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- W1750879921 abstract "We study a location-routing problem in the context of capacitated vehicle routing. The input to k-LocVRP is a set of demand locations in a metric space and a fleet of k vehicles each of capacity Q. The objective is to locate k depots, one for each vehicle, and compute routes for the vehicles so that all demands are satisfied and the total cost is minimized. Our main result is a constant-factor approximation algorithm for k-LocVRP. To achieve this result, we reduce k-LocVRP to the following generalization of k median, which might be of independent interest. Given a metric (V,d), bound k and parameter ρ ∈ ℝ + , the goal in the k median forest problem is to find S ⊆ V with |S| = k minimizing: $$sum_{uin V} d(u,S) quad + quad rhocdot dbig(,mbox{MST}(V/S),big),$$ where d(u,S) = min w ∈ S d(u,w) and $mbox{MST}(V/S)$ is a minimum spanning tree in the graph obtained by contracting S to a single vertex. We give a (3 + ε)-approximation algorithm for k median forest, which leads to a (12 + ε)-approximation algorithm for k-LocVRP, for any constant ε > 0. The algorithm for k median forest is t-swap local search, and we prove that it has locality gap $3+frac2t$ ; this generalizes the corresponding result for k median [3]. Finally we consider the k median forest problem when there is a different (unrelated) cost function c for the MST part, i.e. the objective is $sum_{uin V} d(u,S) ,+ ,c (,mbox{MST}(V/S),)$ . We show that the locality gap for this problem is unbounded even under multi-swaps, which contrasts with the c = d case. Nevertheless, we obtain a constant-factor approximation algorithm, using an LP based approach along the lines of [12]." @default.
- W1750879921 created "2016-06-24" @default.
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- W1750879921 date "2011-01-01" @default.
- W1750879921 modified "2023-10-05" @default.
- W1750879921 title "Locating Depots for Capacitated Vehicle Routing" @default.
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- W1750879921 doi "https://doi.org/10.1007/978-3-642-22935-0_20" @default.
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