Heterogeneous Facility Location without Money on the Line (original) (raw)

The study of facility location in the presence of selfinterested agents has recently emerged as the benchmark problem in the research on mechanism design without money. Here we study the related problem of heterogeneous 2-facility location, that features more realistic assumptions such as: (i) multiple heterogeneous facilities have to be located, (ii) agents' locations are common knowledge and (iii) agents bid for the set of facilities they are interested in. We study the approximation ratio of both deterministic and randomized truthful algorithms when the underlying network is a line. We devise an (n − 1)-approximate deterministic truthful mechanism and prove a constant approximation lower bound. Furthermore, we devise an optimal and truthful (in expectation) randomized algorithm.