – in order to simplify the VCI assignment algorithm — we enforce an additional
constraint that all edges on the same connection path must be assigned with the same VCI.
(a) The number of connection paths containing a particular edge is called the “load” of that edge.
Come up with an example in which all current edge loads are strictly less than
2
k
(for some
k
you
can specify), yet there is no available VCI to assign to a new connection path.
(b) Suppose we always choose a shortest path for a new source/destination connection request, and
always assign the lowest available VCI to a new connection. Give an example of a graph, an integer
k
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 Fall '09
 Shortest path problem, Border Gateway Protocol, VCI, sh ip bgp

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