102,314 research outputs found
Bicriteria Approximation Algorithms for Priority Matroid Median
Fairness considerations have motivated new clustering problems and algorithms
in recent years. In this paper we consider the Priority Matroid Median problem
which generalizes the Priority -Median problem that has recently been
studied. The input consists of a set of facilities and a set of
clients that lie in a metric space , and a matroid over the
facilities. In addition each client has a specified radius and
each facility has an opening cost . The goal is to
choose a subset of facilities to minimize the
subject to two
constraints: (i) is an independent set in (that is ) and (ii) for each client , its distance to an open facility is
at most (that is, ). For this problem we describe the
first bicriteria approximations for fixed constants : the
radius constraints of the clients are violated by at most a factor of and
the objective cost is at most times the optimum cost. We also improve the
previously known bicriteria approximation for the uniform radius setting ( ).Comment: 22 pages, 2 figure
Bicriteria Approximation Algorithms for Priority Matroid Median
Fairness considerations have motivated new clustering problems and algorithms in recent years. In this paper we consider the Priority Matroid Median problem which generalizes the Priority k-Median problem that has recently been studied. The input consists of a set of facilities ? and a set of clients ? that lie in a metric space (? ? ?,d), and a matroid ? = (?,?) over the facilities. In addition, each client j has a specified radius r_j ? 0 and each facility i ? ? has an opening cost f_i > 0. The goal is to choose a subset S ? ? of facilities to minimize ?_{i ? ?} f_i + ?_{j ? ?} d(j,S) subject to two constraints: (i) S is an independent set in ? (that is S ? ?) and (ii) for each client j, its distance to an open facility is at most r_j (that is, d(j,S) ? r_j). For this problem we describe the first bicriteria (c?,c?) approximations for fixed constants c?,c?: the radius constraints of the clients are violated by at most a factor of c? and the objective cost is at most c? times the optimum cost. We also improve the previously known bicriteria approximation for the uniform radius setting (r_j : = L ? j ? ?)
Optimal processor assignment for pipeline computations
The availability of large scale multitasked parallel architectures introduces the following processor assignment problem for pipelined computations. Given a set of tasks and their precedence constraints, along with their experimentally determined individual responses times for different processor sizes, find an assignment of processor to tasks. Two objectives are of interest: minimal response given a throughput requirement, and maximal throughput given a response time requirement. These assignment problems differ considerably from the classical mapping problem in which several tasks share a processor; instead, it is assumed that a large number of processors are to be assigned to a relatively small number of tasks. Efficient assignment algorithms were developed for different classes of task structures. For a p processor system and a series parallel precedence graph with n constituent tasks, an O(np2) algorithm is provided that finds the optimal assignment for the response time optimization problem; it was found that the assignment optimizing the constrained throughput in O(np2log p) time. Special cases of linear, independent, and tree graphs are also considered
Policy-making tool for optimization of transit priority lanes in urban network
Transit improvement is an effective way to relieve traffic congestion and decrease greenhouse gas emissions. Improvement can be in the form of new facilities or giving on-road priority to transit. Although construction of off-road mass transit is not always viable, giving priority to transit can be a low-cost alternative. A framework is introduced for optimization of bus priority at the network level. The framework identifies links on which a bus lane should be located. Allocation of a lane to transit vehicles would increase the utility of transit, although this can be a disadvantage to auto traffic. The approach balances the impact on all stakeholders. Automobile advocates would like to increase traffic road space, and the total travel time of users and total emissions of the network could be reduced by a stronger priority scheme. A bilevel optimization is applied that encompasses an objective function at the upper level and a mode choice, a traffic assignment, and a transit assignment model at the lower level. The proposed optimization helps transport authorities to quantify the outcomes of various strategies of transit priority. A detailed sensitivity analysis is carried out on the relative weight of each factor in the objective function. The proposed framework can also be applied in the context of high-occupancy-vehicle lanes and heavy-vehicle priority lanes
Natural climate solutions
