Strategyproof facility location and the least squares objective

Michal Feldman, Yoav Wilf

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We consider the problem of locating a public facility on a tree, where a set of n strategic agents report their locations and a mechanism determines, either deterministically or randomly, the location of the facility. The contribution of this paper is twofold. First, we introduce, for the first time, a general and clean family of strategyproof (SP) mechanisms for facility location on tree networks. Quite miraculously, all of the deterministic and randomized SP mecha- nisms that have been previously proposed can be cast as special cases of this family. Thus, the proposed mechanism unifies much of the existing literature on SP facility location problems, and simplifies its analysis. Second, we demonstrate the strength of the proposed family of mechanisms by proving new bounds on the approximation of the minimum sum of squares (miniSOS) objective on line and tree networks. For lines, we devise a randomized mechanism that gives 1.5-approximation, and show, through a subtle analysis, that no other randomized SP mechanism can provide a better approximation. For general trees, we construct a randomized mechanism that gives 1.83-approximation. This result provides a separation between deterministic and randomized mechanisms, as it is complemented by a lower bound of 2 for any deterministic mechanism. We believe that the devised family of mechanisms will prove useful in studying approximation bounds for additional objectives.

Original languageEnglish
Title of host publicationEC 2013 - Proceedings of the 14th ACM Conference on Electronic Commerce
PublisherAssociation for Computing Machinery
Number of pages17
ISBN (Print)9781450319621
StatePublished - 2013
Externally publishedYes
Event14th ACM Conference on Electronic Commerce, EC 2013 - Philadelphia, PA, United States
Duration: 16 Jun 201320 Jun 2013

Publication series

NameProceedings of the ACM Conference on Electronic Commerce


Conference14th ACM Conference on Electronic Commerce, EC 2013
Country/TerritoryUnited States
CityPhiladelphia, PA


  • Approximate mechanism design without money
  • Facility location
  • Least squares

Cite this