Related papers: Exponential lower bounds on the size of approximat…
Linear programming has played a key role in the study of algorithms for combinatorial optimization problems. In the field of approximation algorithms, this is well illustrated by the uncapacitated facility location problem. A variety of…
The metric uncapacitated facility location problem (UFL) enjoys a special stature in approximation algorithms as a testbed for various techniques. Two generalizations of UFL are capacitated facility location (CFL) and lower-bounded facility…
Metric facility location is a well-studied problem for which linear programming methods have been used with great success in deriving approximation algorithms. The capacity-constrained generalizations, such as capacitated facility location…
In this paper, we give first constant factor approximation for capacitated knapsack median problem (CKM) for hard uniform capacities, violating the budget only by an additive factor of $f_{max}$ where $f_{max}$ is the maximum cost of a…
In this paper, we study the uniform capacitated $k$-median problem. Obtaining a constant approximation algorithm for this problem is a notorious open problem; most previous works gave constant approximations by either violating the capacity…
Facility location is a prominent optimization problem that has inspired a large quantity of both theoretical and practical studies in combinatorial optimization. Although the problem has been investigated under various settings reflecting…
In this note, we consider the capacitated facility location problem when the transportation costs of the instance satisfy the Monge property. We show that a straightforward dynamic program finds the optimal solution when the demands are…
We study the Capacitated k-Median problem, for which all the known constant factor approximation algorithms violate either the number of facilities or the capacities. While the standard LP-relaxation can only be used for algorithms…
The $k$-Facility Location problem is a generalization of the classical problems $k$-Median and Facility Location. The goal is to select a subset of at most $k$ facilities that minimizes the total cost of opened facilities and established…
In this paper, we give the first constant approximation algorithm for the lower bounded facility location (LBFL) problem with general lower bounds. Prior to our work, such algorithms were only known for the special case where all facilities…
We study the Capacitated k-Median problem for which existing constant-factor approximation algorithms are all pseudo-approximations that violate either the capacities or the upper bound k on the number of open facilities. Using the natural…
We study Facility Location with Matching, a Facility Location problem where, given additional information about which pair of clients is compatible to be matched, we need to match as many clients as possible and assign each matched client…
An important feature of many real world facility location problems are capacity limits on the facilities. We show here how capacity constraints make it harder to design strategy proof mechanisms for facility location, but…
We consider the facility location problem in the one-dimensional setting where each facility can serve a limited number of agents from the algorithmic and mechanism design perspectives. From the algorithmic perspective, we prove that the…
We study the non-uniform capacitated multi-item lot-sizing (\lotsizing) problem. In this problem, there is a set of demands over a planning horizon of $T$ time periods and all demands must be satisfied on time. We can place an order at the…
We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…
We consider the hardness of approximation of optimization problems from the point of view of definability. For many NP-hard optimization problems it is known that, unless P = NP, no polynomial-time algorithm can give an approximate solution…
We first show that a better analysis of the algorithm for The Two-Sage Stochastic Facility Location Problem from Srinivasan \cite{sri07} and the algorithm for The Robust Fault Tolerant Facility Location Problem from Byrka et al \cite{bgs10}…
We study a competitive facility location problem (CFLP), where two firms sequentially open new facilities within their budgets, in order to maximize their market shares of demand that follows a probabilistic choice model. This process is a…
In this article, we consider the following capacitated covering problem. We are given a set $P$ of $n$ points and a set $\mathcal{B}$ of balls from some metric space, and a positive integer $U$ that represents the capacity of each of the…