Smallest-Circle Problem¶
The smallest-circle problem (also known as minimum covering circle problem, bounding circle problem, least bounding circle problem, smallest enclosing circle problem) is a computational geometry problem of computing the smallest circle that contains all of a given set of points in the Euclidean plane.
Core Idea¶
Smallest-Circle Problem is treated here as the recurring computational geometry identity summarized by this source-grounded definition: The smallest-circle problem (also known as minimum covering circle problem, bounding circle problem, least bounding circle problem, smallest enclosing circle problem) is a computational geometry problem of computing the smallest circle that contains all of a given set of points in the Euclidean plane. The smallest-circle problem (also known as minimum covering circle problem, bounding circle problem, least bounding circle problem, smallest enclosing circle problem) is a computational geometry problem of computing the.
Scope of Application¶
-
Emo Welzl proposed a simple randomized algorithm for th. As a consequence of membership in this class, it was shown that the dependence on the dimension of the constant factor in the O(n) time bound, which was factorial for.
-
Megiddo's algorithm. The solution of the subproblem is either the solution of the unconstrained problem or it is used to determine the half-plane where the unconstrained solution center is located.
-
Other algorithms. Chakraborty and Chaudhuri propose a linear-time method for selecting a suitable initial circle and a pair of boundary points on that circle.
-
Other algorithms. Each step of the algorithm includes as one of the two boundary points a new vertex of the convex hull, so if the hull has h vertices this method can be.
-
Other algorithms. At each step, a point not covered by the current sphere is used to find a larger sphere that covers a new subset of points, including the point found.
Clarity¶
A clear use of Smallest-Circle Problem names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is The smallest-circle problem (also known as minimum covering circle problem, bounding circle problem, least bounding circle problem, smallest enclosing circle problem) is a computational geometry problem of computing the smallest circle that contains all of a given set of points in the.
Manages Complexity¶
Smallest-Circle Problem compresses multiple computational geometry details into a stable diagnostic relation. The source shows both the central mechanism—it also states that performance is improved by dynamically re-ordering the points so that those that are found to be outside a circle are subsequently considered earlier, but this requires a change in the structure of the algorithm to store P as a "global".—and the practical consequence—subsequently, the smallest-circle.
Abstract Reasoning¶
- Type the carrier. Identify the computational geometry entities to which the claim applies.
- State the relation. Use the source-grounded identity: The smallest-circle problem (also known as minimum covering circle problem, bounding circle problem, least bounding circle problem, smallest enclosing circle problem) is a computational geometry problem of computing the smallest circle that contains all of a given set of points in the Euclidean plane.
- Check operation and conditions.
Knowledge Transfer¶
Within the home domain. Knowledge about Smallest-Circle Problem transfers literally when a new case preserves the same carrier type, relation, and recognition test. As a consequence of membership in this class, it was shown that the dependence on the dimension of the constant factor in the O(n) time bound, which was factorial for Seidel's method, could be reduced to subexponential. The solution of the.
Relationships to Other Abstractions¶
Current abstraction Smallest-Circle Problem Domain-specific
Parents (1) — more general patterns this builds on
-
Smallest-Circle Problem is a kind of Computational problem Domain-specific
The smallest-circle problem maps a finite point set to a minimum-radius enclosing circle.
Hierarchy path (1) — routes to 1 parentless root
- Smallest-Circle Problem → Computational problem → Function (Mapping)
Neighborhood in Abstraction Space¶
Smallest-Circle Problem sits in a crowded region of the domain-specific corpus (37th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Combinatorial Optimization & Discrete Structures (31 abstractions)
Nearest neighbors
- Newton–Gauss line — 0.89
- Filling radius — 0.88
- Incidence (geometry) — 0.88
- Skip list — 0.87
- Tractable Problem — 0.87
Computed from structural-signature embeddings · 2026-10-08