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

Optimal binary search tree — where it appears

The search tree of least expected depth for a stated set of access frequencies. It is computed by an interval recurrence, it beats a balanced tree by whatever the access skew is worth, and the cost of computing it is what usually stops anybody from doing so.

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

Also named here as transitions — the same set of essays touches all of them, so they are one junction rather than several.

01234567891011120123456789101112123456789101112123456789101112345678910123456789123456781234567123456123451234123121one unit = one subproblem given a value91 cells, 364 transitions, 4.0 per cell

The cells are not the cost

This field opened by pricing a dynamic program in subproblems — 29,737 calls became 56 cells and the class changed. That is right when a cell is cheap. A table over intervals has 8,385 cells and considers 349,504 transitions to fill them, and the cubic in its bound is inside the cell rather than in the table.

tables · Table 01234567891011120123456789101112122332223333122222332231222222223122222233122222221222222122222122221222122121one unit = one subproblem given a value91 cells, 156 transitions, 1.7 per cell

The argmin that cannot go backwards

The same triangular table, the same ninety-one cells, the same tree at the end of it — and 364 transitions one way against 156 the other. At 256 keys the ratio is 38. What removes the factor is not a property of the recurrence but a property of the numbers it is given, and the recurrence does not mention them.

tables · Table

Named alongside it

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

Complexity classCost modelDynamic programmingInterval dpMeasured countRecurrenceSubproblemTransitionsCurve fittingMatrix-chainMonotonicityOverlapping subproblems

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