Dead branch — where it appears
Named by 4 essays across 4 fields — each of them below, with the objects they name alongside it.
Flat in the budget, and not
One saving is eleven times at every error budget, because it is a property of the alphabet. The other moves between ninety-eight and a hundred and five, because it follows the share of extensions that find nothing. Two savings, two shapes, and neither line crosses the other.
Asking about symbols that are not there
A search extends an interval by every character of the alphabet, and on a deep branch almost all of them produce an empty interval. That is a full rank walk whose entire result is the discovery that nothing was there.
The branches that find nothing
An approximate search over a twenty-symbol alphabet attempts sixteen thousand eight hundred extensions and nine thousand two hundred of them produce an empty interval. That is a full rank walk whose entire result is the discovery that nothing was there.
A looser budget wastes a larger share
More errors permitted means more work, and the fraction of that work which was never going to help rises with it — from thirty-one per cent at no errors to seventy-five at two. The saving is worth most where the search is most expensive.
Named alongside it
The objects these essays reach for when they reach for this one.
Backtracking searchInterval symbolsAlphabet sizeDescentError budgetRankSelf-indexWavelet treeApproximate matchingBidirectional indexCompound walk