Check — where it appears
Named by 9 essays across 4 fields — each of them below, with the objects they name alongside it.
Where two searches should stop
Search from both ends of a shortest-path query at once and the two frontiers meet somewhere in the middle, having expanded about two thirds of what one search would. Stop at the first vertex both searches have finished, and on five of forty weighted grids the path returned is longer than the shortest. The rule that is always right stops on a different condition, and on one of those grids it also stops sooner.
A node costs two ranks
The left child's interval is the position minus the right child's. A descent that calls rank on both children returns exactly the same symbols at twice the cost, and nothing about the answer can see it.
A document already in the answer
The same walk, with the chain's test replaced by a lookup in the answer so far. It reports the same documents at the same cost, and two exchanged lines make it lose nine of seventeen without failing.
A saving quoted without its collection
A check asking whether a compressed document array is smaller than the plain one passes on the rounding whenever the document count is not a power of two. It would report a saving of nothing as sixteen per cent, on a collection that has no redundancy at all.
One set, three orders
The symbols an interval holds do not depend on the tree's shape. The order they come out in does, and a search that accumulates a running count as it reads them computes a plausible number that is wrong on eighty per cent of queries.
A walk that does not prune
Remove the emptiness test and the descent visits every node of the tree, returns exactly the same symbols with exactly the same intervals, and costs sixty per cent more. No test of the answer can see it.
Where the sparse representation loses
At every row marked, Elias–Fano costs twice the plain vector. The crossing is at one row in four, which is a sampling rate a real index uses — so the choice between the two is a choice, not an improvement.
A price with no structure under it
A class in this collection has charged Elias–Fano's price for several strands and stores an array of positions searched by binary search. The accounting is right about space to a bit per thousand and wrong about one operation by a factor of eight.
Two factors that do not multiply
Eleven times and seventy-eight times against the same baseline, so an index with both should be eight hundred and sixty. It is seventy-eight, and the shortfall is eleven — the first factor, exactly, because the second operation already contains it.
Named alongside it
The objects these essays reach for when they reach for this one.
Wavelet treeIndex sizeInterval symbolsDescentOperation countRankBidirectional indexBit vectorCorrectnessDocument arrayElias fanoInvariant