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Insertion Heuristics for (1,2)-TSP

In: Operations Research Proceedings 2023

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  • Ekin Ergen

    (Technische Universität Berlin)

Abstract

Insertion heuristics are approximation algorithms that are widely used in practice to solve the traveling salesperson problem (TSP) which is arguably among the most prominent problems in combinatorial optimization. In this paper, we analyze well-known variants of insertion heuristics restricted to instances with edge weights in $$\{1,2\}$$ { 1 , 2 } , deriving the exact approximation ratio of 7/4 for multiple variants. These ratios yield the first tight bounds known for arbitrary insertion heuristic and the farthest insertion heuristic for any class on which TSP is NP-complete.

Suggested Citation

  • Ekin Ergen, 2025. "Insertion Heuristics for (1,2)-TSP," Lecture Notes in Operations Research, in: Guido Voigt & Malte Fliedner & Knut Haase & Wolfgang Brüggemann & Kai Hoberg & Joern Meissner (ed.), Operations Research Proceedings 2023, chapter 0, pages 543-549, Springer.
    • Handle: RePEc:spr:lnopch:978-3-031-58405-3_69
    DOI: 10.1007/978-3-031-58405-3_69
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