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Computer Science > Data Structures and Algorithms

arXiv:2410.06764 (cs)
[Submitted on 9 Oct 2024]

Title:An Optimal Algorithm for the Stacker Crane Problem on Fixed Topologies

Authors:Yike Chen, Ke Shi, Chao Xu
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Abstract:The Stacker Crane Problem (SCP) is a variant of the Traveling Salesman Problem. In SCP, pairs of pickup and delivery points are designated on a graph, and a crane must visit these points to move objects from each pickup location to its respective delivery point. The goal is to minimize the total distance traveled. SCP is known to be NP-hard, even on tree structures. The only positive results, in terms of polynomial-time solvability, apply to graphs that are topologically equivalent to a path or a cycle.
We propose an algorithm that is optimal for each fixed topology, running in near-linear time. This is achieved by demonstrating that the problem is fixed-parameter tractable (FPT) when parameterized by both the cycle rank and the number of branch vertices.
Subjects: Data Structures and Algorithms (cs.DS); Optimization and Control (math.OC)
Cite as: arXiv:2410.06764 [cs.DS]
  (or arXiv:2410.06764v1 [cs.DS] for this version)
  https://doi.org/10.48550/arXiv.2410.06764

Submission history

From: Chao Xu [view email]
[v1] Wed, 9 Oct 2024 10:52:29 UTC (213 KB)
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