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What is tree decomposition of a constraint problem?

  • A.Grouping variables into nodes so the result forms a tree
  • B.Splitting the problem into independent subproblems entirely
  • C.Removing edges until the constraint graph becomes a tree
  • D.Ordering the variables so that assignment proceeds down a tree

Answer: A

A tree decomposition collects variables into overlapping clusters arranged in a tree, so the tree algorithm applies to the clusters and the cost is exponential only in the largest cluster size. That size minus one is the treewidth. Independence, edge deletion and simple ordering are different ideas. A measure of how far a graph is from being a tree, and an algorithm whose cost depends on that measure rather than on size, is a powerful and widely reused construction.

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