We show how an Euler tour for a tree on n vertices with maximum degree d can be stored in 2 n + o (n) bits such that queries take O (\log n) time and updates take O (d \log^{1 + \epsilon time.
We show how a collection of Euler-tour trees for a forest on n vertices can be stored in 2 n + o (n) bits such that simple queries take constant time, more complex queries take logarithmic time and updates take polylogarithmic amortized time.
R
an Euler tour for a tree
a collection of Euler-tour trees for a forest
D
with maximum degree d
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queries take O (\log n) time
simple queries take constant time, more complex queries take logarithmic time
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O (d \log^{1 + \epsilon
polylogarithmic amortized