Core Concepts
This paper investigates the Mechanism Design aspects of the m-Capacitated Facility Location Problem (m-CFLP) on a line. It proposes truthful mechanisms with bounded approximation ratios for two frameworks: (1) m facilities with equal capacity and no spare capacity, and (2) two facilities with abundant capacity.
Abstract
The paper focuses on the Mechanism Design aspects of the m-Capacitated Facility Location Problem (m-CFLP) on a line. It considers two main frameworks:
m-CFLP with equi-capacitated facilities and no spare capacity:
In this framework, there are m facilities with equal capacity k, and the total capacity equals the number of agents (n = mk).
The paper proposes two truthful mechanisms: the Propagating Median Mechanism (PMM) and the Propagating InnerPoint Mechanism (PIPM).
Both PMM and PIPM have bounded approximation ratios with respect to the Social Cost (SC) and the Maximum Cost (MC), in contrast with the impossibility results known for the classic m-Facility Location Problem.
The paper also provides lower bounds on the approximation ratio for any truthful and deterministic mechanism in this framework.
2-CFLP with abundant facilities:
In this framework, there are two facilities with capacities c1 and c2 such that c1 + c2 ≥ n and c1, c2 ≥ ⌊n/2⌋.
The paper proposes the Extended InnerGap (EIG) Mechanism, which generalizes and includes previously proposed mechanisms (InnerPoint, InnerChoice, and InnerGap).
The EIG Mechanism is shown to be strong group strategyproof (truthful) and to achieve bounded approximation ratios with respect to the SC and MC.
The paper also provides lower bounds on the approximation ratio for any truthful and deterministic mechanism in this framework, demonstrating the optimality or near-optimality of the EIG Mechanism.
Stats
The total number of agents is n.
The number of facilities is m.
The capacity of each facility is k, where n = mk.
The capacities of the two facilities are c1 and c2, where c1 + c2 ≥ n and c1, c2 ≥ ⌊n/2⌋.