Nonlinear bipartite matching

Berstein, Yael; Onn, Shmuel

doi:10.1016/j.disopt.2007.11.002

Cited by 24 publications

(26 citation statements)

References 13 publications

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“…This is a transplant option for candidates who have a living donor who is medically able, but cannot donate a kidney to their intended candidate because they are incompatible (i.e., poorly matched) [1]. In this application, or application to resource allocation (such as in scheduling in a power grid) [5,20], or pattern recognition [19], data arrives sequentially and randomly, so that matching decisions must be made in real-time, taking into account the uncertainty of future requirements for supply or demand, or the uncertainty of the sequence of classification tasks to be undertaken. The choice of matching decisions can be cast as an optimal control problem for a dynamic matching model.…”

Section: Introductionmentioning

confidence: 99%

Approximate optimality with bounded regret in dynamic matching models

Buýić

Meyn

2015

SIGMETRICS Perform. Eval. Rev.

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We consider a discrete-time bipartite matching model with random arrivals of units of supply and demand that can wait in queues located at the nodes in the network. A control policy determines which are matched at each time. The focus is on the infinite-horizon average-cost optimal control problem. A relaxation of the stochastic control problem is proposed, which is found to be a special case of an inventory model, as treated in the classical theory of Clark and Scarf. The optimal policy for the relaxation admits a closed-form expression. Based on the policy for this relaxation, a new matching policy is proposed. For a parameterized family of models in which the network load approaches capacity, this policy is shown to be approximately optimal, with bounded regret, even though the average cost grows without bound.

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Section: Introductionmentioning

confidence: 99%

Approximate optimality with bounded regret in dynamic matching models

Buýić

Meyn

2015

SIGMETRICS Perform. Eval. Rev.

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“…where τ u is a regularization parameter. Note that all the constraints (40), (41), (42), (43), (49), and (50) are linear in π i,j . The NOVA Algorithm for optimizing π is described in Algorithm 1.…”

Section: A Access Optimizationmentioning

confidence: 99%

“…Having these access probabilities, the new placement of the files will be S i = {ζ i (j)∀j ∈ S i }. We note that the constraints (42), (43), and (44) for the access from the modified placement of the servers will already be satisfied. The Placement Optimization subproblem is to find the optimal permutations ζ i (j).…”

Section: Placement Optimizationmentioning

confidence: 99%

Video Streaming in Distributed Erasure-Coded Storage Systems: Stall Duration Analysis

Al-Abbasi

Aggarwal

2018

IEEE/ACM Trans. Networking

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The demand for global video has been burgeoning across industries. With the expansion and improvement of videostreaming services, cloud-based video is evolving into a necessary feature of any successful business for reaching internal and external audiences. This paper considers video streaming over distributed systems where the video segments are encoded using an erasure code for better reliability thus being the first work to our best knowledge that considers video streaming over erasure-coded distributed cloud systems. The download time of each coded chunk of each video segment is characterized and ordered statistics over the choice of the erasure-coded chunks is used to obtain the playback time of different video segments. Using the playback times, bounds on the moment generating function on the stall duration is used to bound the mean stall duration. Moment generating function based bounds on the ordered statistics are also used to bound the stall duration tail probability which determines the probability that the stall time is greater than a pre-defined number. These two metrics, mean stall duration and the stall duration tail probability, are important quality of experience (QoE) measures for the end users. Based on these metrics, we formulate an optimization problem to jointly minimize the convex combination of both the QoE metrics averaged over all requests over the placement and access of the video content. The non-convex problem is solved using an efficient iterative algorithm. Numerical results show significant improvement in QoE metrics for cloud-based video as compared to the considered baselines.

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“…However, often such a set is not available (see e.g. [8] for the important case of bipartite matching). We now show how to reduce convex discrete optimization to many linear discrete optimization counterparts when a set covering all edge-directions is not offhand available.…”

Section: Pseudo Polynomial Reduction When Edge-directions Are Not Avamentioning

confidence: 99%

Convex Discrete Optimization

Onn

2008

Encyclopedia of Optimization

Self Cite

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We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial optimization problems and convex integer programming problems in variable dimension. We discuss some of the many applications of this theory including to quadratic programming, matroids, bin packing and cutting-stock problems, vector partitioning and clustering, multiway transportation problems, and privacy and confidential statistical data disclosure. Highlights of our work include a strongly polynomial time algorithm for convex and linear combinatorial optimization over any family presented by a membership oracle when the underlying polytope has few edge-directions; a new theory of so-termed n-fold integer programming, yielding polynomial time solution of important and natural classes of convex and linear integer programming problems in variable dimension; and a complete complexity classification of high dimensional transportation problems, with practical applications to fundamental problems in privacy and confidential statistical data disclosure.

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Nonlinear bipartite matching

Cited by 24 publications

References 13 publications

Approximate optimality with bounded regret in dynamic matching models

Approximate optimality with bounded regret in dynamic matching models

Video Streaming in Distributed Erasure-Coded Storage Systems: Stall Duration Analysis

Convex Discrete Optimization

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