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Optimum Free-Table Routing in the Optimised Degree Six 3-Modified Chordal Ring Network

R. N. Farah, S. L. E. Chien, M. Othman
2017 Journal of Communications  
The optimised degree six 3-modified chordal ring, 6 3 is a parallel processing network topology for large networks modelled after Graph Theory.  ...  Lemmas were presented based on the developed routing scheme of 6 3 regarding conditions for the existence of layer shortest paths in its networks, along with the algorithm to be translated into a source  ...  the networks of the degree six chordal ring topology, the optimised degree six 3modified chordal ring, 6 3 .  ... 
doi:10.12720/jcm.12.12.677-682 fatcat:642qo55wk5fhvmw77nwoasmp6a

Some graph properties of the optimised degree six 3-modified chordal ring network

Stephen Lim Een-Chien, R. N. Farah, M. Othman
2017 Malaysian Journal of Fundamental and Applied Sciences  
This paper discusses the degree six 3-modified chordal ring, CHR6o3, and presents its graph theoretical properties of symmetry and Hamiltonicity.  ...  One such graph model that has gained attention by researchers since its founding is the chordal ring, based on an undirected circulant graph.  ...  One such improvement was increasing the degree of the topology, yielding the degree four traditional chordal ring, 4 [2] ; the degree six traditional chordal ring, 6 [3] ; and the degree five traditional  ... 
doi:10.11113/mjfas.v12n4.518 fatcat:5ddgn6wg2vgm5pou2oeyknciau

Symmetry properties of chordal rings of degree 3

Lali Barrière
2003 Discrete Applied Mathematics  
Both algorithms are based on the study of the 4-and 6-cycles of the graph. This approach is also applied to the characterization of the automorphisms-group of chordal rings.  ...  We believe that these results produce useful tools for further works as, in particular, the study of compact routing schemes, and the study of optical routing protocols in edge-transitive chordal rings  ...  Moreover, the tessellation has been also used to derive compact routing schemes in chordal rings of degree 4 [23] .  ... 
doi:10.1016/s0166-218x(02)00569-3 fatcat:pzlwnm5tuvdpfbaq7kr6o5vfge

Page 6380 of Mathematical Reviews Vol. , Issue 99i [page]

1999 Mathematical Reviews  
Amin (Huntsville, AL) 991:68012 68M10 Narayanan, L. (3-CONC-C; Montreal, PQ); Opatrny, J. (3-CONC-C; Montreal, PQ) Compact routing on chordal rings of degree 4.  ...  Summary: “A chordal ring G(n;c) of degree 4 is a ring of n nodes with chords connecting each vertex i to the vertex (i +c) mod n.  ... 

A survey on interval routing

Cyril Gavoille
2000 Theoretical Computer Science  
These results are classiÿed in several themes: characterization, compactness and shortest path, dilation and stretch factor, speciÿc class of graphs (interconnection networks, bounded degree, planar, chordal  ...  We survey in this paper the classical results, and also the most recent results, in the ÿeld of Interval Routing, a well-known strategy to code in a compact way distributed routing algorithms.  ...  4 plane graph of bounded degree of compactness ( √ n).  ... 
doi:10.1016/s0304-3975(99)00283-2 fatcat:gxqzru4kurdafgbrofsehe6zdm

Page 6797 of Mathematical Reviews Vol. , Issue 2002I [page]

2002 Mathematical Reviews  
This algorithm categorised the regular chordal rings of degree 3 into two types, depending on whether n mod 4 = 0.” 2002i:68005 68M10 05C90 68R10 90B10 Adler, Micah (1-MA-C; Amherst, MA); Leighton, Tom  ...  (MAL-UPMCI-MU; Serdang) Boolean routing on regular chordal ring network. (English summary) J. Inst. Math. Comput. Sci. Comput. Sci. Ser. 12 (2001), no. 1, 55-66.  ... 

Routing for generalized chordal rings

Bruce W. Arden, Kit-Ming W. Tang
1990 Proceedings of the 1990 ACM annual conference on Cooperation - CSC '90  
A recursive routing algorithm is presented for generalized chordal ring (GCR) graphs. This algorithm consists of two parts.  ...  The inherent symmetry and the modular arithmetic connectivity of the GCR are exploited to achieve a parallel tyme complexity of O(log, diameter) and a serial time complexity of O(diameter).  ...  In a recent report we have shown that these Cayley graphs can be represented as generalized chordal rings (GCR) [4] . In this paper we present a recursive routing algorithm for GCR graphs.  ... 
doi:10.1145/100348.100390 dblp:conf/acm/ArdenT90 fatcat:5hwxifsnhnddrjbixt2tux3tri

Gossiping in chordal rings under the line model

Lali Barrière, Johanne Cohen, Margarida Mitjana
2001 Theoretical Computer Science  
Since the chordal rings are competitors of networks as meshes or tori because of theirs short diameter and bounded degree, it is of interest to ask whether they can support intensive c o m m unications  ...  Our gossip algorithms are based on the so-called 3-phase gossip method 15]. For that purpose, the Section 3 gives a decomposition of the chordal ring into disjoint cycles.  ...  Chordal rings can support compact 25] and fault-tolerance 2] routing functions.  ... 
doi:10.1016/s0304-3975(00)00213-9 fatcat:irddrgcgqzdqrdv24boerlgd2u

