We present improved approximation algorithms in stochastic optimization. We prove that the multi-stage stochastic versions of covering integer programs (such as set cover and vertex cover) admit essentially the same a...
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We consider the problem of dividing indivisible goods fairly among n agents who have additive and submodular valuations for the goods. Our fairness guarantees are in terms of the maximin share, that is defined to be t...
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We introduce and study a class of optimization problems we coin replenishment problems with fixed turnover times: a very natural model that has received little attention in the literature. Nodes with capacity for stor...
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To cope with the high-level penetration of electric vehicles (EVs), an intelligent scheduling mechanism for EV charging is required for maintaining the electricity grid within the operating limits, mitigating the dema...
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ISBN:
(纸本)9781450357678
To cope with the high-level penetration of electric vehicles (EVs), an intelligent scheduling mechanism for EV charging is required for maintaining the electricity grid within the operating limits, mitigating the demand peaks, and maximizing the benefit of intermittent renewable energy. This paper studies the scheduling optimization problem of EV charging in the presence of discrete charging options with minimum power requirements. We present an approximation algorithm to solve the scheduling optimization problem of EV charging, which has a provably small parameterized gap with the optimal solution. We also present a pruning scheme and specific conditions that can improve the running time in practice. Based on this algorithm, we further provide a fast heuristic with a significant reduction in the running time. Finally, extensive simulations show our algorithms can produce close-to-optimal solutions in practice.
We consider some poorly studied clustering problems. The paper purpose is to present a short survey on some new results on the computational complexity of these problems, and on efficient algorithms with performance g...
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We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the...
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ISBN:
(纸本)9781577357605
We consider optimal route planning when the objective function is a general nonlinear and non-monotonic function. Such an objective models user behavior more accurately, for example, when a user is risk-averse, or the utility function needs to capture a penalty for early arrival. It is known that as nonlinearity arises, the problem becomes NP-hard and little is known about computing optimal solutions when in addition there is no monotonicity guarantee. We show that an approximately optimal non-simple path can be efficiently computed under some natural constraints. In particular, we provide a fully polynomial approximation scheme under hop constraints. Our approximation algorithm can extend to run in pseudo-polynomial time under a more general linear constraint that sometimes is useful. As a by-product, we show that our algorithm can be applied to the problem of finding a path that is most likely to be on time for a given deadline.
In this paper we give randomized approximation algorithms for stochastic cumulative VRPs for split and unsplit deliveries. The approximation ratios are 2(1 + alpha) and 7 respectively, where a is the approximation rat...
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ISBN:
(纸本)9783319292212;9783319292205
In this paper we give randomized approximation algorithms for stochastic cumulative VRPs for split and unsplit deliveries. The approximation ratios are 2(1 + alpha) and 7 respectively, where a is the approximation ratio for the metric TSP. The approximation factor is further reduced for trees and paths. These results extend the results in [Technical note - approximation algorithms for VRP with stochastic demands. Operations Research, 2012] and [Routing vehicles to minimize fuel consumption. Operations Research Letters, 2013].
The most basic form of the max-sum dispersion problem ( MSD ) is as follows: given n points in R q and an integer k, select a set of k points such that the sum of the pairwise distances within the set is maximal. This...
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The most basic form of the max-sum dispersion problem ( MSD ) is as follows: given n points in R q and an integer k, select a set of k points such that the sum of the pairwise distances within the set is maximal. This is a prominent diversity problem, with wide applications in web search and information retrieval, where one needs to find a small and diverse representa- tive subset of a large dataset. The problem has recently received a great deal of attention in the computational geometry and operations research communities; and since it is NP-hard, research has focused on efficient heuristics and approximation algorithms. Several classes of distance functions have been considered in the literature. Many of the most common distances used in applications are induced by a norm in a real vector space. The focus of this thesis is on MSD over these geometric instances. We provide for it simple and fast polynomial-time approximation schemes (PTASs), as well as improved constant-factor approximation algorithms. We pay special attention to the class of negative-type distances, a class that includes Euclidean and Manhattan distances, among many others. In order to exploit the properties of this class, we apply several techniques and results from the theory of isometric embeddings. We explore the following variations of the MSD problem: matroid and matroid-intersection constraints, knapsack constraints, and the mixed-objective problem that maximizes a combi- nation of the sum of pairwise distances with a submodular monotone function. In addition to approximation algorithms, we present a core-set for geometric instances of low dimension, and we discuss the efficient implementation of some of our algorithms for massive datasets, using the streaming and distributed models of computation.
We study the prize-collecting version of the node-weighted Steiner tree problem (NWPCST) restricted to planar graphs. We give a new primal-dual Lagrangian-multiplier-preserving (LMP) 3-approximation algorithm for plan...
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We consider the problem of scheduling with renewable speed-up resources. Given m identical machines, n jobs and c different discrete resources, the task is to schedule each job non-preemptively onto one of the machine...
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ISBN:
(纸本)9783959770187
We consider the problem of scheduling with renewable speed-up resources. Given m identical machines, n jobs and c different discrete resources, the task is to schedule each job non-preemptively onto one of the machines so as to minimize the makespan. In our problem, a job has its original processing time, which could be reduced by utilizing one of the resources. As resources are different, the amount of the time reduced for each job is different depending on the resource it uses. Once a resource is being used by one job, it can not be used simultaneously by any other job until this job is finished, hence the scheduler should take into account the job-To-machine assignment together with the resource-To-job assignment. We observe that, the classical unrelated machine scheduling problem is actually a special case of our problem when m = c, i.e., the number of resources equals the number of machines. Extending the techniques for the unrelated machine scheduling, we give a 2-approximation algorithm when both m and c are part of the input. We then consider two special cases for the problem, with m or c being a constant, and derive PTASes (Polynomial Time approximation Schemes) respectively. We also establish the relationship between the two parameters m and c, through which we are able to transform the PTAS for the case when m is constant to the case when c is a constant. The relationship between the two parameters reveals the structure within the problem, and may be of independent interest.
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