A general branch-and-bound tree is a branch-and-bound tree which is allowed to use general
\ndisjunctions. We construct a packing instance, a set covering instance, and
\na Traveling Salesman Problem instance, such that any general branch-and-bound tree that solves
\nthese instances must be of exponential size. We also verify that an exponential lower bound on
\nthe size of general branch-and-bound trees persists when we add Gaussian noise to the coefficients
\nof the cross polytope, thus showing that polynomial-size “smoothed analysis\u201d upper bound is not
\npossible. The results in this paper can be viewed as the branch-and-bound analog of the seminal
\npaper by Chvatal et al., who proved lower bounds for the Chvatal-Gomory rank.<\/p>\n","protected":false},"excerpt":{"rendered":"
A general branch-and-bound tree is a branch-and-bound tree which is allowed to use general disjunctions. We construct a packing instance, a set covering instance, and a Traveling Salesman Problem instance, such that any general branch-and-bound tree that solves these instances must be of exponential size. 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