Branch and Bound Branch and Bound OptimizationOptimization

• In an exhaustive search, all possible trees in a search space are generated for comparison

• At each node, if the tree is optimal we retain it• As the number of taxa becomes large, this

approach becomes intractable• Thus, there is a need for an approach that can

effectively prune the search space so that finding solution may become more feasible

• One such approach is the branch-and-bound method

Exhaustive SearchExhaustive Search• Search for optimal trees

by evaluating every possible tree

• Feasible only for <=11 taxa, as processing costs rapidly increase after that

• Figure shows exhaustive search for a 5-taxa tree

Branch and BoundBranch and Bound• Focuses on pruning the search space by ignoring families of trees

that can not possible produce a better answer than the best one already found

• Traverse a search tree in a depth-first sequence

• Trees that have longer tree length than the previously examined ones are ignored

• MP (Maximum Parsimony tree, i.e. the topology with the minimum tree length) is determined by evaluating tree lengths for a group of trees that have potentially shorter length

• Faster than an exhaustive search, but still impractical for large numbers of taxa

Branch and Bound Branch and Bound MethodologyMethodology

• When a node is encountered that has a higher tree-length than the minimum tree length, all the subsequent expansions for the tree are pruned away

• This corresponds to taking a subset of m taxa, where m<n (n = current minimum found) and computing tree length

• If this tree length is larger than the tree length we have for any n taxa configuration, the m tree topology and all its children are aborted from further consideration