Soft-capacitated Facility Location Research Articles

Algorithms for online data management problems considering the storage capacities

A mind-boggling amount of data will be generated every day. It is natural to consider clustering the data and putting each cluster into some place for storing. In reality, the arrival time of the data is unknown in advance and new data keep joining appropriate cluster upon arrival. This scenario can be captured as the online facility location problem. Usually, the places for storing the data have limited capacities. Therefore, the online capacitated facility location problem (O-CFLP) is proposed.Designing algorithms with bounded competitive ratios for the O-CFLP is impossible. This fact stimulates us to study special cases of the O-CFLP. We pay attention on the online soft capacitated facility location problem and its prize-collecting version, and we design dual-fitting competitive algorithms for them.

Approximating the $$\tau $$-relaxed soft capacitated facility location problem

In this paper, we consider the $$\tau $$ -relaxed soft capacitated facility location problem ( $$\tau $$ -relaxed SCFLP), which extends several well-known facility location problems like the squared metric soft capacitated facility location problem (SMSCFLP), soft capacitated facility location problem (SCFLP), squared metric facility location problem and uncapacitated facility location problem. In the $$\tau $$ -relaxed SCFLP, we are given a facility set $$\mathcal {F}$$ , a client set and a parameter $$\tau \ge 1$$ . Every facility $$i \in \mathcal {F}$$ has a capacity $$u_i$$ and an opening cost $$f_i$$ , and can be opened multiple times. If facility i is opened l times, this facility can be connected by at most $$l u_i$$ clients and incurs an opening cost of $$l f_i$$ . Every facility-client pair has a connection cost. Under the assumption that the connection costs are non-negative, symmetric and satisfy the $$\tau $$ -relaxed triangle inequality, we wish to open some facilities (once or multiple times) and connect every client to an opened facility without violating the capacity constraint so as to minimize the total opening costs as well as connection costs. As our main contribution, we propose a primal-dual based $$(3 \tau + 1)$$ -approximation algorithm for the $$\tau $$ -relaxed SCFLP. Furthermore, our algorithm not only extends the applicability of the primal-dual technique but also improves the previous approximation guarantee for the SMSCFLP from $$11.18+ \varepsilon $$ to 10.

MpUFLP: Universal facility location problem in the p-th power of metric space

We propose and study the MpUFLP (universal facility location problem in the p-th power of metric space) in this paper, where the universal facility location problem (UFLP) extends several classical facility location problems like the uncapacitated facility location, hard-capacitated facility location, soft-capacitated facility location, incremental-cost facility location, concave-cost facility location, etc. In UFLP, a set of facilities, a set of clients, as well as the distances between them are given. Each facility has its specific cost function w.r.t. the amount of clients assigned to that facility. The goal is to assign the clients to facilities such that the sum of facility cost and service cost is minimized. In traditional facility location problems, the unit service cost is proportional to the distance between the client and its assigned facility and thus metric. However, in our work, this assumption is removed and a generalized version of universal facility location problem is proposed, which is the so-called MnUFLP. When p=2, it is also known as l22 measure considered by Jain and Vazirani [J. ACM'01] and Fernandes et al. [Math. Program.'15]. Particularly in this case, we extend their work to include the aforementioned variants of facility location and a local search based (11.18+ε)-approximation algorithm is proposed. Furthermore, the reanalysis of the proposed algorithm gives a p-related performance guarantee for general p.

Data-Locality-Aware User Grouping in Cloud Radio Access Networks

Cellular base band units of the future are expected to reside in a cloud data center which provides computation resources, content storage and caching, and a natural place to perform multi-user precoding, thus addressing both cost and performance concerns of cellular systems. Multi-user precoding relies on efficient user grouping schemes to maximize multiplexing gains. However, traditional user grouping schemes are unaware of data center constraints, and may induce a large number of data transfers across racks when fetching requested data to a certain rack for precoding. When congestion occurs in the data center network, the delay of data transfers across racks may exceed the channel coherence time. This would kill multi-user MIMO transmissions as channel state information becomes outdated. In this paper, we design a novel data-locality-aware user grouping schemes which preferentially group users whose requested data are located under the same rack. We also design user grouping algorithms which adapt to the congestion level in the cloud data center. Specifically, a regularized spectral efficiency maximization problem is proposed where the number of data transfers across racks is introduced as a regularization term. By adjusting the weight of the regularization term according to the congestion level, we gradually suppress data transfers across racks in forming user groups when congestion occurs. We reduce the above problem to a soft-capacitated facility location problem, and we devise a 2-approximation user grouping algorithm. At last, we conduct simulations which show that our proposed algorithm performs close to the optimal in practical scenarios, and study the tradeoff between higher spectral efficiency and lower data transfer cost.

