On the complexity of a set-union problem

We consider a simple data structure supporting the following operations: (i) create a new singleton set; (ii) create a new set which is the union of two pre-existing sets; (iii) determine whether a given element is in a particular set. We prove both lower and upper bounds for an implementation of su...

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Bibliographic Details
Published inProceedings 38th Annual Symposium on Foundations of Computer Science pp. 110 - 115
Main Authors Lipton, R.J., Martino, P.J., Neitzke, A.
Format Conference Proceeding
LanguageEnglish
Published IEEE 1997
Subjects
Computer science
Costs
Data analysis
Data structures
Mathematics
Upper bound
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Summary:We consider a simple data structure supporting the following operations: (i) create a new singleton set; (ii) create a new set which is the union of two pre-existing sets; (iii) determine whether a given element is in a particular set. We prove both lower and upper bounds for an implementation of such a data structure. In a restricted model we show that no deterministic implementation can be better than the "trivial" one that takes O(n/sup 2/) time. In a parallel model where the operations come in at most O(1g n) stages we exhibit a sub-quadratic implementation.
ISBN:9780818681974
0818681977
ISSN:0272-5428
DOI:10.1109/SFCS.1997.646099