@inproceedings{9469740d2170441998b075ac5f5c201c,

title = "Partitioning trees of supply and demand",

abstract = "Assume that a tree T has a number ns of {"}supply vertices{"} and all the other vertices are {"}demand vertices.{"} Each supply vertex is assigned a positive number called a supply, while each demand vertex is assigned a positive number called a demand. One wish to partition T into exactly ns subtrees by deleting edges from T so that each subtree contains exactly one supply vertex whose supply is no less than the sum of demands of all demand vertices in the subtree. The {"}partition problem{"} is a decision problem to ask whether T has such a partition. The {"}maximum partition problem{"} is an optimization version of the partition problem. In this paper, we give three algorithms for the problems. First is a linear-time algorithm for the partition problem. Second is a pseudo-polynomial-time algorithm for the maximum partition problem. Third is a fully polynomial-time approximation scheme (FPTAS) for the maximum partition problem.",

keywords = "Algorithm, Approximation, Demand, FPTAS, Maximum partition problem, Partition problem, Supply, Tree",

author = "Takehiro Ito and Xiao Zhou and Takao Nishizeki",

year = "2002",

doi = "10.1007/3-540-36136-7_53",

language = "English",

isbn = "3540001425",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

pages = "612--623",

booktitle = "Algorithms and Computation - 13th International Symposium, ISAAC 2002, Proceedings",

note = "13th Annual International Symposium on Algorithms and Computation, ISAAC 2002 ; Conference date: 21-11-2002 Through 23-11-2002",

}