Re: [Roll] do we need a dominating set?
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Re: [Roll] do we need a dominating set?



On Nov 18, 2009, at 2:08 PM, Michael Richardson wrote:


"Philip" == Philip Levis <pal at cs.stanford.edu> writes:
"Pascal" == Pascal Thubert <(pthubert)"
<pthubert at cisco.com>> writes:

   Pascal> A dominating set is a connected set of routers that enables
   Pascal> connectivity for all, that is all nodes in the network is
   Pascal> connected to at least one member of the dominating set.

So, in a straight tree arrangement, the dominating set is the
non-leaf nodes.  In a linear arrangement, the dominating set is
all the nodes, except for the last one.  Is this correct?

Philip> No. Unfortunately, that's not the definition of a dominating
   Philip> set.  Dominating set is a precise term that's been used for
Philip> decades in graph algorithms. It helps to not try to redefine
   Philip> such terms, as all it does is lead to confusion.

   Philip> Here's the wikipedia page for dominating set:

   Philip> http://en.wikipedia.org/wiki/Dominating_set

So my examples are correct interpretations of Pascal's definition, but
what we've defined does not go by that term. :-)

Yes. :)

What Pascal defined is called a "connected dominating set."

Phil


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