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Properties and applications of data structures, such as space lower bounds, or time complexity of insertion and deletion of objects.
9
votes
2
answers
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O(n)-space, polylog-time subtree sums in incremental forests?
Consider a forest $G$ of $n$ vertices $v_1, \dots, v_n$ arranged left to right with edges from child to parent always going to the left, i.e. if the parent of vertex $v_i$ is $v_j$, then $j < i$.
Addi …
2
votes
O(n)-space, polylog-time subtree sums in incremental forests?
Thanks to Dmytro Taranovsky for the thorough answer. Here's my attempt to rephrase his answer in my own words.
Without loss of generality, assume that $G$ consists of a single tree.
First, we reduce t …