Approximating soft-capacitated facility location problem with uncertainty

In this paper we devise the stochastic and robust approaches to study the soft-capacitated facility location problem with uncertainty. We first present a new stochastic soft-capacitated model called The 2-Stage Soft Capacitated Facility Location Problem and solve it via an approximation algorithm by reducing it to linear-cost version of 2-stage facility location problem and dynamic facility location problem. We then present a novel robust model of soft-capacitated facility location, The Robust Soft Capacitated Facility Location Problem. To solve it, we improve the approximation algorithm proposed by Byrka et al. (LP-rounding algorithms for facility-location problems. CoRR, 2010a) for RFTFL and then treat it similarly as in the stochastic case. The improvement results in an approximation factor of $$\alpha + 4$$ for the robust fault-tolerant facility location problem, which is best so far.

Soft-capacitated facility location game

We study the soft-capacitated facility location game which is an extension of the facility location game of Pal and Tardos. We propose a 6-approximate cross-monotonic cost-sharing method. Numerical tests indicate that the method is effective.

Approximation Algorithms for Soft-Capacitated Facility Location in Capacitated Network Design

Answering an open question published in Operations Research (54, 73–91, 2006) in the area of network design and logistic optimization, we present the first constant-factor approximation algorithms for the problem combining facility location and cable installation in which capacity constraints are imposed on both facilities and cables. We study the problem of designing a minimum cost network to serve client demands by opening facilities for service provision and installing cables for service shipment. Both facilities and cables have capacity constraints and incur buy-at-bulk costs. This Max SNP-hard problem arises in diverse applications and is shown in this paper to admit a combinatorial 19.84-approximation algorithm of cubic running time. This is achieved by an integration of primal-dual schema, Lagrangian relaxation, demand clustering and bi-factor approximation. Our techniques extend to several variants of this problem, which include those with unsplitable demands or requiring network connectivity, and provide constant-factor approximate algorithms in strongly polynomial time.

Improved approximation of the general soft-capacitated facility location problem

The soft-capacitated facility location problem, where each facility is composed of a variable number of fixed-capacity production units, has been recently studied in several papers, especially in the metric case. In this paper, we only consider the general problem where connection costs do not systematically satisfy the triangle inequality property. We show that an adaptation of the set covering greedy heuristic, where the subproblem is approximately solved by a fully polynomial-time approximation scheme based on cost scaling and dynamic programming, achieves a logaritmic approximation ratio of (1 + ε)H(n) for the problem, where n is the number of customers to be served and H is the harmonic series. This improves the previous bound of 2H(n) for this problem.

Approximation algorithms for facility location problems with a special class of subadditive cost functions

In this article we focus on approximation algorithms for facility location problems with subadditive costs. As examples of such problems, we present three facility location problems with stochastic demand and exponential servers, respectively inventory. We present a ( 1 + ε , 1 ) -reduction of the facility location problem with subadditive costs to the soft capacitated facility location problem, which implies the existence of a 2 ( 1 + ε ) -approximation algorithm. For a special subclass of subadditive functions, we obtain a 2-approximation algorithm by reduction to the linear cost facility location problem.

Approximation Algorithms for Metric Facility Location Problems

In this paper we present a 1.52-approximation algorithm for the metric uncapacitated facility location problem, and a 2-approximation algorithm for the metric capacitated facility location problem with soft capacities. Both these algorithms improve the best previously known approximation factor for the corresponding problem, and our soft-capacitated facility location algorithm achieves the integrality gap of the standard linear programming relaxation of the problem. Furthermore, we will show, using a result of Thorup, that our algorithms can be implemented in quasi-linear time.