432 research outputs found
Improved approximation algorithm for k-level UFL with penalties, a simplistic view on randomizing the scaling parameter
The state of the art in approximation algorithms for facility location
problems are complicated combinations of various techniques. In particular, the
currently best 1.488-approximation algorithm for the uncapacitated facility
location (UFL) problem by Shi Li is presented as a result of a non-trivial
randomization of a certain scaling parameter in the LP-rounding algorithm by
Chudak and Shmoys combined with a primal-dual algorithm of Jain et al. In this
paper we first give a simple interpretation of this randomization process in
terms of solving an aux- iliary (factor revealing) LP. Then, armed with this
simple view point, Abstract. we exercise the randomization on a more
complicated algorithm for the k-level version of the problem with penalties in
which the planner has the option to pay a penalty instead of connecting chosen
clients, which results in an improved approximation algorithm
A new approximation algorithm for the multilevel facility location problem
In this paper we propose a new integer programming formulation for the multi-level facility location problem and a novel 3-approximation algorithm based on LP rounding. The linear program we are using has a polynomial number of variables and constraints, being thus more efficient than the one commonly used in the approximation algorithms for this type of problems
Unconstrained and Constrained Fault-Tolerant Resource Allocation
First, we study the Unconstrained Fault-Tolerant Resource Allocation (UFTRA)
problem (a.k.a. FTFA problem in \cite{shihongftfa}). In the problem, we are
given a set of sites equipped with an unconstrained number of facilities as
resources, and a set of clients with set as corresponding
connection requirements, where every facility belonging to the same site has an
identical opening (operating) cost and every client-facility pair has a
connection cost. The objective is to allocate facilities from sites to satisfy
at a minimum total cost. Next, we introduce the Constrained
Fault-Tolerant Resource Allocation (CFTRA) problem. It differs from UFTRA in
that the number of resources available at each site is limited by .
Both problems are practical extensions of the classical Fault-Tolerant Facility
Location (FTFL) problem \cite{Jain00FTFL}. For instance, their solutions
provide optimal resource allocation (w.r.t. enterprises) and leasing (w.r.t.
clients) strategies for the contemporary cloud platforms.
In this paper, we consider the metric version of the problems. For UFTRA with
uniform , we present a star-greedy algorithm. The algorithm
achieves the approximation ratio of 1.5186 after combining with the cost
scaling and greedy augmentation techniques similar to
\cite{Charikar051.7281.853,Mahdian021.52}, which significantly improves the
result of \cite{shihongftfa} using a phase-greedy algorithm. We also study the
capacitated extension of UFTRA and give a factor of 2.89. For CFTRA with
uniform , we slightly modify the algorithm to achieve
1.5186-approximation. For a more general version of CFTRA, we show that it is
reducible to FTFL using linear programming
An approximation algorithm for a facility location problem with stochastic demands
In this article we propose, for any , a -approximation algorithm for a facility location problem with stochastic demands. This problem can be described as follows. There are a number of locations, where facilities may be opened and a number of demand points, where requests for items arise at random. The requests are sent to open facilities. At the open facilities, inventory is kept such that arriving requests find a zero inventory with (at most) some pre-specified probability. After constant times, the inventory is replenished to a fixed order up to level. The time interval between consecutive replenishments is called a reorder period. The problem is where to locate the facilities and how to assign the demand points to facilities at minimal cost per reorder period such that the above mentioned quality of service is insured. The incurred costs are the expected transportation costs from the demand points to the facilities, the operating costs (opening costs) of the facilities and the investment in inventory (inventory costs). \u
Lotsize optimization leading to a -median problem with cardinalities
We consider the problem of approximating the branch and size dependent demand
of a fashion discounter with many branches by a distributing process being
based on the branch delivery restricted to integral multiples of lots from a
small set of available lot-types. We propose a formalized model which arises
from a practical cooperation with an industry partner. Besides an integer
linear programming formulation and a primal heuristic for this problem we also
consider a more abstract version which we relate to several other classical
optimization problems like the p-median problem, the facility location problem
or the matching problem.Comment: 14 page
- …