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.