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The 15 pages that link to Approximation algorithm, each with the reason it gives.

• Graph coloringNarrower topic: For general graphs, efficiently approximating the chromatic number is itself a major challenge.

• Computational complexity theoryRelated: Approximation provides useful answers when exact optimization is computationally intractable.

• NP-completenessRelated: Hardness often motivates useful near-optimal solutions when exact optimization is intractable.

• Greedy algorithmRelated: When greedy choices are not exact, their quality may still admit a formal guarantee.

• Combinatorial optimizationRelated: Approximation guarantees offer tractable alternatives when exact optimization is too costly.

• NP-hardnessRelated: Approximation methods address optimization problems whose exact solutions are NP-hard to compute efficiently.

• HeuristicCompared with: It distinguishes formal quality guarantees from heuristic methods that may offer none.

• Linear programming relaxationRelated: Rounding a relaxation's solution can yield an approximate discrete solution.

• Hamiltonian cycleRelated: For weighted tours, approximation methods address optimization when exact search is expensive.

• Kruskal's algorithmCompared with: Kruskal's algorithm is exact for its objective, unlike methods that settle for approximate solutions.

• Prim's algorithmNarrower topic: Prim's algorithm is an exact polynomial-time method, unlike approximation methods needed for harder optimization problems.

• Theoretical computer scienceBroader topic: It offers useful solutions when exact optimization is computationally intractable.

• Clique problemRelated: The maximum-clique problem is difficult to approximate within strong guarantees.

• Erdős–Pósa theoremRelated: Packing and covering bounds can inform approximation methods for hitting cycles.

• Richard M. KarpRelated: Hardness results associated with Karp’s problems motivate approximate solutions.