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The Minmax Regret Longest Path of a Tree with Interval Edge Lengths

Năm XB 2023 Tạp chí / Hội thảo Lecture Notes in Networks and Systems Volume 847 LNNS Đơn vị CNTT DOI / Link https://doi.org/10.1007/978-3-031-49529-8_35 ↗

Tác giả

Tóm tắt

This paper focuses on tackling the challenge of determining the longest path on a tree represented as T=(V,E), where the edges are assigned interval lengths. We employ the minmax regret concept as a metric to quantify robustness. The longest path associated with this concept is referred to as the minmax regret longest path on the tree T. Initially, we establish certain structural properties pertaining to both the longest and second longest paths within the tree. Then we reset the problem as a formulation regarding the longest and second longest path with respect to candidate scenarios. We finally devise a combinatorial algorithm capable of identifying the minmax regret longest path within the tree in O(|L|^2|V|) time with L being the set of leaf nodes.

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