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An Optimal Family of Directed, Bounded-Degree Broadcast Networks

Michael J. Dinneen, Nian (Alfred)Zhou
2003 Electronical Notes in Theoretical Computer Science  
We also presents a 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  ... 
doi:10.1016/s1571-0661(04)81013-2 fatcat:35u77zyknvgpbflr2njn33d4wa

Algebraic constructions of efficient broadcast networks [article]

Michael J. Dinneen, Vance Faber, Michael R. Fellows
1995 arXiv   pre-print
It has previously been shown that hypercubes are 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.  ... 
arXiv:math/9504212v1 fatcat:4xxl7la7jrcihbcvgyng6iz2ki

Bounds on Contention Management in Radio Networks [chapter]

Mohsen Ghaffari, Bernhard Haeupler, Nancy Lynch, Calvin Newport
2012 Lecture Notes in Computer Science  
Our results prove that the Decay strategy, commonly used for local 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.  ... 
doi:10.1007/978-3-642-33651-5_16 fatcat:jnvnjzpi6raurllxq5ohbhx6qe

Degree- and time-constrained broadcast networks

Michael J. Dinneen, Geoffrey Pritchard, Mark C. Wilson
2002 Networks  
We consider the problem 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.  ... 
doi:10.1002/net.10018 fatcat:sgwch6t635hcnmccnskddwknai

Round Robin Is Optimal for Fault-Tolerant Broadcasting on Wireless Networks [chapter]

Andrea E. F. Clementi, Angelo Monti, Riccardo Silvestri
2001 Lecture Notes in Computer Science  
Concerning oblivious fault-tolerant distributed protocols, we provide 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.  ... 
doi:10.1007/3-540-44676-1_38 fatcat:lnsfwahenrejppebzopycex5i4

Round Robin is optimal for fault-tolerant broadcasting on wireless networks

Andrea E.F. Clementi, Angelo Monti, Riccardo Silvestri
2004 Journal of Parallel and Distributed Computing  
Concerning oblivious fault-tolerant distributed protocols, we provide 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.  ... 
doi:10.1016/j.jpdc.2003.09.002 fatcat:atpnlglv7jchppyrioi6ekfc5u

Broadcast Throughput in Radio Networks: Routing vs. Network Coding [chapter]

Noga Alon, Mohsen Ghaffari, Bernhard Haeupler, Majid Khabbazian
2013 Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms  
that 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  ... 
doi:10.1137/1.9781611973402.132 dblp:conf/soda/AlonGHK14 fatcat:hjvnny2igbf5pplhgenxsn3c5q

A mobility-transparent deterministic broadcast mechanism for ad hoc networks

S. Basagni, D. Bruschi, I. Chlamtac
1999 IEEE/ACM Transactions on Networking  
We show that the proposed protocol is simple and easy to implement, and that it is 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.  ... 
doi:10.1109/90.811446 fatcat:qrj5yxnxpfbgxi4lfypvbwd6jq

Bounds on Contention Management in Radio Networks [article]

Mohsen Ghaffari and Bernhard Haeupler and Nancy Lynch and Calvin Newport
2012 arXiv   pre-print
Our results prove that the Decay strategy, commonly used for local 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.  ... 
arXiv:1206.0154v2 fatcat:b4piut5v2ndbpbe7fayxfrva2y

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.  ... 

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.  ... 

Distributed Broadcast in Wireless Networks with Unknown Topology [article]

Andrea E.F. Clementi, Angelo Monti, Riccardo Silvestri
2001 arXiv   pre-print
Such connections, combined with a set 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.  ... 
arXiv:cs/0107011v1 fatcat:s3fhkk3b2vfzdgbie5ajp7r4jm

Designing broadcasting algorithms in the postal model for message-passing systems

A. Bar-Noy, S. Kipnis
1994 Mathematical Systems Theory  
In many message-passing systems, such = distributedmemory parallel computers and high-speed communication 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.  ... 
doi:10.1007/bf01184933 fatcat:tcrewzjfu5hjzi2qdqifo6jxme

Designing broadcasting algorithms in the postal model for message-passing systems

Amotz Bar-Noy, Shlomo Kipnis
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 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.  ... 
doi:10.1145/140901.140903 dblp:conf/spaa/Bar-NoyK92 fatcat:2f7hia3plnhw7g7zhzgn6ehxxe

Distributed multi-broadcast in unknown radio networks

Andrea E. F. Clementi, Angelo Monti, Riccardo Silvestri
2001 Proceedings of the twentieth annual ACM symposium on Principles of distributed computing - PODC '01  
Finally, for any constant a > 0, we provide 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.  ... 
doi:10.1145/383962.384040 dblp:conf/podc/ClementiMS01 fatcat:3haqmcesqfgwncippm656vt7ei
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