Where does heap collide?

A heap is a tree-based data structure in which every parent value is ordered consistently against its children, so that the smallest (or largest) item always sits at the root and can be read off at once: this ordering, called the heap property, makes the structure the standard way to build a priority queue and to sort a list. Williams introduced the heap in his 1964 Algorithm 232: Heapsort, and Floyd's 1964 Algorithm 245: Treesort refined how the structure is built and maintained. Here the heap is an abstract arrangement of ordered values in a tree, judged by how quickly it returns and updates the top item, and it is neither the region of a running program's memory that shares its name nor the ancient puzzle about vague words.[1][2]

Unit

One ordered tree of values obeying the heap property, sized by its number of nodes

Recovery means

Not applicable

Measured by

Judged by the cost of its operations, such as the logarithmic time to insert an item or extract the root

The heap gives its name to the sorites paradox, the ancient puzzle of vagueness: a great pile of grains is plainly a heap, and removing a single grain from a heap surely still leaves a heap, yet repeating that step must eventually leave one grain, or none, which is no heap at all. The word sorites comes from the Greek for heap, and the paradox exposes how a vague word has no sharp boundary between where it applies and where it does not. Dummett's 1975 Wang's paradox and Fine's 1975 Vagueness, truth and logic gave modern logical treatments of how such words behave. Here the heap is not a thing at all but a test case for reasoning about vague description, and the question is where a word stops applying, a concern with no bearing on a memory region or a priority-queue structure.[3][4]

Unit

A borderline case used to probe a vague predicate, not a counted object

Recovery means

Not applicable

Measured by

Explored by logical analysis of tolerance principles and boundary cases, not by physical measurement