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Subset DP is dynamic programming indexed by subsets of a finite ground set, usually encoded by bit masks. A recurrence builds a subset from smaller subsets or removes one chosen element. There are $2^n$ subsets of an $n$-element set, so many such methods require exponential space or time despite avoiding factorial enumeration.

For a shortest path visiting a given set, $D(S,v)$ stores the best cost of a path visiting exactly $S$ and ending at $v$. The recurrence $D(S,v)={\min }_{u\in S\setminus \{v\}}(D(S\setminus \{v\},u)+c_{uv})$ retains the endpoint because it controls the next edge cost. Initial states and prohibited edges must be specified separately.