Exact incremental BPE maintains the canonical tokenization state after every appended byte. The recent algorithm of Jiang and Gong (2026) does this in
O(log2t) worst-case time, where
t is the maximum canonical token length. Its centroid search visits
O(logt) components and can pay another
O(logt) for ordered point location at each one. Within Jiang and Gong's normalized/proper merge-stage model, we change only that local search. Each interval is weighted by the size of the recursive component it selects, so a move from size
m to size
m′ costs
O(1+log(m/m′)). These charges telescope, giving
O(logt) time per append and
O(nlogt) over an
n-byte stream, with the same BPE semantics and asymptotic space. We also construct a normalized proper BPE family over a fixed alphabet where count-balanced search uses
Θ(log2t) probes on a reachable update, while the weighted search uses
Θ(logt). A Rust implementation matches the predicted probe counts on every tested instance. On ordinary vocabularies the queried degrees are small, however, and the improvement is a worst-case guarantee rather than an average-speed result.