Embedding of Binomial Trees in Hypercubes with Link Faults

Wu, Jie; Fernández, Eduardo B.; Luo, Yingqiu

doi:10.1006/jpdc.1998.1482

Cited by 11 publications

(6 citation statements)

References 10 publications

(11 reference statements)

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“…Lo et al [12] has identified the binomial tree as an ideal computation structure for parallel divide and conquer algorithms. Binomial trees can easily be embedded into a fully connected graph with constant dilation 1 (c.f., [41]). In an one-to-one transmission, the binomial tree at each step at most doubles the informed number of nodes and thus, it gives an optimal broadcasting time.…”

Section: A Binomial Tree-based Methodsmentioning

confidence: 93%

Broadcasting Methods in MANETS: An Overview

Mkwawa

Kouvatsos

2011

Network Performance Engineering

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Abstract. Broadcasting in mobile ad hoc networks (MANETs) is an information dissemination process of sending a message from a source node to all other nodes of the network. Even though it has been studied extensively for wired networks, broadcasting in MANETs poses more challenging problems because of the variable and unpredictable characteristics of its medium as well as the fluctuation of the signal strength and propagation with respect to time and environment. Furthermore, node mobility creates a continuously changing communication topology in which routing paths break and new ones form dynamically. In this context, efficient broadcasting in Mobile Ad hoc networks is crucial for providing control and routing information for multicast and point to point communication protocols. This paper presents an overview on the state of the art of broadcasting methods in MANETs and makes recommendations on how to improve the efficiency and performance of tree and cluster based broadcasting methods.

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Section: A Binomial Tree-based Methodsmentioning

confidence: 93%

Broadcasting Methods in MANETS: An Overview

Mkwawa

Kouvatsos

2011

Network Performance Engineering

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“…(1) LTQ 2 is a graph consisting of four nodes labeled with 00, 01, 10, and 11, respectively, connected by four edges (00, 01), (00, 10), (01, 11), and (10,11).…”

Section: Preliminariesmentioning

confidence: 99%

Embedding of Binomial Trees in Locally Twisted Cubes with Link Faults

You¹

2014

AMR

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As a newly introduced interconnection network for parallel computing, the locally twisted cube possesses many desirable properties. In this paper, binomial tree embeddings in locally twisted cubes are studied. We present two major results in this paper: (1) For any integern≥ 2, ann-dimensional binomial treeBncan be embedded inLTQnwith dilation 1 by randomly choosing any vertex inLTQnas the root. (2) For any integern≥ 2, ann-dimensional binomial treeBncan be embedded inLTQnwith up ton− 1 faulty links inlog(n− 1) steps where dilation = 1. The results are optimal in the sense that the dilations of all embeddings are 1.

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“…In this sense, the incomplete hypercube-type architecture is a fault-tolerant architecture for the relevant complete hypercube with faulty nodes. The reliable communication on the cube-based system for fault-tolerant applications is investigated carefully in [30][31][32][33][34]. The structural properties of a regular incomplete hypercube denoted by I n k with size 2 n + 2 k for 0 ≤ k < n (denoted by I n n−m with size 2 n + 2 n m for 1 ≤ m ≤ n in this paper) are discussed in detail in [25,27].…”

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confidence: 99%

Incomplete crossed hypercubes

Zhang

Pan

2008

J Supercomput

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In this paper, a new interconnection network called the incomplete crossed hypercube is proposed for connecting processors of parallel computing systems. The incomplete crossed hypercube architecture denoted by CI n n−m is made by combining two complete crossed hypercubes CQ n and CQ n−m for 1 ≤ m ≤ n. Several topological properties of CI n n−m are analyzed. In particular, accurate mean internode distance formulas of both CQ n and CI n n−m are given. Compared with the incomplete enhanced hypercube EI n n−m , CI n n−m has shorter mean internode distance for large n. An optimal routing algorithm for CI n n−m is also described which guarantees the generation of a shortest path from a node to another in CI n n−m .

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Embedding of Binomial Trees in Hypercubes with Link Faults

Cited by 11 publications

References 10 publications

Broadcasting Methods in MANETS: An Overview

Broadcasting Methods in MANETS: An Overview

Embedding of Binomial Trees in Locally Twisted Cubes with Link Faults

Incomplete crossed hypercubes

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