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Design patterns in beeping algorithms: Examples, emulation, and analysis

机译:蜂鸣声算法的设计模式:示例,仿真和分析

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摘要

We consider networks of processes which interact with beeps. In the basicmodel defined by Cornejo and Kuhn (2010), processes can choose in each roundeither to beep or to listen. Those who beep are unable to detect simultaneousbeeps. Those who listen can only distinguish between silence and the presenceof at least one beep. We refer to this model as $BL$ (beep or listen). Strongermodels exist where the nodes can detect collision while they are beeping($B_{cd}L$), listening ($BL_{cd}$), or both ($B_{cd}L_{cd}$). Beeping modelsare weak in essence and even simple tasks are difficult or unfeasible within. We present a set of generic building blocks (design patterns) which seem tooccur frequently in the design of beeping algorithms. They include multi-slotphases: the fact of dividing the main loop into a number of specialised slots;exclusive beeps: having a single node beep at a time in a neighbourhood (withinone or two hops); adaptive probability: increasing or decreasing theprobability of beeping to produce more exclusive beeps; internal (resp.peripheral) collision detection: for detecting collision while beeping (resp.listening). Based on these patterns, we provide algorithms for a number ofbasic problems, including colouring, 2-hop colouring, degree computation, 2-hopMIS, and collision detection (in $BL$). The patterns make it possible toformulate these algorithms in a rather concise and elegant way. Their analysesare more technical; one of them improves significantly upon that of the bestknown MIS algorithm by Jeavons et al. (2016). Finally, inspired by a techniquefrom Afek et al. (2013), our last contribution is to show that any Las Vegasalgorithm relying on collision detection can be transposed into a Monte Carloalgorithm without collision detection at the cost of a logarithmic slowdown,which we prove is optimal.
机译:我们考虑与蜂鸣声相互作用的进程网络。在Cornejo和Kuhn(2010)定义的基础模型中,过程可以在每个环路中选择哔哔声或倾听。那些哔哔声无法检测到同时缺乏。那些倾听的人只能区分沉默和至少一个嘟嘟声的存在。我们将此模型称为$ BL $(蜂鸣声或倾听)。 Switerermodels存在节点可以在蜂鸣声中检测到冲突的位置($ b_ {cd} l $),侦听($ bl_ {cd} $),或两者($ b_ {cd} l_ {cd} $)。令人作呕的型号薄弱,甚至简单的任务在内心难以或不可行。我们展示了一组通用构建块(设计模式),它们通常在蜂鸣声算法的设计中经常。它们包括多槽手:将主循环分成多个专业插槽的事实;独家发出哔哔声:在邻域(内部或两跳内)时具有单个节点蜂鸣声;自适应概率:增加或降低蜂鸣的可行性以产生更多独家哔哔声;内部(RESP.PERITWAL)碰撞检测:用于在蜂鸣声(RESP.Listening)的同时检测碰撞。基于这些模式,我们为数字问题提供了算法,包括着色,2跳着色,度数计算,2-Hopmis和碰撞检测(以$ BL $)为。模式使得可以以相当简洁和优雅的方式进行这些算法。他们的分析更多技术;其中一个通过Jeavons等人来提高了最佳知识的MIS算法的显着。 (2016)。最后,由Techniquefrom Afek等人启发。 (2013),我们的最后贡献是表明,依赖于碰撞检测的任何LAS Vegasalgorithm都可以转换成蒙特卡罗algorithm,而没有以对数减速的成本进行碰撞检测,我们证明是最佳的。

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