Sum of Root-Leaf Distance Interdiction Problems on Trees

Xiucui Guan, Panos M. Pardalos and Binwu Zhang
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Xiucui Guan: Southeast University
Binwu Zhang: Hohai University

Chapter Chapter 7 in Inverse Combinatorial Optimization Problems, 2025, pp 171-201 from Springer

Abstract: Abstract This chapter explores the interdiction problems on sum of root-leaf distance on trees (Int-SRD). First, the problems (Int-SRD) under weighted l 1 $$l_1$$ norm, bottleneck Hamming, and unit sum Hamming distance are solved in polynomial time and are shown to be N P $$\mathcal {N}\mathcal {P}$$ -hard under weighted sum Hamming distance and weighted node cost. Subsequently, recognizing that the original solution does not account for the shortest root-leaf distance, a shortest path constraint is added, leading to the formulation of the double interdiction problem (DIT H∞ $$_{H\infty }$$ ) and its minimal cost version. These problems are shown to be N P $$\mathcal {N}\mathcal {P}$$ -hard and are addressed through a combination of dynamic programming and binary search algorithms in pseudo-polynomial time.

Keywords: Sum of root-leaf distance interdiction problems; Upgrading edges/nodes; Cardinality constraint; Double interdiction problem; Trees (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-031-91175-0_7

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DOI: 10.1007/978-3-031-91175-0_7

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