Expected time complexity of the auction algorithm and the push relabel algorithm for maximum bipartite matching on random graphs

Naparstek, Oshri; Leshem, Amir

doi:10.1002/rsa.20578

Cited by 11 publications

(5 citation statements)

References 20 publications

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“…The M factor can be easily improved to N if players have IDs, which can be achieved distributely [24]. If some limited communication is allowed, more sophisticated algorithms to distributedly compute the matching are possible, based on gossip, message passing, or auctions [36], [37]. These algorithms do not need a consensus phase, eliminating the N factor.…”

Section: Discussionmentioning

confidence: 99%

My Fair Bandit: Distributed Learning of Max-Min Fairness with Multi-player Bandits

Bistritz¹,

Baharav²,

Leshem³

et al. 2020

Preprint

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Consider N cooperative but non-communicating players where each plays one out of M arms for T turns. Players have different utilities for each arm, representable as an N × M matrix. These utilities are unknown to the players. In each turn players receive noisy observations of their utility for their selected arm. However, if any other players selected the same arm that turn, they will all receive zero utility due to the conflict. No other communication or coordination between the players is possible. Our goal is to design a distributed algorithm that learns the matching between players and arms that achieves max-min fairness while minimizing the regret. We present an algorithm and prove that it is regret optimal up to a log log T factor. This is the first max-min fairness multi-player bandit algorithm with (near) order optimal regret.

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Section: Discussionmentioning

confidence: 99%

My Fair Bandit: Distributed Learning of Max-Min Fairness with Multi-player Bandits

Bistritz¹,

Baharav²,

Leshem³

et al. 2020

Preprint

Self Cite

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“…The following known result on perfect matching in random bipartite graphs was proven by Erdős and Rényi in [16]: The next theorem proven in [17] shows that for random bipartite graphs with p ≥ …”

Section: A Expected Number Of Iterations Of the Matching Algorithmmentioning

confidence: 94%

A fast matching algorithm for asymptotically optimal distributed channel assignment

Naparstek

Leshem

2013

2013 18th International Conference on Digital Signal Processing (DSP)

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The channel assignment problem is a special case of a very well studied combinatorial optimization problem known as the assignment problem. In this paper we introduce an asymptotically optimal fully distributed algorithm for the maximum cardinality matching problem. We show that with high probability, the running time of the algorithm on random bipartite graphs is less than O N log(N) log(Np) . We then show that the proposed algorithm can be used to produce asymptotically optimal solutions for the max sum assignment problem.

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“…Theorem (Naparstek and Leshem [39]). Let G = (U, V, E) be a random bipartite graph with |U | = |V | = N and p ≥ (1+ ) log(N ) N .…”

Section: B Expected Number Of Iterations Of Fast Matching Algorithmmentioning

confidence: 99%

“…The next theorem proven in [39] shows that for random bipartite graphs with p ≥ (1+ ) log(N ) N the number of iterations until the convergence of the algorithm is less than cN log(N )…”

Section: B Expected Number Of Iterations Of Fast Matching Algorithmmentioning

confidence: 99%

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Distributed Energy Efficient Channel Allocation

Naparstek

Zafaruddin

Leshem

et al. 2019

IEEE Trans. on Green Commun. Netw.

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Design of energy efficient protocols for modern wireless systems has become an important area of research. In this paper, we propose a distributed optimization algorithm for the channel assignment problem for multiple interfering transceiver pairs that cannot communicate with each other. We first modify the auction algorithm for maximal energy efficiency and show that the problem can be solved without explicit message passing using the carrier sense multiple access (CSMA) protocol. We then develop a novel scheme by converting the channel assignment problem into perfect matchings on bipartite graphs. The proposed scheme improves the energy efficiency and does not require any explicit message passing or a shared memory between the users. We derive bounds on the convergence rate and show that the proposed algorithm converges faster than the distributed auction algorithm and achieves near-optimal performance under Rayleigh fading channels. We also present an asymptotic performance analysis of the fast matching algorithm for energy efficient resource allocation and prove the optimality for large enough number of users and number of channels. Finally, we provide numerical assessments that confirm the energy efficiency gains compared to the state of the art.

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Expected time complexity of the auction algorithm and the push relabel algorithm for maximum bipartite matching on random graphs

Cited by 11 publications

References 20 publications

My Fair Bandit: Distributed Learning of Max-Min Fairness with Multi-player Bandits

My Fair Bandit: Distributed Learning of Max-Min Fairness with Multi-player Bandits

A fast matching algorithm for asymptotically optimal distributed channel assignment

Distributed Energy Efficient Channel Allocation

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