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An Optimal Family of Directed, Bounded-Degree Broadcast Networks

2003
*
Electronical Notes in Theoretical Computer Science
*

We also presents a

doi:10.1016/s1571-0661(04)81013-2
fatcat:35u77zyknvgpbflr2njn33d4wa
*family**of**optimal*(∆, ∆ + 1)*broadcast*digraphs. That is, digraphs with a proven maximum number*of*nodes, having maximum*degree*∆ and*broadcast*time at most ∆ + 1. ... We present, for the first time, a set*of*largest-known directed*networks*satisfied specified*bounds*on node*degree*and*broadcast*time. ... Because the order*of*A i+1 equals to 2 i+2 − 1 is the upper*bound*and i + 1 is the*degree**of*A i+1 , each A ∆ is*optimal*(∆, ∆+1)*broadcast*digraph. ✷ We now give another example*of**an**optimal**broadcast*...##
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Algebraic constructions of efficient broadcast networks
[article]

1995
*
arXiv
*
pre-print

It has previously been shown that hypercubes are

arXiv:math/9504212v1
fatcat:4xxl7la7jrcihbcvgyng6iz2ki
*optimal*for*degree*k and*broadcast*diameter k. A construction employing dihedral groups is shown to be*optimal*for*degree*k and*broadcast*diameter k+1. ... Cayley graph techniques are introduced for the problem*of*constructing*networks*having the maximum possible number*of*nodes, among*networks*that satisfy prescribed*bounds*on the parameters maximum node ... Further computational exploration will undoubtedly reveal further record-breaking constructions for small parameter values, and perhaps suggest additional in nite*families**of**optimal*constructions. ...##
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Bounds on Contention Management in Radio Networks
[chapter]

2012
*
Lecture Notes in Computer Science
*

Our results prove that the Decay strategy, commonly used for local

doi:10.1007/978-3-642-33651-5_16
fatcat:jnvnjzpi6raurllxq5ohbhx6qe
*broadcast*in the classical setting, is*optimal*. ... The local*broadcast*problem assumes that processes in a wireless*network*are provided messages, one by one, that must be delivered to their neighbors. ... These lower*bounds*also show that the existing constructions*of*Ad Hoc Selective*Families*are*optimal*. ...##
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Degree- and time-constrained broadcast networks

2002
*
Networks
*

We consider the problem

doi:10.1002/net.10018
fatcat:sgwch6t635hcnmccnskddwknai
*of*constructing*networks*with as many nodes as possible, subject to upper*bounds*on the*degree*and*broadcast*time. ... This paper includes the results*of**an*extensive empirical study*of**broadcasting*in small regular graphs using a stochastic search algorithm to approximate the*broadcast*time. ... We also thank Paul Hafner for teaching us how t o i n v estigate Cayley graphs with the Magma system and for his comments on*an*earlier version*of*this paper. ...##
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Round Robin Is Optimal for Fault-Tolerant Broadcasting on Wireless Networks
[chapter]

2001
*
Lecture Notes in Computer Science
*

Concerning oblivious fault-tolerant distributed protocols, we provide

doi:10.1007/3-540-44676-1_38
fatcat:lnsfwahenrejppebzopycex5i4
*an*OðDnÞ lower*bound*where n is the number*of*nodes*of*the*network*and D is the source eccentricity in the fault-free part*of*the*network*... We study the completion time*of**broadcast*operations on static ad hoc wireless*networks*in presence*of*unpredictable and dynamical faults. ... More importantly, Paolo suggested us to investigate the issue*of*fault tolerance in wireless*networks*. ...##
###
Round Robin is optimal for fault-tolerant broadcasting on wireless networks

2004
*
Journal of Parallel and Distributed Computing
*

Concerning oblivious fault-tolerant distributed protocols, we provide

doi:10.1016/j.jpdc.2003.09.002
fatcat:atpnlglv7jchppyrioi6ekfc5u
*an*OðDnÞ lower*bound*where n is the number*of*nodes*of*the*network*and D is the source eccentricity in the fault-free part*of*the*network*... We study the completion time*of**broadcast*operations on static ad hoc wireless*networks*in presence*of*unpredictable and dynamical faults. ... More importantly, Paolo suggested us to investigate the issue*of*fault tolerance in wireless*networks*. ...##
###
Broadcast Throughput in Radio Networks: Routing vs. Network Coding
[chapter]

2013
*
Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms
*

that

doi:10.1137/1.9781611973402.132
dblp:conf/soda/AlonGHK14
fatcat:hjvnny2igbf5pplhgenxsn3c5q
*of*the*optimal**network*coding algorithm. ... Whether such a gap exists for wireless*networks*has been*an*open question*of*great interest. ... This would lead to*an*O(1/ log 2 n) messages-per-round*bound*on the throughput*of*routing and would show that*network*coding is strictly necessary for asymptotically*optimal**broadcast*algorithms in radio ...##
###
A mobility-transparent deterministic broadcast mechanism for ad hoc networks

