188,217 research outputs found
A Nearly Optimal Deterministic Online Algorithm for Non-Metric Facility Location
In the online non-metric variant of the facility location problem, there is a
given graph consisting of a set of facilities (each with a certain opening
cost), a set of potential clients, and weighted connections between them.
The online part of the input is a sequence of clients from , and in response
to any requested client, an online algorithm may open an additional subset of
facilities and must connect the given client to an open facility.
We give an online, polynomial-time deterministic algorithm for this problem,
with a competitive ratio of . The
result is optimal up to loglog factors. Our algorithm improves over the
-competitive
construction that first reduces the facility location instance to a set cover
one and then later solves such instance using the deterministic algorithm by
Alon et al. [TALG 2006]. This is an asymptotic improvement in a typical
scenario where .
We achieve this by a more direct approach: we design an algorithm for a
fractional relaxation of the non-metric facility location problem with
clustered facilities. To handle the constraints of such non-covering LP, we
combine the dual fitting and multiplicative weight updates approach. By
maintaining certain additional monotonicity properties of the created
fractional solution, we can handle the dependencies between facilities and
connections in a rounding routine.
Our result, combined with the algorithm by Naor et al. [FOCS 2011] yields the
first deterministic algorithm for the online node-weighted Steiner tree
problem. The resulting competitive ratio is on
graphs of nodes and terminals.Comment: STACS 202
Scalable Facility Location for Massive Graphs on Pregel-like Systems
We propose a new scalable algorithm for facility location. Facility location
is a classic problem, where the goal is to select a subset of facilities to
open, from a set of candidate facilities F , in order to serve a set of clients
C. The objective is to minimize the total cost of opening facilities plus the
cost of serving each client from the facility it is assigned to. In this work,
we are interested in the graph setting, where the cost of serving a client from
a facility is represented by the shortest-path distance on the graph. This
setting allows to model natural problems arising in the Web and in social media
applications. It also allows to leverage the inherent sparsity of such graphs,
as the input is much smaller than the full pairwise distances between all
vertices.
To obtain truly scalable performance, we design a parallel algorithm that
operates on clusters of shared-nothing machines. In particular, we target
modern Pregel-like architectures, and we implement our algorithm on Apache
Giraph. Our solution makes use of a recent result to build sketches for massive
graphs, and of a fast parallel algorithm to find maximal independent sets, as
building blocks. In so doing, we show how these problems can be solved on a
Pregel-like architecture, and we investigate the properties of these
algorithms. Extensive experimental results show that our algorithm scales
gracefully to graphs with billions of edges, while obtaining values of the
objective function that are competitive with a state-of-the-art sequential
algorithm
On the competitive facility location problem with a Bayesian spatial interaction model
The competitive facility location problem arises when businesses plan to enter a new market or expand their presence. We introduce a Bayesian spatial interaction model which provides probabilistic estimates on location-specific revenues and then formulate a mathematical framework to simultaneously identify the location and design of new facilities that maximise revenue. To solve the allocation optimisation problem, we develop a hierarchical search algorithm and associated sampling techniques that explore geographic regions of varying spatial resolution. We demonstrate the approach by producing optimal facility locations and corresponding designs for two large-scale applications in the supermarket and pub sectors of Greater London
On modeling the single period spare parts distribution system design problem by mixed integer linear optimization
Efficiency and effectiveness of spare parts logistics play a significant role in changing customers’ service levels. A company providing high quality after-sales support to their customers gains competitive advantages. To study a single period multi commodity spare parts distribution system design problem, we present a mathematical model in the form of a mixed integer linear programming problem formulation. The mathematical model incorporates facility location decisions and vehicle size selection as well as routing decisions. The problem formulation minimizes the total cost including opening and operating costs of the depots and transportation costs for the vehicles. In order to define and solve a realistic spare parts distribution system design problem, we use aggregation on the commodity flow data to reduce the size of the problem and generate the outbound distribution routes from the regional depots to the service points apriori to simplify the mathematical model. The main focus of this study is the apriori route generation; we aim to observe the impact of different route sets obtained by different heuristic methods. The solution quality and the computation time to solve the problems to optimality are used to compare the performance of the three routing heuristic
Mechanism Design with Strategic Mediators
We consider the problem of designing mechanisms that interact with strategic
agents through strategic intermediaries (or mediators), and investigate the
cost to society due to the mediators' strategic behavior. Selfish agents with
private information are each associated with exactly one strategic mediator,
and can interact with the mechanism exclusively through that mediator. Each
mediator aims to optimize the combined utility of his agents, while the
mechanism aims to optimize the combined utility of all agents. We focus on the
problem of facility location on a metric induced by a publicly known tree. With
non-strategic mediators, there is a dominant strategy mechanism that is
optimal. We show that when both agents and mediators act strategically, there
is no dominant strategy mechanism that achieves any approximation. We, thus,
slightly relax the incentive constraints, and define the notion of a two-sided
incentive compatible mechanism. We show that the -competitive deterministic
mechanism suggested by Procaccia and Tennenholtz (2013) and Dekel et al. (2010)
for lines extends naturally to trees, and is still -competitive as well as
two-sided incentive compatible. This is essentially the best possible. We then
show that by allowing randomization one can construct a -competitive
randomized mechanism that is two-sided incentive compatible, and this is also
essentially tight. This result also closes a gap left in the work of Procaccia
and Tennenholtz (2013) and Lu et al. (2009) for the simpler problem of
designing strategy-proof mechanisms for weighted agents with no mediators on a
line, while extending to the more general model of trees. We also investigate a
further generalization of the above setting where there are multiple levels of
mediators.Comment: 46 pages, 1 figure, an extended abstract of this work appeared in
ITCS 201
Truthful Facility Assignment with Resource Augmentation: An Exact Analysis of Serial Dictatorship
We study the truthful facility assignment problem, where a set of agents with
private most-preferred points on a metric space are assigned to facilities that
lie on the metric space, under capacity constraints on the facilities. The goal
is to produce such an assignment that minimizes the social cost, i.e., the
total distance between the most-preferred points of the agents and their
corresponding facilities in the assignment, under the constraint of
truthfulness, which ensures that agents do not misreport their most-preferred
points.
We propose a resource augmentation framework, where a truthful mechanism is
evaluated by its worst-case performance on an instance with enhanced facility
capacities against the optimal mechanism on the same instance with the original
capacities. We study a very well-known mechanism, Serial Dictatorship, and
provide an exact analysis of its performance. Although Serial Dictatorship is a
purely combinatorial mechanism, our analysis uses linear programming; a linear
program expresses its greedy nature as well as the structure of the input, and
finds the input instance that enforces the mechanism have its worst-case
performance. Bounding the objective of the linear program using duality
arguments allows us to compute tight bounds on the approximation ratio. Among
other results, we prove that Serial Dictatorship has approximation ratio
when the capacities are multiplied by any integer . Our
results suggest that even a limited augmentation of the resources can have
wondrous effects on the performance of the mechanism and in particular, the
approximation ratio goes to 1 as the augmentation factor becomes large. We
complement our results with bounds on the approximation ratio of Random Serial
Dictatorship, the randomized version of Serial Dictatorship, when there is no
resource augmentation
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