Lightweight Coloring and Desynchronization for Networks

Motskin, Arik; Roughgarden, Tim; Škraba, Primož; Guibas, Leonidas J.

doi:10.1109/infcom.2009.5062165

Cited by 37 publications

(62 citation statements)

References 16 publications

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“…Extension to the setting with a general interfere graph (see e.g., [6], [12]) appears to be much more difficult. Unlike the single hop setting, where perfect desynchrony is capacity achieving, approaches like graph coloring only yield feasible transmission schemes (or matchings) and they are not guaranteed to be capacity achieving as the maximum weighted matching in [17] and the dynamic frame sizing algorithm in [8].…”

Section: Discussionmentioning

confidence: 99%

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Anchored desynchronization

Lien

Chang

et al. 2012

2012 Proceedings IEEE INFOCOM

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Abstract-Distributed algorithms based on pulse-coupled oscillators have been recently proposed in [4], [14] for achieving desynchronization of a system of identical nodes. Though these algorithms are shown to work properly by various computer simulations, they are still lack of rigorous theoretical proofs for both the convergence of the algorithms and the rates of convergence for these algorithms. On the other hand, all the nodes are not likely to be identical in many practical applications. In particular, there might be a node that needs to interact with the "outside" world and thus may not have the freedom to adjust its local clock. Motivated by all these, in this paper we consider the desynchronization problem in a system where there exists an anchored node that never adjusts the phase of its oscillator. For such a system, we propose a generic anchored desynchronization algorithm that achieves -desynchrony (defined in [4]) in O(n 2 ln( n )) rounds of firings. We also prove that our algorithm converges even for the generalized processor sharing (GPS) scheme, where every node is assigned a weight and the amount of resource received by a node is proportional to its weight. In comparison with the original algorithm in [4], we show that the rate of convergence of the original algorithm in [4] is not always better than ours and it is only better in the asymptotic regime.

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Section: Discussionmentioning

confidence: 99%

“…Analogous to the derivation for the recursive equation for the state vector in (12), the governing dynamics of the system with generalized processor sharing can be represented as…”

Section: Generalized Processor Sharingmentioning

confidence: 99%

Anchored desynchronization

Lien

Chang

et al. 2012

2012 Proceedings IEEE INFOCOM

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“…They studied biologically inspired strategies for solving a desynchronization problem. Follow-up work generalized the results to multihop networks [11,17]. Cornejo and Kuhn [10] introduced the discrete (i.e., round-based) beeping model studied in this paper.…”

Section: Comparison To Existing Beep Resultsmentioning

confidence: 78%

“…Cornejo and Kuhn [10] introduced the discrete (i.e., round-based) beeping model studied in this paper. They motivated this model by noting the continuous model in [11,12,17] was unrealistic and yielded trivial solutions to desynchronization, they then demonstrated how to solve desynchronization without these assumptions. Around this same time, Afek et al [3] described a maximal independent set (MIS) algorithm in a strong version of the discrete beeping model.…”

Section: Comparison To Existing Beep Resultsmentioning

confidence: 99%

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The Computational Power of Beeps

Gilbert

Newport

2015

Lecture Notes in Computer Science

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In this paper, we study the quantity of computational resources (state machine states and/or probabilistic transition precision) needed to solve specific problems in a single hop network where nodes communicate using only beeps. We begin by focusing on randomized leader election. We prove a lower bound on the states required to solve this problem with a given error bound, probability precision, and (when relevant) network size lower bound. We then show the bound tight with a matching upper bound. Noting that our optimal upper bound is slow, we describe two faster algorithms that trade some state optimality to gain efficiency. We then turn our attention to more general classes of problems by proving that once you have enough states to solve leader election with a given error bound, you have (within constant factors) enough states to simulate correctly, with this same error bound, a logspace TM with a constant number of unary input tapes: allowing you to solve a large and expressive set of problems. These results identify a key simplicity threshold beyond which useful distributed computation is possible in the beeping model.

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Brief Announcement: Fully Lattice Linear Algorithms

Gupta

Kulkarni²

2022

Lecture Notes in Computer Science

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Lattice-linear systems allow nodes to execute asynchronously. We introduce eventually lattice-linear algorithms, where lattices are induced only among the states in a subset of the state space. The algorithm guarantees that the system transitions to a state in one of the lattices. Then, the algorithm behaves lattice linearly while traversing to an optimal state through that lattice.We present a lattice-linear self-stabilizing algorithm for service demand based minimal dominating set (SDMDS) problem. Using this as an example, we elaborate the working of, and define, eventually lattice-linear algorithms. Then, we present eventually lattice-linear self-stabilizing algorithms for minimal vertex cover (MVC), maximal independent set (MIS), graph colouring (GC) and 2-dominating set problems (2DS).Algorithms for SDMDS, MVC and MIS converge in 1 round plus n moves (within 2n moves), GC in n + 4m moves, and 2DS in 1 round plus 2n moves (within 3n moves). These results are an improvement over the existing literature. We also present experimental results to show performance gain demonstrating the benefit of lattice-linearity.

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Lightweight Coloring and Desynchronization for Networks

Cited by 37 publications

References 16 publications

Anchored desynchronization

Anchored desynchronization

The Computational Power of Beeps

Brief Announcement: Fully Lattice Linear Algorithms

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