On a Leasing Variant of the Online Connected Facility Location Problem

Abstract

In the leasing optimization model, resources are leased for K different time periods, instead of being acquired for unlimited duration. The goal is to use these temporary resources to maintain a dynamic infrastructure that serves n requests while minimizing the total cost. We propose and study a leasing variant of the online connected facility location problem, which we call the online connected facility leasing problem. In this problem each client that arrives must be connected to a temporary facility, which in turn must be connected to a root facility using permanent edges. We present an algorithm that is O(K · lg n)-competitive if the scaling factor is M = 1.

Online Algorithmic Study of Facility Location Problems: A Survey

“…-Connected Facility Location in the Online Setting problem (OCFL) [ -OFL in the leasing framework, with deadlines [46], price-fluctuation [42], connectedness [47], and dormant fees [48] -OFL in dynamic environments [52]- [54] Fotakis [19] raised the important question of whether one can design a generic framework that can establish the competitive ratios of existing online algorithms for the metric OFL and its variants. He observed that, in nearly all of these algorithms, the distances to the nearest facility from each client form a feasible dual approximate solution.…”

“…For the so-called progressive model, in which lease prices can vary by a maximum of 1 between two consecutive days, they proposed an online deterministic O((L + lmax cmax ) log n)competitive algorithm, with L denoting the number of lease options, c max the cost of the longest lease type, and l max the longest lease length. c: Connectedness: Santos de Lima et al [47] introduced the leasing variant of connected OFL. We refer to this variant as a connected OFLL.…”

“…Clients in connected OFLLs are required to establish a temporary connection to leased facilities, which are then required to establish a permanent connection to a root facility. Santos de Lima et al [47] developed an online deterministic algorithm for connected OFLL with an O(L log n)-competitive ratio, for M = 1 scaling factor, with n denoting the number of clients and L the number of lease options [17], [45].…”

“…Their result for the deadline variant is achieved by formulating the latter as a primal-dual program and using techniques similar to those in [19], [42], [44] to solve it. The algorithm of Santos de Lima et al [47] for connected OFLL draws upon ideas from the algorithm of Lee et al [29] for OCFL and the algorithm of [44] for the metric OFLL, discussed earlier.…”

Parking permit and network leasing problems

“…In Chapter 12, we review the primal-dual approximation algorithm for the facility leasing problem by Nagarajan and Williamson [60], and we show how to extend it to obtain a 3-approximation algorithm for the facility leasing problem with penalties. (This result was published in [21].) We also discuss results in the literature for the online versions of those problems.…”