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Unformatted text preview: s a special case in which the edges contain no more than two nodes.
We consider a hypergraph with m nodes and assume coordinate vectors xj ∈ Rp , j = 1, . . . , m, are
associated with the nodes. Some nodes are ﬁxed and their coordinate vectors xj are given. The
other nodes are free, and their coordinate vectors will be the optimization variables in the problem.
The objective is to place the free nodes in such a way that some measure of the physical size of the
nets is small.
As an example application, we can think of the nodes as modules in an integrated circuit, placed
at positions xj ∈ R2 . Every edge is an interconnect network that carries a signal from one module
to one or more other modules.
To deﬁne a measure of the size of a net, we store the vectors xj as columns of a matrix X ∈ Rp×m .
For each edge S in the hypergraph, we use XS to denote the p × |S | submatrix of X with the
columns associated with the nodes of S . We deﬁne
fS (X ) = inf XS − y 1T . (41) y as the size...
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- Fall '13
- The Aeneid