Tight Approximation Bounds on a Simple Algorithm for Minimum Average Search Time in Trees
<|reference_start|>Tight Approximation Bounds on a Simple Algorithm for Minimum Average Search Time in Trees: The graph invariant EPT-sum has cropped up in several unrelated fields in later years: As an objective function for hierarchical clustering, as a more fine-grained version of the classical edge ranking problem, and, specifically when the input is a vertex-weighted tree, as a measure of average/expected search length in a partially ordered set. The EPT-sum of a graph $G$ is defined as the minimum sum of the depth of every leaf in an edge partition tree (EPT), a rooted tree where leaves correspond to vertices in $G$ and internal nodes correspond to edges in $G$.   A simple algorithm that approximates EPT-sum on trees is given by recursively choosing the most balanced edge in the input tree $G$ to build an EPT of $G$. Due to its fast runtime, this balanced cut algorithm can be used in practice, and has earlier been analysed to give a 1.62-approximation on trees. In this paper, we show that the balanced cut algorithm gives a 1.5-approximation of EPT-sum on trees, which amounts to a tight analysis and answers a question posed by Cicalese et al. in 2014.<|reference_end|>
@article{høgemo2024tight,
    title={Tight Approximation Bounds on a Simple Algorithm for Minimum Average
  Search Time in Trees},
    author={Svein H{o}gemo},
    journal={arXiv preprint arXiv:2402.05560},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.05560},
    primaryClass={cs.DS}
}