### Abstract

Given a rooted tree T with node profits and node demands, the capacitated subtree of a tree problem (CSTP) consists of finding a rooted subtree of the maximum profit, subject to having total demand no larger than the given capacity H. We first define the so-called critical item for CSTP and find upper bounds on the optimal value of CSTP in O(n^{2}) time, where n is the number of nodes in T. We then present our branch-and-bound algorithm for solving CSTP and illustrate the algorithm by using an example. Finally, we implement our branch-and-bound algorithm by using one of the developed upper bounds and compare the computational results with those given by the branch-and-bound version of CPLEX and given by a dynamic programming algorithm for CSTP whose complexity is O(nH), The comparison shows that our branch-and-bound algorithm performs much better than both CPLEX and the dynamic programming algorithm, especially when n and H are large, for example, in the range of [50, 500] and [5000, 10,000], respectively.

Original language | English |
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Pages (from-to) | 737-748 |

Number of pages | 12 |

Journal | Computers and Operations Research |

Volume | 24 |

Issue number | 8 |

DOIs | |

Publication status | Published - 1997 Aug |

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### All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Modelling and Simulation
- Management Science and Operations Research