 |  Introduction to Algorithms, 2/e Thomas H. Cormen,
Dartmouth College
Charles E. Leiserson,
Massachusetts Institute of Technology
Ronald L. Rivest,
Massachusetts Institute of Technology
Clifford Stein,
Columbia University
Data Structures for Disjoint Sets
Chapter Overview - Chapter 21| Some applications involve grouping n distinct elements into a collection of disjoint sets. Two important operations are then finding which set a given element belongs to and uniting two sets. This chapter explores methods for maintaining a data structure that supports these operations. Section 21.1 describes the operations supported by a disjoint-set data structure and presents a simple application. In Section 21.2, we look at a simple linked-list implementation for disjoint sets. A more efficient representation using rooted trees is given in Section 21.3. The running time using the tree representation is linear for all practical purposes but is theoretically superlinear. Section 21.4 defines and discusses a very quickly growing function and its very slowly growing inverse, which appears in the running time of operations on the tree-based implementation, and then uses amortized analysis to prove an upper bound on the running time that is just barely superlinear. |
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2002 McGraw-Hill Higher Education