Approximation Schemes for Capacitated Vehicle Routing on Graphs of Bounded Treewidth, Bounded Doubling, or Highway Dimension
نویسندگان
چکیده
In this article, we present Approximation Schemes for Capacitated Vehicle Routing Problem (CVRP) on several classes of graphs. CVRP, introduced by Dantzig and Ramser in 1959 [ 14 ], are given a graph G=(V,E) with metric edges costs, depot r ∈ V , vehicle bounded capacity Q . The goal is to find minimum cost collection tours the that returns depot, each visiting at most nodes, such they cover all nodes. This generalizes classic TSP has been studied extensively. more general setting, node v demand d total tour must be no than Either served one (unsplittable) or can multiple (splittable). best-known approximation algorithm graphs ratio α +2(1-ε) (for unsplittable) +1-ε splittable) some fixed \(ε \gt \frac{1}{3000}\) where best TSP. Even case trees, 4/3 5 ] it an open question if there scheme simple class Das Mathieu 15 presented time n log O(1/ε) Euclidean plane ℝ 2 No other known any metrics (without further restrictions ). make significant progress problem presenting Quasi-Polynomial Time (QPTAS) treewidth, highway dimensions, doubling dimensions. For comparison, our result implies run O(log 6 n/ε )
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ژورنال
عنوان ژورنال: ACM Transactions on Algorithms
سال: 2023
ISSN: ['1549-6333', '1549-6325']
DOI: https://doi.org/10.1145/3582500