10,082 research outputs found
Strongly Polynomial Primal-Dual Algorithms for Concave Cost Combinatorial Optimization Problems
We introduce an algorithm design technique for a class of combinatorial
optimization problems with concave costs. This technique yields a strongly
polynomial primal-dual algorithm for a concave cost problem whenever such an
algorithm exists for the fixed-charge counterpart of the problem. For many
practical concave cost problems, the fixed-charge counterpart is a well-studied
combinatorial optimization problem. Our technique preserves constant factor
approximation ratios, as well as ratios that depend only on certain problem
parameters, and exact algorithms yield exact algorithms.
Using our technique, we obtain a new 1.61-approximation algorithm for the
concave cost facility location problem. For inventory problems, we obtain a new
exact algorithm for the economic lot-sizing problem with general concave
ordering costs, and a 4-approximation algorithm for the joint replenishment
problem with general concave individual ordering costs
Separable Concave Optimization Approximately Equals Piecewise-Linear Optimization
We study the problem of minimizing a nonnegative separable concave function
over a compact feasible set. We approximate this problem to within a factor of
1+epsilon by a piecewise-linear minimization problem over the same feasible
set. Our main result is that when the feasible set is a polyhedron, the number
of resulting pieces is polynomial in the input size of the polyhedron and
linear in 1/epsilon. For many practical concave cost problems, the resulting
piecewise-linear cost problem can be formulated as a well-studied discrete
optimization problem. As a result, a variety of polynomial-time exact
algorithms, approximation algorithms, and polynomial-time heuristics for
discrete optimization problems immediately yield fully polynomial-time
approximation schemes, approximation algorithms, and polynomial-time heuristics
for the corresponding concave cost problems.
We illustrate our approach on two problems. For the concave cost
multicommodity flow problem, we devise a new heuristic and study its
performance using computational experiments. We are able to approximately solve
significantly larger test instances than previously possible, and obtain
solutions on average within 4.27% of optimality. For the concave cost facility
location problem, we obtain a new 1.4991+epsilon approximation algorithm.Comment: Full pape
Clustering of auto supplier plants in the U.S.: GMM spatial logit for large samples
A linearized version of Pinkse and Slade’s (1998) spatial probit estimator is used to account for the tendency of auto supplier plants to cluster together. By reducing estimation to two steps – standard probit or logit followed by two-stage least squares – linearization produces a model that can be estimated using large datasets. Our results imply significant clustering among older plants. Supplier plants are more likely to be in counties that are near assembly plants, that include interstate highways, and that are near other counties with supplier plants. New plants show no additional tendency toward clustering beyond that shown by older plants.Automobile supplies industry
Integrals, Partitions, and Cellular Automata
We prove that where
is the decreasing function that satisfies , for . When
is an integer and we deduce several combinatorial results. These
include an asymptotic formula for the number of integer partitions not having
consecutive parts, and a formula for the metastability thresholds of a
class of threshold growth cellular automaton models related to bootstrap
percolation.Comment: Revised version. 28 pages, 2 figure
Entry & Exit: The Lifecyle of a Hedge Fund
Using data from the TASS/Tremont hedge fund database, this article performs an empirical analysis of the evolution of the hedge fund industry within an industrial organization framework.Hedge Funds, Entry, Exit, Evolution, Hedge Fund Performance, Hedge Fund Styles, Incumbents, Entrants, Lifecyle, Competition, Market for Ideas,
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