Facility Location Problems with Capacity Constraints: Two Facilities and Beyond
Authors: Gennaro Auricchio, Zihe Wang, Jie Zhang
IJCAI 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper, we investigate the Mechanism Design aspects of the m-Capacitated Facility Location Problem (m-CFLP) on a line. ... For both of these frameworks, we propose truthful mechanisms with bounded approximation ratios with respect to the Social Cost (SC) and the Maximum Cost (MC). |
| Researcher Affiliation | Academia | Gennaro Auricchio1 , Zihe Wang2 and Jie Zhang1 1University of Bath, Department of Computer Science 2Renmin University of China |
| Pseudocode | Yes | Mechanism 1 (Propagating Median Mechanism (PMM)). Let n be the total number of agents, m the number of facilities to place, and k = n m N the capacity of each facility. Let us set r = m+1 2 . The routine of the PMM is as follows: (i) First, we locate the facility yr at one of the medians of Ir, i.e. yr = xk(r 1)+ k+1 2 . (ii) Second, we determine the positions of the other facilities via the following iterative routine. For any l r, let us be given the position of the l-th facility, namely yl. Then the position of the (l + 1)-th facility is yl+1 = max{xkl+1, xkl + dl}, where dl is the distance between yl and xkl := maxx Il x. Similarly, given l r and the position of the l-th facility, namely yl, the (l 1)-th facility is placed at yl 1 = min{xk(l 1), xk(l 1)+1 dl}, where dl is the distance between yl and xk(l 1)+1 := minx Il x. (iii) Finally, all the agents in Ij are assigned to yj. |
| Open Source Code | No | The paper does not provide concrete access to source code for the methodology described. |
| Open Datasets | No | The paper is theoretical and does not use or reference any datasets for empirical evaluation. |
| Dataset Splits | No | The paper is theoretical and does not involve empirical validation with dataset splits. |
| Hardware Specification | No | The paper does not provide specific hardware details for running experiments, as it is a theoretical work. |
| Software Dependencies | No | The paper does not provide specific ancillary software details or version numbers, as it is a theoretical work. |
| Experiment Setup | No | The paper is theoretical and does not describe an experimental setup with hyperparameters or system-level training settings. |