Minimallength

Minimallength is a term used in mathematics, computer science, and related fields to denote the smallest possible length of an object that satisfies a given set of constraints. It is typically expressed as the minimum value of a length functional over a specified class of admissible objects, such as curves, paths, or sequences.

In geometry and metric spaces, the minimallength between two points is the length of a shortest path connecting them. In Euclidean space this is the straight line segment. More generally, in curved spaces or manifolds, minimallength paths are geodesics, which locally minimize length with respect to the underlying metric.

In graph theory and network optimization, minimallength often refers to the length of the shortest route between two vertices, where length is determined by edge weights or costs. Algorithms such as Dijkstra’s, Bellman–Ford, and A* are used to compute minimallength paths efficiently in many practical settings. The concept extends to directed or weighted graphs, networks with constraints, and dynamic environments.

Minimallength problems also arise in computational geometry and shape optimization, where one seeks the shortest polygonal chain, spline, or curve that meets boundary conditions or passes through prescribed points. In such contexts, additional constraints (like obstacle avoidance, monotonicity, or fixed endpoints) can complicate the problem and may render exact solutions computationally challenging.

In summary, minimallength captures the objective of achieving the smallest possible length under specified rules, with applications ranging from routing and robotics to geometric design and theory. See also shortest path, geodesic, and length functional.