Our thanks for inputs by L. Almond, A. Baccini, A. Bowman, S. CookPatton, J. Evans, K. Holl, R. Lalasz, A. Nassikas, M. Spalding, M. Wolosin, and expert elicitation respondents. Our thanks for datasets developed by the Hansen lab and the NESCent grasslands working group (C. Lehmann, D. Griffith, T. M. Anderson, D. J. Beerling, W. Bond, E. Denton, E. Edwards, E. Forrestel, D. Fox, W. Hoffmann, R. Hyde, T. Kluyver, L. Mucina, B. Passey, S. Pau, J. Ratnam, N. Salamin, B. Santini, K. Simpson, M. Smith, B. Spriggs, C. Still, C. Strömberg, and C. P. Osborne). This study was made possible by funding from the Doris Duke Charitable Foundation. Woodbury was supported in part by USDA-NIFA Project 2011-67003-30205 Data deposition: A global spatial dataset of reforestation opportunities has been deposited on Zenodo (https://zenodo.org/record/883444). This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1710465114/-/DCSupplemental.Peer reviewedPublisher PD
Pareto Optimal Allocation under Uncertain Preferences
The assignment problem is one of the most well-studied settings in social
choice, matching, and discrete allocation. We consider the problem with the
additional feature that agents' preferences involve uncertainty. The setting
with uncertainty leads to a number of interesting questions including the
following ones. How to compute an assignment with the highest probability of
being Pareto optimal? What is the complexity of computing the probability that
a given assignment is Pareto optimal? Does there exist an assignment that is
Pareto optimal with probability one? We consider these problems under two
natural uncertainty models: (1) the lottery model in which each agent has an
independent probability distribution over linear orders and (2) the joint
probability model that involves a joint probability distribution over
preference profiles. For both of the models, we present a number of algorithmic
and complexity results.Comment: Preliminary Draft; new results & new author
New methodology for optimizing transit priority at the network level
A new methodology for optimizing transit road space priority at the network level is proposed. Transit vehicles carry large numbers of passengers within congested road space efficiently. This aids justification of transit priority. Almost all studies that have investigated transit priority lanes focus at a link or an arterial road level, and no study has investigated road space allocation for priority from a network perspective. The aim of the proposed approach is to find the optimum combination of exclusive lanes in an existing operational transport network. Mode share is assumed variable, and an assignment is performed for both private and transit traffic. The problem is formulated by using bilevel programming, which minimizes the total travel time. The approach is applied to an example network and the results are discussed. The approach can identify the optimal combination of transit priority lanes and achieve the global optimum of the objective function. Areas for further development are discussed
Priority allocation decisions in large scale MTO/MTS multi-product manufacturing systems : Technical report
In this paper, the authors consider a single stage multi-product manufacturing facility producing a large number of end-products for delivery within a service constraint for the customer lead-time. The manufacturing facility is modeled as a multi-product, multi-priority queuing system. In order to reduce inventory costs, an e±cient priority allocation between items consists in producing some items according to a Make-To-Stock (MTS) policy and others according to a Make-To-Order (MTO)policy epending on their features (costs, required lead-time, demand rates). The authors propose a general optimization procedure that gives a near-optimal °ow control (MTO or MTS) to associate with each product and the corresponding near-optimal priority strategy. We illustrate e±ciency of our procedure via several examples and by a numerical analysis. In addition, we show numerically that a small number of priority classes is su±cient to obtain near-optimal performances.Make-to-Stock (MTS); Make-to-Order (MTO); Priority allocation; Scheduling rule; Heterogeneous multi-product queuing system
Combining Outcome-Based and Preference-Based Matching: A Constrained Priority Mechanism
We introduce a constrained priority mechanism that combines outcome-based
matching from machine-learning with preference-based allocation schemes common
in market design. Using real-world data, we illustrate how our mechanism could
be applied to the assignment of refugee families to host country locations, and
kindergarteners to schools. Our mechanism allows a planner to first specify a
threshold for the minimum acceptable average outcome score that should
be achieved by the assignment. In the refugee matching context, this score
corresponds to the predicted probability of employment, while in the student
assignment context it corresponds to standardized test scores. The mechanism is
a priority mechanism that considers both outcomes and preferences by assigning
agents (refugee families, students) based on their preferences, but subject to
meeting the planner's specified threshold. The mechanism is both strategy-proof
and constrained efficient in that it always generates a matching that is not
Pareto dominated by any other matching that respects the planner's threshold.Comment: This manuscript has been accepted for publication by Political
Analysis and will appear in a revised form subject to peer review and/or
input from the journal's editor. End-users of this manuscript may only make
use of it for private research and study and may not distribute it furthe
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