Shortestalso

Shortestalso is an informal term used in mathematical and computational discussions to describe a class of optimization problems that aim to produce the shortest possible object that also satisfies an additional constraint. The term is not part of formal theory with a canonical definition and appears mainly in forums, blog posts, and informal papers, where it functions as a shorthand rather than a rigorously defined notion.

Definition and interpretation: In its generic form, a shortestalso problem asks for an object o drawn from a set O such that a length function L(o) is minimized among all objects that satisfy a secondary property P. That is, find o in O with P(o) true and L(o) minimal. Depending on context, O could be sequences, paths, strings, graphs, or coded messages, and P could represent feasibility, safety, reliability, pattern constraints, or other criteria.

Examples: In graph-based routing, a shortestalso path between two nodes could be the route with minimal length that also guarantees a reliability above a threshold. In string processing, one might seek the shortest string that matches a pattern and also satisfies a symmetry constraint. In data encoding, the shortestalso codeword would minimize length while ensuring a detection or correction property.

Computational aspects: Finding a shortestalso object is often harder than finding a strictly shortest object because the secondary constraint adds complexity. In general, the problem can be NP-hard. Practical approaches include augmented search algorithms, constraint checks during traversal, or problem-specific reductions to known solvable cases.

See also: shortest path problem, constrained optimization, multi-criteria optimization, Pareto optimality.