1999
*
IEEE/ACM Transactions on Networking
*

We show that the proposed protocol is simple and easy to implement, and that it is

doi:10.1109/90.811446
fatcat:qrj5yxnxpfbgxi4lfypvbwd6jq
*optimal*in*networks*in which assumptions on the maximum number*of*the neighbors*of*a node can be made. ... Index Terms-Ad hoc*networks*,*broadcast*protocols, distributed algorithms, mobile computing. ... Finally, when*an*assumption can be made on the*degree**of*the*network*, we showed that our solution is*optimal*. ...##
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Bounds on Contention Management in Radio Networks
[article]

2012
*
arXiv
*
pre-print

Our results prove that the Decay strategy, commonly used for local

arXiv:1206.0154v2
fatcat:b4piut5v2ndbpbe7fayxfrva2y
*broadcast*in the classical setting, is*optimal*. ... The local*broadcast*problem assumes that processes in a wireless*network*are provided messages, one by one, that must be delivered to their neighbors. ... Fix some n > 2 and randomized*broadcast*algorithm A B . With probability at least 1/2, A B requires at least ⌊(n−1)/2⌋ rounds to solve*broadcast*in the lollipop*network**of*size n. Spread*Network*. ...##
###
Page 8492 of Mathematical Reviews Vol. , Issue 2002K
[page]

2002
*
Mathematical Reviews
*

Since then, many papers have proposed constructions

*of**bounded*-*degree**networks*having a small*broadcast*time, but so far the*optimality**of*(+) has been*an*open question. ...*of*general lower*bounds*for*broadcasting*and gossiping. ...##
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Page 2863 of Mathematical Reviews Vol. , Issue 2003d
[page]

2003
*
Mathematical Reviews
*

in-

*degree**of*the*network*, respectively. ... The maximum in-*degree*A*of*a*network*is the maximum*of*the in-*degrees**of*its nodes. “We propose a new method that leads to several improve- ments in deterministic gossiping. ...##
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Distributed Broadcast in Wireless Networks with Unknown Topology
[article]

2001
*
arXiv
*
pre-print

Such connections, combined with a set

arXiv:cs/0107011v1
fatcat:s3fhkk3b2vfzdgbie5ajp7r4jm
*of*new lower and upper*bounds*on the size*of*the above*families*, allow us to derive new lower*bounds*and new distributed protocols for the*broadcast*and multi-*broadcast*...*of*nodes n, the maximum eccentricity D, the maximum in-*degree*Delta, and the congestion c*of*the*networks*. ... Our results*Broadcast*. Our first contribution is the construction*of*a*family**of*graphs that yields*an*Ω(n log D) lower*bound*on the completion time*of*DB protocols on unknown*networks*. ...##
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Designing broadcasting algorithms in the postal model for message-passing systems

1994
*
Mathematical Systems Theory
*

In many message-passing systems, such = distributedmemory parallel computers and high-speed communication

doi:10.1007/bf01184933
fatcat:tcrewzjfu5hjzi2qdqifo6jxme
*networks*, the exact structure*of*the underlying communication*network*may be ignored. ... In such systems it is assumed that the*network*creates a complete communication graph between the processors, in which passing messages is associated with communication la- ... Finally, we analyze a*family**of**broadcasting*algorithms that are based on*degree*-d trees. ...##
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Designing broadcasting algorithms in the postal model for message-passing systems

1992
*
Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures - SPAA '92
*

In many message-passing systems, such = distributedmemory parallel computers and high-speed communication

doi:10.1145/140901.140903
dblp:conf/spaa/Bar-NoyK92
fatcat:2f7hia3plnhw7g7zhzgn6ehxxe
*networks*, the exact structure*of*the underlying communication*network*may be ignored. ... In such systems it is assumed that the*network*creates a complete communication graph between the processors, in which passing messages is associated with communication la- ... Finally, we analyze a*family**of**broadcasting*algorithms that are based on*degree*-d trees. ...##
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Distributed multi-broadcast in unknown radio networks

2001
*
Proceedings of the twentieth annual ACM symposium on Principles of distributed computing - PODC '01
*

Finally, for any constant a > 0, we provide

doi:10.1145/383962.384040
dblp:conf/podc/ClementiMS01
fatcat:3haqmcesqfgwncippm656vt7ei
*an*O((D + c)d 2 log (2+~) n) deterministic upper*bound*for the same task where d is the maximum in-*degree**of*the*network*. ... One*of*the most frequent tasks in multi-hop synchronous radio*networks*is the multi-*broadcast*operation: it consists in performing r independent message*broadcasts*through a*network**of*n nodes. ...*An*interesting future research goal is that*of*reducing the gap between upper and lower*bounds*for larger maximum in-*degree*d. ...
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