TY - JOUR
T1 - Top-down analysis of path compression
AU - Seidel, Raimund
AU - Sharir, Micha
PY - 2005
Y1 - 2005
N2 - We present a new analysis of the worst-case cost of path compression, which is an operation that is used in various well-known "union-find" algorithms. In contrast to previous analyses which are essentially based on bottom-up approaches, our method proceeds top-down, yielding recurrence relations from which the various bounds arise naturally. In particular the famous quasilinear bound involving the inverse Ackermann function can be derived without having to introduce the Ackermann function itself.
AB - We present a new analysis of the worst-case cost of path compression, which is an operation that is used in various well-known "union-find" algorithms. In contrast to previous analyses which are essentially based on bottom-up approaches, our method proceeds top-down, yielding recurrence relations from which the various bounds arise naturally. In particular the famous quasilinear bound involving the inverse Ackermann function can be derived without having to introduce the Ackermann function itself.
KW - Disjoint sets data structure
KW - Inverse Ackermann function
KW - Path compression
KW - Union-find problem
UR - http://www.scopus.com/inward/record.url?scp=20544465452&partnerID=8YFLogxK
U2 - 10.1137/S0097539703439088
DO - 10.1137/S0097539703439088
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AN - SCOPUS:20544465452
SN - 0097-5397
VL - 34
SP - 515
EP - 525
JO - SIAM Journal on Computing
JF - SIAM Journal on Computing
IS - 3
ER -