Randomized metarounding

Carr, Robert D.; Vempala, Santosh

doi:10.1002/rsa.10033

Cited by 105 publications

(107 citation statements)

References 8 publications

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“…In a sequence of recent work that initiated from theoretical computer science [8,20,25,32], a polynomial-time convex decomposition technique is designed for converting fractional solution for an NP-hard problem, modelled as a linear integer program, into a weighted combination of integer solutions. Such a decomposition technique enables a randomized auction framework that automatically translates a centralized cooperative approximation algorithm into an auction mechanism, achieving the same social welfare approximation ratio as the plug-in approximation algorithm does, while guaranteeing truthful bidding.…”

Section: Related Workmentioning

confidence: 99%

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Randomized auction design for electricity markets between grids and microgrids

ZhangLinquan

LiZongpeng

2014

SIGMETRICS Perform. Eval. Rev.

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This work studies electricity markets between power grids and microgrids, an emerging paradigm of electric power generation and supply. It is among the first that addresses the economic challenges arising from such grid integration, and represents the first power auction mechanism design that explicitly handles the Unit Commitment Problem (UCP), a key challenge in power grid optimization previously investigated only for centralized cooperative algorithms. The proposed solution leverages a recent result in theoretical computer science that can decompose an optimal fractional (infeasible) solution to NP-hard problems into a convex combination of integral (feasible) solutions. The end result includes randomized power auctions that are (approximately) truthful and computationally efficient, and achieve small approximation ratios for grid-wide social welfare under UCP constraints and temporal demand correlations. Both power markets with grid-to-microgrid and microgrid-to-grid energy sales are studied, with an auction designed for each, under the same randomized power auction framework. Trace driven simulations are conducted to verify the efficacy of the two proposed inter-grid power auctions.

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Section: Related Workmentioning

confidence: 99%

“…Applying the recent convex decomposition technique [8,20,25], we decompose the optimal fractional solution into a convex combination of integral solutions each with a fractional weight that sums up to 1. This step requires a separation oracle, an effective polynomial-time approximation algorithm to WDP1 satisfying:…”

Section: The Randomized Auction Frameworkmentioning

confidence: 99%

Randomized auction design for electricity markets between grids and microgrids

ZhangLinquan

LiZongpeng

2014

SIGMETRICS Perform. Eval. Rev.

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“…(See, e.g. [6], for a polynomial-time procedure.) Fixing the parameter α to a suitable value to be specified later, the algorithm does the following.…”

Section: Final Remarksmentioning

confidence: 99%

When LP Is the Cure for Your Matching Woes: Improved Bounds for Stochastic Matchings

Bansal

Gupta

et al. 2011

Algorithmica

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Consider a random graph model where each possible edge e is present independently with some probability p e . Given these probabilities, we want to build a large/heavy matching in the randomly generated graph. However, the only way we can find out whether an edge is present or not is to query it, and if the edge is indeed present in the graph, we are forced to add it to our matching. Further, each vertex i is allowed to be queried at most t i times. How should we adaptively query the edges to maximize the expected weight of the matching? We consider several matching problems in this general framework (some of which arise in kidney exchanges and online dating, and others arise in modeling online advertisements); we give LP-rounding based constant-factor approximation algorithms for these problems. Our main results are the following:• We give a 4 approximation for weighted stochastic matching on general graphs, and a 3 approximation on bipartite graphs. This answers an open question from [Chen et al. ICALP 09].• Combining our LP-rounding algorithm with the natural greedy algorithm, we give an improved 3.46 approximation for unweighted stochastic matching on general graphs.• We introduce a generalization of the stochastic online matching problem [Feldman et al. FOCS 09] that also models preference-uncertainty and timeouts of buyers, and give a constant factor approximation algorithm.

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“…Carr and Vempala [5] showed how to construct a convex combination of points in Q I dominating αx * using a polynomial number of calls to an α-integrality-gap-verifier for Q I . Lavi and Swamy [19] modified the construction to get an exact convex decomposition αx * = i∈N λ i x i for the case of packing linear programs.…”

Section: A Fast Algorithm For Convex Decompositionsmentioning

confidence: 99%

Towards More Practical Linear Programming-Based Techniques for Algorithmic Mechanism Design

Elbassioni¹,

Mehlhorn

Ramezani

2015

Algorithmic Game Theory

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R. Lavi and C. Swamy (FOCS 2005, J. ACM 58(6), 25, 2011) introduced a general method for obtaining truthful-in-expectation mechanisms from linear programming based approximation algorithms. Due to the use of the Ellipsoid method, a direct implementation of the method is unlikely to be efficient in practice. We propose to use the much simpler and usually faster multiplicative weights update method instead. The simplification comes at the cost of slightly weaker approximation and truthfulness guarantees. Keywords Algorithmic game theory · Mechanism design · Approximation algorithmsA preliminary version of these results was presented at SAGT 2015 [8].

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Randomized metarounding

Cited by 105 publications

References 8 publications

Randomized auction design for electricity markets between grids and microgrids

Randomized auction design for electricity markets between grids and microgrids

When LP Is the Cure for Your Matching Woes: Improved Bounds for Stochastic Matchings

Towards More Practical Linear Programming-Based Techniques for Algorithmic Mechanism Design

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