On the communication and streaming complexity of maximum bipartite matching

Goel, Ashish; Kapralov, Michael; Khanna, Sanjeev

doi:10.1137/1.9781611973099.41

Cited by 113 publications

(209 citation statements)

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“…Our lower bounds for matching provide an Ω(n 2 ) lower bound for simultaneous protocols, and a n 1+Ω(1/ log log n) lower bound for one-way communication follows from [15]. We don't know any lower bound better than Ω(n log n) for general protocols or even for 2-round protocols.…”

Section: What Is Knownmentioning

confidence: 92%

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Economic efficiency requires interaction

Dobzinski

Nisan

Oren

2019

Games and Economic Behavior

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We study the necessity of interaction between individuals for obtaining approximately efficient economic allocations. We view this as a formalization of Hayek's classic point of view that focuses on the information transfer advantages that markets have relative to centralized planning. We study two settings: combinatorial auctions with unit demand bidders (bipartite matching) and combinatorial auctions with subadditive bidders. In both settings we prove that non-interactive protocols require exponentially larger communication costs than do interactive ones, even ones that only use a modest amount of interaction.

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Section: What Is Knownmentioning

confidence: 92%

“…This was done in [15] who give a n 1+Ω(1/ log log n) lower bound for improving the 2/3 approximation. To the best of our knowledge no better lower bound is known even for getting an exact maximum matching.…”

Section: Streaming and Semi-streamingmentioning

confidence: 99%

Economic efficiency requires interaction

Dobzinski

Nisan

Oren

2019

Games and Economic Behavior

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“…Related work has also been done in networked distributed computing models, e.g., [LPSP08]. "One-way" communication models are used to analyze streaming or semi-streaming models and some upper bounds (e.g., [Kap12]) as well as weak lower bounds [GKK12] are known for approximate matchings in these models. For "r-way" protocols, a super-linear communication lower bound was recently shown by [GO13] for exact matchings, in an incomparable model 1 .…”

Section: More Context and Related Modelsmentioning

confidence: 99%

Welfare Maximization with Limited Interaction

Alon

Nisan

Raz

et al. 2015

2015 IEEE 56th Annual Symposium on Foundations of Computer Science

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We continue the study of welfare maximization in unit-demand (matching) markets, in a distributed information model where agent's valuations are unknown to the central planner, and therefore communication is required to determine an efficient allocation. Dobzinski, Nisan and Oren (STOC'14) showed that if the market size is n, then r rounds of interaction (with logarithmic bandwidth) suffice to obtain an n 1/(r+1) -approximation to the optimal social welfare. In particular, this implies that such markets converge to a stable state (constant approximation) in time logarithmic in the market size.We obtain the first multi-round lower bound for this setup. We show that even if the allowable perround bandwidth of each agent is n ε(r) , the approximation ratio of any r-round (randomized) protocol is no better than Ω(n 1/5 r+1 ), implying an Ω(log log n) lower bound on the rate of convergence of the market to equilibrium. Our construction and technique may be of interest to round-communication tradeoffs in the more general setting of combinatorial auctions, for which the only known lower bound is for simultaneous (r = 1) protocols [DNO14].

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“…However, a better algorithm is known under the assumption of random edge arrivals by [13], who achieve a 1/2+ approximation for a constant > 0. On the lower bound side, it is known that noÕ(n) space algorithm can achieve a better than 1 − 1/e approximation [7,10].…”

Section: Related Workmentioning

confidence: 99%

Approximating matching size from random streams

Kapralov¹,

Khanna²,

Sudan³

2013

Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms

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We present a streaming algorithm that makes one pass over the edges of an unweighted graph presented in random order, and produces a polylogarithmic approximation to the size of the maximum matching in the graph, while using only polylogarithmic space. Prior to this work the only approximations known were a folkloreÕ( √ n) approximation with polylogarithmic space in an n vertex graph and a constant approximation with Ω(n) space. Our work thus gives the first algorithm where both the space and approximation factors are smaller than any polynomial in n.Our algorithm is obtained by effecting a streaming implementation of a simple "local" algorithm that we design for this problem. The local algorithm produces a O(k · n 1/k ) approximation to the size of a maximum matching by exploring the radius k neighborhoods of vertices, for any parameter k. We show, somewhat surprisingly, that our local algorithm can be implemented in the streaming setting even for k = Ω(log n/ log log n). Our analysis exposes some of the problems that arise in such conversions of local algorithms into streaming ones, and gives techniques to overcome such problems.

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On the communication and streaming complexity of maximum bipartite matching

Cited by 113 publications

References 0 publications

Economic efficiency requires interaction

Economic efficiency requires interaction

Welfare Maximization with Limited Interaction

Approximating matching size from random streams

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