Algorithms & Data Structures
the bound is a claim, and it is checkable
Concept

Greedy — where it appears

A method that builds its answer one choice at a time, taking whichever option looks best now and never revisiting it. It is cheap and often good, and each step's cost is the cost of evaluating every remaining option against the goal, which is where its price is paid.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

11010³cap on the depthphrases9.8% more phrasesevery occurrence consideredthe earliest only4,096 charactersworst at cap 4

The cap an automaton cannot see

A state of a suffix automaton stands for a set of occurrences and hands back one of them. So a capped parse driven by it can ask whether the earliest occurrence is shallow enough and cannot ask whether any occurrence is — which costs up to 9.8% of the phrases, and only at the caps that bind.

bounds · Parse 0100200cells a query, selections included2,5005,00010,00030,00012.3 jumps6.2 jumps3.5 jumps0.8 jumpsmean queries between jumps, and jumps a streamthe corners, never fittedfitted once, keptfull refit on the counterone landmark, on the counterone landmark, every 5,0006 maps, 30,000 queries a streamcounter: window 2,000, threshold a half

A refit that changes one landmark

Choosing four landmarks again after traffic moves costs hundreds of thousands of cells of search, and on drifting streams it never paid. Keeping three and re-choosing the fourth costs a fifth as much — 0.19 of a full selection, not the twelfth the earlier page guessed. On drifting streams, refitting on the counter goes from a loss of up to 13% to within 2% of fitting once, and it wins where the destination moves six cells. When the destination jumps, it is the cheapest policy measured, 12% under the corners at one jump in 10,000 queries — unless the jumps come as often as one in 2,500.

graphs · Graph 11.051.101.15price, as a share of a full selectionfresh queries' cells against all candidates00.050.100.150.200.252 nearest4 nearest6 nearest8 nearest12 nearestall 2424 refits, 4 mapsdashed: the unrestricted refit

The candidates near where the queries end

Re-choosing one landmark after the traffic moves tried every candidate as the replacement, and most of them could not win. Tried only on the four candidates nearest the new destination, the refit costs 0.085 of a full selection — the twelfth an earlier page guessed — against 0.236, and its placements serve fresh queries within 3% as well. Where the full search's winner lies further away, the refit was barely worth making. A refit that cheap still cannot follow a destination that jumps every 2,500 queries; what holds the counter back was never the refit's price.

graphs · Graph

Named alongside it

The objects these essays reach for when they reach for this one.

Break-evenHeuristic searchHonest limitLandmarkParameter choicePreprocessingQuery distributionSamplingShortest pathConstructionDefinitionDepth cap

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