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Empirical Analysis Of Heuristic and Approximation Algorithms for the Mutual-Visibility Problem

Created by
  • Haebom

Author

Vanja Stojanovi c, Bor Panger\v{s}i\v{c}

Outline

To address the lack of empirical analysis of the NP-complete mutual visibility (MV) problem, this paper implements three algorithms (direct randomized heuristic, hypergraph-based approximation, and genetic algorithm) and evaluates them on various synthetic graph datasets (including datasets with analytically known $\mu(G)$ values).

Takeaways, Limitations

For small graphs, the algorithm consistently achieves MV set sizes that meet theoretical bounds.
For large instances, the solution size deviates significantly from the theoretical limit.
The absence of strict boundaries made absolute quality assessment difficult.
Verification results on known optimal graphs show that genetic algorithms and other heuristics perform best.
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