@inproceedings{fd9b119fe7e2469687a40ab057939153,

title = "Nested set union",

abstract = "We consider a version of the classic disjoint set union (union-find) problem in which there are two partitions of the elements, rather than just one, but restricted such that one partition is a refinement of the other. We call this the nested set union problem. This problem occurs in a new algorithm to find dominators in a flow graph. One can solve the problem by using two instances of a data structure for the classical problem, but it is natural to ask whether these instances can be combined. We show that the answer is yes: the nested problem can be solved by extending the classic solution to support two nested partitions, at the cost of at most a few bits of storage per element and a small constant overhead in running time. Our solution extends to handle any constant number of nested partitions.",

keywords = "data structures, disjoint set union, union-find",

author = "Larkin, {Daniel H.} and Tarjan, {Robert E.}",

year = "2014",

doi = "10.1007/978-3-662-44777-2_51",

language = "English (US)",

isbn = "9783662447765",

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

publisher = "Springer Verlag",

pages = "618--629",

booktitle = "Algorithms, ESA 2014 - 22nd Annual European Symposium, Proceedings",

address = "Germany",

note = "22nd Annual European Symposium on Algorithms, ESA 2014 ; Conference date: 08-09-2014 Through 10-09-2014",

}