## ملخص

We consider the SINR wireless model with uniform power. In this model the success of a transmission is determined by the ratio between the strength of the transmission signal and the noise produced by other transmitting processors plus ambient noise. The local broadcasting problem is a fundamental problem in this setting. Its goal is producing a schedule in which each processor successfully transmits a message to all its neighbors. This problem has been studied in various variants of the setting, where the best currently-known algorithm has running time O(Δ+log^{2}n) in n-node networks with feedback, where Δ is the maximum neighborhood size [9]. In the latter setting processors receive free feedback on a successful transmission. We improve this result by devising a local broadcasting algorithm with time O(Δ+lognloglogn) in networks with feedback. Our result is nearly tight in view of the lower bounds Ω(Δ) and Ω(logn) [13]. Our results also show that the conjecture that Ω(Δ+log^{2}n) time is required for local broadcasting [9] is not true in some settings. We also consider a closely related problem of distant-k coloring. This problem requires each pair of vertices at geometrical distance of at most k transmission ranges to obtain distinct colors. Although this problem cannot be always solved in the SINR setting, we are able to compute a solution using an optimal number of Steiner points (up to constant factors). We employ this result to devise a local broadcasting algorithm that after a preprocessing stage of O(log∗n⋅(Δ+lognloglogn)) time obtains a local-broadcasting schedule of an optimal (up to constant factors) length O(Δ). This improves upon previous local-broadcasting algorithms in various settings whose preprocessing time was at least O(Δlogn) [3,10,5,]. Finally, we prove a surprising phenomenon regarding the influence of the path-loss exponent α on performance of algorithms. Specifically, we show that in vacuum (α = 2) any local broadcasting algorithm requires Ω(Δlogn) time, while on earth (α > 2) better results are possible as illustrated by our O(Δ+lognloglogn)-time algorithm.

اللغة الأصلية | الإنجليزيّة |
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عنوان منشور المضيف | Structural Information and Communication Complexity - 22nd International Colloquium, SIROCCO 2015, Post-Proceedings |

المحررون | Christian Scheideler |

ناشر | Springer Verlag |

الصفحات | 164-178 |

عدد الصفحات | 15 |

رقم المعيار الدولي للكتب (المطبوع) | 9783319252575 |

المعرِّفات الرقمية للأشياء | |

حالة النشر | نُشِر - 2015 |

الحدث | 22nd International Colloquium on Structural Information and Communication Complexity, SIROCCO 2015 - Montserrat, أسبانيا المدة: ١٤ يوليو ٢٠١٥ → ١٦ يوليو ٢٠١٥ |

### سلسلة المنشورات

الاسم | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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مستوى الصوت | 9439 |

رقم المعيار الدولي للدوريات (المطبوع) | 0302-9743 |

رقم المعيار الدولي للدوريات (الإلكتروني) | 1611-3349 |

### !!Conference

!!Conference | 22nd International Colloquium on Structural Information and Communication Complexity, SIROCCO 2015 |
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الدولة/الإقليم | أسبانيا |

المدينة | Montserrat |

المدة | ١٤/٠٧/١٥ → ١٦/٠٧/١٥ |

### ملاحظة ببليوغرافية

Publisher Copyright:© Springer International Publishing Switzerland 2015.