Multihop Local Pooling for Distributed Throughput Maximization in Wireless Networks

G. Zussman, A. Brzezinski, E. Modiano
2008 2008 Proceedings IEEE INFOCOM - The 27th Conference on Computer Communications  
Efficient operation of wireless networks requires distributed scheduling and routing algorithms that take into account interference constraints.  ...  However, previous work regarding Local Pooling focused mostly on single-hop interference or single-hop traffic. In this paper, we study the multihop implications of Local Pooling.  ...  (a) 2-hop and (b) 3-hop interference graphs of a 6-ring network graph Fig. 4 . 4 The relations between the OLoP-Satisfying class and other graph classes: P -perfect,P -non-perfect, WC -weakly chordal  ... 
doi:10.1109/infocom.2007.169 fatcat:sp47g62vjrfbdntl4q4kprhwde

Multihop Local Pooling for Distributed Throughput Maximization in Wireless Networks

G. Zussman, A. Brzezinski, E. Modiano
2008 IEEE INFOCOM 2008 - The 27th Conference on Computer Communications  
Efficient operation of wireless networks requires distributed scheduling and routing algorithms that take into account interference constraints.  ...  However, previous work regarding Local Pooling focused mostly on single-hop interference or single-hop traffic. In this paper, we study the multihop implications of Local Pooling.  ...  (a) 2-hop and (b) 3-hop interference graphs of a 6-ring network graph Fig. 4 . 4 The relations between the OLoP-Satisfying class and other graph classes: P -perfect,P -non-perfect, WC -weakly chordal  ... 
doi:10.1109/infocom.2008.169 dblp:conf/infocom/ZussmanBM08 fatcat:mwjavrrap5gw3ihcw4bnmau3uy

Collective Tree Spanners of Graphs [chapter]

Feodor F. Dragan, Chenyu Yan, Irina Lomonosov
2004 Lecture Notes in Computer Science  
This leads, for example, to a routing scheme of deviation (2 c/2 ) with addresses and routing tables of size O(log 3 n/ log log n) bits per vertex on the class of c-chordal graphs. Introduction.  ...  We discuss also an application of the collective tree spanners to the problem of designing compact and efficient routing schemes in graphs.  ...  Observe that in interval routing schemes the local memory requirement increases with the degree of the vertex. Routing labeling schemes aim at overcoming the problem of large degree vertices.  ... 
doi:10.1007/978-3-540-27810-8_7 fatcat:daxmekb27rdkloslvevy6yf3qu

Collective tree spanners of graphs

Feodor F. Dragan, Chenyu Yan, Irina Lomonosov
2006 SIAM Journal on Discrete Mathematics  
This leads, for example, to a routing scheme of deviation (2 c/2 ) with addresses and routing tables of size O(log 3 n/ log log n) bits per vertex on the class of c-chordal graphs. Introduction.  ...  We discuss also an application of the collective tree spanners to the problem of designing compact and efficient routing schemes in graphs.  ...  Observe that in interval routing schemes the local memory requirement increases with the degree of the vertex. Routing labeling schemes aim at overcoming the problem of large degree vertices.  ... 
doi:10.1137/s089548010444167x fatcat:rswyda6nxnaktkko64uehgbdja

Multidimensional interval routing schemes

Michele Flammini, Giorgio Gambosi, Umberto Nanni, Richard B. Tan
1998 Theoretical Computer Science  
, hypercubes and chordal rings.  ...  Interval routing scheme (k-IRS) is a compact routing scheme on general networks. It has been studied extensively and recently been implemented on the latest generation INMOS Transputer Router chip.  ...  Section 4 contains specific results on interconnection networks trees, rings, grids, tori, hypercubes and chordal rings.  ... 
doi:10.1016/s0304-3975(97)00070-4 fatcat:7yjsj5tapfc7lll4w4x26jhaqa

On Compact and Efficient Routing in Certain Graph Classes [chapter]

Feodor F. Dragan, Irina Lomonosov
2004 Lecture Notes in Computer Science  
It is interesting to investigate which other classes of graphs admit routing schemes with labels not depending on vertex degrees that route messages along near-optimal path.  ...  Unfortunately, for every shortest path routing strategy and for all , there is a graph of degree bounded by for which (n log ) bit routing tables are required simultaneously on (n) vertices [20] .  ...  As he has shown, our old method-without considering special (Q-simple) paths-could result in a scheme with labels of size O(log 3 n) bits per vertex and O(log log n) routing protocol even on chordal bipartite  ... 
doi:10.1007/978-3-540-30551-4_36 fatcat:4mkouo5v45h27gv2jgvclcqmru

On compact and efficient routing in certain graph classes

Feodor F. Dragan, Irina Lomonosov
2007 Discrete Applied Mathematics  
We show that, by constructing a family of special spanning trees, one can achieve a routing scheme of deviation 2R with labels of size O(log 3 n/ log log n) bits per vertex and O(1) routing protocol for  ...  We design a routing scheme for graphs admitting induced acyclic (R, D)-clustering where the induced radius and the induced diameter of each cluster are at most 2.  ...  As he has shown, our old method-without considering special (Q-simple) paths-could result in a scheme with labels of size O(log 3 n) bits per vertex and O(log log n) routing protocol even on chordal bipartite  ... 
doi:10.1016/j.dam.2007.03.011 fatcat:q5epqia5uvd4rnh4gnau77s73m
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