Unformatted text preview: e graph with vertex set
and
edge set
. We denote by
(or
) and
the number of vertices and edges in , respectively. Let
.
denotes the induced subgraph of by . We use
to
denote the path with consecutive vertices
.
Let and be positive integers with
. In [8], we have repglobal routing as a collection
resented a
of nonempty subsets of
such that each elebelongs to exactly
subsets of
.
is
ment of
called the density of the global routing, and a
global routing is also called a way global routing with density . Each
in
is referred to as a net of the global routing. We note
that a global routing
is a multiple set; two equal sets in
represent two different nets in the global routing. Note also that
a net of cardinality corresponds to an pin net. For simplicity,
pin nets are allowed to ensure that each element of
appears exactly
subsets of
.
and
be global routings and a positive integer.
Let
and
as multiple set is denoted by
The union of
, and
is the union of
’s.
Having given a global routing a local and mathematical view, we
further view the track with ID on the th side of an Sbox as a
vertex
and a switc...
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 Fall '13
 Border Gateway Protocol, Disjoint union, Autonomous system, P13, global routings

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