pnthSBDeterministic

pnthSBDeterministic is a deterministic algorithmic variant in the pnthSB family used for structured enumeration and selection tasks. It is designed to compute the p-th item or p-th structured subset in a fixed, non-random order, ensuring reproducible results across runs.

Origins and context: The pnthSB family appears in research on combinatorial generation and deterministic sampling. pnthSBDeterministic contrasts with stochastic variants by replacing probabilistic choices with deterministic tie-breaking rules such as lexicographic ordering or priority-based selection.

Algorithmic idea: Given an input domain D with n elements and a selection parameter p, the method constructs the p-th element or p-th subset in a predefined order. It maintains a state that records the ranking of candidates and uses deterministic rules to advance to the next candidate until the target position is reached.

Applications: It is used when reproducibility is essential, such as formal benchmarking, testing of predicate functions, or in educational contexts to illustrate enumeration order. It also finds use in constraint programming or combinatorial libraries that expose a deterministic enumeration API.

Complexity: Time complexity is typically proportional to the number of steps required to reach the p-th item, plus the cost of evaluating candidate structures. Space usage is the maintained state, usually O(n) or O(k) for k-subset problems, depending on the exact implementation and the nature of the enumeration task.

See also: combinatorial generation, lexicographic order, deterministic algorithms.