You're configuring a large network of workstations, which we'll model as an undirected graph G; the nodes of G represent individual workstations and the edges represent direct communication links. The workstations all need access to a common core database, which contains data necessary for basic operating system functions.
You could replicate this database on each workstation; this would make lookups very fast from any workstation, but you d have to manage a huge number of copies. Alternately, you could keep a single copy of the database on one workstation and have the remaining workstations issue requests for data over the network G; but this could result in large delays for a workstation that s many hops away from the site of the database.
So you decide to look for the following compromise: You want to maintain a small number of copies, but place them so that any workstation either has a copy of the database or is connected by a direct link to a workstation that has a copy of the database. In graph terminology, such a set of locations is called a dominating set.
Thus we phrase the Dominating Set Problem as follows. Given the network G, and a number k, is there a way to place k copies of the database at k different nodes so that every node either has a copy of the database or is connected by a direct link to a node that has a copy of the database?
Show that Dominating Set is NP-complete.
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