A grid embedding into the star graph for image analysis solutions

Nassif, N.; Bagherzadeh, Nader

doi:10.1016/s0020-0190(96)00165-2

Cited by 5 publications

(2 citation statements)

References 2 publications

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“…Since the seminal work by Akers and Krishnamurthy [1], the 'star graphs' have been recognized as viable candidates for interconnection networks because (a) a star graph has some appealing properties such as symmetry, recursiveness, maximal connectivity, sublogarithmic vertex degree, sublogarithmic diameter, and excellent graph embedding abilities [5,15,22,23] and (b) a number of efficient parallel algorithms have been developed on star graphs [2][3][4]6,10,18,21,24]. Previous work on the fault tolerance of star graphs was mainly focused on their fault-tolerant routing strategies [7,8,11,20] and their fault-tolerant graph embedding abilities [13,14,16,17,26].…”

Section: Introductionmentioning

confidence: 99%

Largest connected component of a star graph with faulty vertices

Yang

Megson

Tang

et al. 2008

International Journal of Computer Mathematics

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In order to make a full evaluation of an interconnection network, it is essential to estimate the minimum size of a largest connected component of this network provided the faulty vertices in the network may break its connectedness. Star graphs are recognized as promising candidates for interconnection networks. This article addresses the size of a largest connected component of a faulty star graph. We prove that, in an n-star graph (n ≥ 3) with up to 2n − 4 faulty vertices, all fault-free vertices but at most two form a connected component. Moreover, all fault-free vertices but exactly two form a connected component if and only if the set of all faulty vertices is equal to the neighbourhood of a pair of fault-free adjacent vertices. These results show that star graphs exhibit excellent fault-tolerant abilities in the sense that there exists a large functional network in a faulty star graph.

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Section: Introductionmentioning

confidence: 99%

Largest connected component of a star graph with faulty vertices

Yang

Megson

Tang

et al. 2008

International Journal of Computer Mathematics

View full text Add to dashboard Cite

show abstract

“…More specifically, growth in the node degree and diameter is sub-logarithmic to the network size in the star network, but logarithmic in the hypercube. Various networks have been mapped to the star network [4,20,25]. A treatment of communication aspects for this network is presented in [8,10,11,24,26].…”

Section: Introductionmentioning

confidence: 99%