A note on data structures for maintaining bipartitions

Authors:
Gruia Calinescu
Affiliations:
Department of Computer Science, Illinois Institute of Technology, Chicago, IL 60616, USA
Venue:
Journal of Discrete Algorithms
Year:
2007

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Abstract

We consider the following problem: given a ground set U of elements {1,2,...,n}, and a set S of bipartitions of U, design a data structure to support the following three operations: Report(S)-report the partition of U induced by S, Insert(P,S)-add a new bipartition P to S, and Delete(P,S)-delete the existing partition P from S, where the partition of U induced by S is given by two elements of U being in the same class if and only if they are in the same class for every bipartition of S. We describe a straightforward deterministic data structure with an amortized bound of O(n) per update, which is optimal.