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Some Observations on Equivalence Handling Methods
May 1981 (vol. 30 no. 5)
pp. 361-362
| ASCII Text | x | ||
| N.V. Murray, "Some Observations on Equivalence Handling Methods," IEEE Transactions on Computers, vol. 30, no. 5, pp. 361-362, May, 1981. | |||
| BibTex | x | ||
| @article{ 10.1109/TC.1981.1675795, author = {N.V. Murray}, title = {Some Observations on Equivalence Handling Methods}, journal ={IEEE Transactions on Computers}, volume = {30}, number = {5}, issn = {0018-9340}, year = {1981}, pages = {361-362}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.1981.1675795}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Computers TI - Some Observations on Equivalence Handling Methods IS - 5 SN - 0018-9340 SP361 EP362 EPD - 361-362 A1 - N.V. Murray, PY - 1981 KW - UNION-FIND KW - Equivalence KW - partition KW - path compression KW - tree balancing VL - 30 JA - IEEE Transactions on Computers ER - | |||
The online disjoint set union problem is solved essentially by implementing two operations which manipulate disjoint sets. FIND(x) computes the name of the unique set of which x is a member. UNION(A,B) merges the two sets A and B into one new set named either A or B. Given a set of n elements, we may perform f = n FIND's and n-1 intermixed UNION's in time 0(fa(f,n)) and space 0(n), where a(f,n) is related to a functional inverse of Ackermann's function and grows slowly. We show that certain modifications to the UNION operation that are convenient in some applications do not affect the running time complexity. We also show that under appropriate input restrictions, UNION and FIND can be made to run in linear time. However, the space required is 0(n+e), where e is the number of equivalence pairs to be processed.
Index Terms:
UNION-FIND, Equivalence, partition, path compression, tree balancing
Citation:
N.V. Murray, "Some Observations on Equivalence Handling Methods," IEEE Transactions on Computers, vol. 30, no. 5, pp. 361-362, May 1981, doi:10.1109/TC.1981.1675795
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