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Ring star problem

The ring star problem (RSP) is a NP-hard problem in combinatorial optimization.

Version
v1 · 2026-09-28 · History
Domain-specific #
11817
Domain group
Formal Sciences
Origin domain
Operations Research
Subdomains
Combinatorial Optimization, Network Design → Operations Research

Core Idea

Ring star problem is treated here as the recurring computing and information systems identity summarized by this source-grounded definition: The ring star problem (RSP) is a NP-hard problem in combinatorial optimization. The ring star problem (RSP) is a NP-hard problem in combinatorial optimization. In a complete weighted mixed graph, the ring star problem aims to find a minimum cost ring star subgraph formed by a cycle (ring part) and a set of arcs (star part) such that each arc's child node belongs to the cycle and each arc's parent node does not.

Scope of Application

  • Documented setting. Some applications of RSP arise in the context of telecommunications, transports or logistics.

  • Exact formulations. The first MILP for solving RSP was introduced in 2004 alongside valid inequalities that improve the formulation.

  • Exact formulations. Several exact formulations have since been introduced in order to solve the Ring star problem such as a graph-layers based ILP and a st-chains formulation.

  • Variants of the ring star problem. Many variants of the ring star problem have been studied since 2006.

  • Heuristics. The first heuristic for RSP, a general variable neighborhood search has been introduced in order to obtain approximate solutions more quickly.

Clarity

A clear use of Ring star problem names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is The ring star problem (RSP) is a NP-hard problem in combinatorial optimization. The strongest recognition evidence in the frozen account is: Many variants of the ring star problem have been studied since 2006.

Manages Complexity

Ring star problem compresses multiple computing and information systems details into a stable diagnostic relation. The source shows both the central mechanism—the first MILP for solving RSP was introduced in 2004 alongside valid inequalities that improve the formulation.—and the practical consequence—in 2020, an ant colony optimization heuristic outperforms the evolutionary algorithm heuristic. This compression makes cases comparable while leaving parameters, conventions, exceptions, and evidential quality explicit.

Abstract Reasoning

  1. Type the carrier. Identify the computing and information systems entities to which the claim applies.
  2. State the relation. Use the source-grounded identity: The ring star problem (RSP) is a NP-hard problem in combinatorial optimization.
  3. Check operation and conditions. Several exact formulations have since been introduced in order to solve the Ring star problem such as a graph-layers based ILP and a st-chains formulation.
  4. Demand recognition evidence. Many variants of the ring star problem have been studied since 2006.
  5. Test variation.

Knowledge Transfer

Within the home domain. Knowledge about Ring star problem transfers literally when a new case preserves the same carrier type, relation, and recognition test. Some applications of RSP arise in the context of telecommunications, transports or logistics. The first MILP for solving RSP was introduced in 2004 alongside valid inequalities that improve the formulation. Beyond the home domain. No canonical parent is asserted for Ring star problem. An outside case receives the specialist name only when the same typed roles and rejection conditions can be filled literally; otherwise the comparison remains an analogy pending later graph densification.

Relationships to Other Abstractions

Local relationship map for Ring star problemParents appear above the current abstraction, mutual partners to the right, and children below. Node labels state whether each abstraction is prime or domain-specific; colors identify relation types.Ring star problemDOMAINDomain-specific abstraction: Computational problem — is a kind ofComputationalproblemDOMAIN

Current abstraction Ring star problem Domain-specific

Parents (1) — more general patterns this builds on

  • Ring star problem is a kind of Computational problem Domain-specific

    The ring-star problem specifies combinatorial network instances, feasible ring-star designs, and an optimization objective.

Hierarchy path (1) — routes to 1 parentless root

Neighborhood in Abstraction Space

Ring star problem sits in a sparse region of the domain-specific corpus (80th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Combinatorial Optimization & Discrete Structures (31 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08