The partial line digraph technique in the design of large interconnection networks

The following problem arises in the design of some interconnection networks for distributed systems. Namely, to construct digraphs with given maximum out-degree, reduced diameter, easy routing, good connectivity, and good expandability. To this end, a method based on the concept of partial line digr...

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Vydané v:	IEEE transactions on computers Ročník 41; číslo 7; s. 848 - 857
Hlavní autori:	Fiol, M.A., Llado, A.S.
Médium:	Journal Article Publikácia
Jazyk:	English
Vydavateľské údaje:	New York, NY IEEE 01.07.1992 Institute of Electrical and Electronics Engineers
Predmet:	68 Computer science 68W Algorithms Algorithms and computation in mathematics Anàlisi matemàtica Applied sciences Classificació AMS Communication networks Computer science; control theory; systems Computer systems and distributed systems. User interface Councils Delay Distributed computing Exact sciences and technology Fault tolerance Intelligent networks Matemàtiques i estadística Multiprocessor interconnection networks Proposals Routing Software Very large scale integration Àrees temàtiques de la UPC Fault tolerance Computer network Shortest path Routing Computer system Distributed system Directed graph Message transmission
ISSN:	0018-9340
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Abstract	The following problem arises in the design of some interconnection networks for distributed systems. Namely, to construct digraphs with given maximum out-degree, reduced diameter, easy routing, good connectivity, and good expandability. To this end, a method based on the concept of partial line digraph is presented. This proposal, which turns out to be a generalization of the so-called line digraph technique, allows digraphs that satisfy all the above-mentioned requirements to be obtained. In particular, it is shown that the partial line digraphs of Kautz digraphs solve the (d, N) digraph problem, i.e. to minimize the diameter D in a digraph of maximum out-degree d and number of vertices N, for any N in the range d/sup D-1/+d/sup D-2/+. . .+1<or=N<or=d/sup D/+d/sup D-1/.< >
AbstractList	The following problem arises in the design of some interconnection networks for distributed systems. Namely, to construct digraphs with given maximum out-degree, reduced diameter, easy routing, good connectivity, and good expandability. To this end, a method based on the concept of partial line digraph is presented. This proposal, which turns out to be a generalization of the so-called line digraph technique, allows digraphs that satisfy all the above-mentioned requirements to be obtained. In particular, it is shown that the partial line digraphs of Kautz digraphs solve the (d, N) digraph problem, i.e. to minimize the diameter D in a digraph of maximum out-degree d and number of vertices N, for any N in the range d(D-1) d(D-2) . . . 1 N d(D) d(D-1) The following problem arises in the design of some interconnection networks for distributed systems. Namely, to construct digraphs with given maximum out-degree, reduced diameter, easy routing, good connectivity, and good expandability. To this end, a method based on the concept of partial line digraph is presented. This proposal, which turns out to be a generalization of the so-called line digraph technique, allows digraphs that satisfy all the above-mentioned requirements to be obtained. In particular, it is shown that the partial line digraphs of Kautz digraphs solve the (d, N) digraph problem, i.e. to minimize the diameter D in a digraph of maximum out-degree d and number of vertices N, for any N in the range d/sup D-1/+d/sup D-2/+. . .+1<or=N<or=d/sup D/+d/sup D-1/.< > The following problem arises in the design of some interconnection networks for distributed systems. Namely, to construct digraphs with given maximum out-degree, reduced diameter, easy routing, good connectivity, and good expandability. To this end, a new method based on the concept of partial line digraph is presented. This proposal, which turns out to be a generalization of the so-called line digraph technique, allows us to obtain digraphs that satisfy all the above-mentioned requirements. In particular it is shown that the partial line digraphs of Kautz digraphs solve the (d. digraph problem-i.e. to minimize the diameter D in a digraph of maximum outdegree d and number of vertices S-for any in the range Index Terms- Communication network, connectivity maximization, (d. Y) digraph problem, expandability, fault-tolerance, line digraph, routing algorithm. an-l + (P2+ . . . + 1 5 -1- 5 drl + P1.
Author	Llado, A.S. Fiol, M.A.
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Cites_doi	10.1109/TC.1984.1676455 10.1007/BFb0059429 10.1109/TC.1985.1676569 10.1109/TC.1981.1675809 10.1145/800046.801653 10.1109/C-M.1981.220290 10.1109/TC.1982.1676084 10.1016/0743-7315(86)90008-0 10.1007/BF01110285 10.1016/0095-8956(80)90091-X 10.1109/TC.1983.1676323 10.1002/jgt.3190130603 10.1109/TC.1979.1675402
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References	ref12 f brega (ref9) 1985 fiol (ref11) 1990; 29b ref14 plesnik (ref22) 1974; 29 ref10 kautz (ref20) 1969 ref1 ref17 ref16 ref18 de bruijn (ref6) 1946; a49 chartrand (ref7) 1986 reddy (ref24) 1980 ref25 bermond (ref2) 1983; 82 ref21 kautz (ref19) 1968 ref8 geller (ref15) 1970; 186 fiol (ref13) 1988; 25c (ref4) 0 ref3 ref5 reddy (ref23) 1982
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SubjectTerms	68 Computer science 68W Algorithms Algorithms and computation in mathematics Anàlisi matemàtica Applied sciences Classificació AMS Communication networks Computer science; control theory; systems Computer systems and distributed systems. User interface Councils Delay Distributed computing Exact sciences and technology Fault tolerance Intelligent networks Matemàtiques i estadística Multiprocessor interconnection networks Proposals Routing Software Very large scale integration Àrees temàtiques de la UPC
Title	The partial line digraph technique in the design of large interconnection networks
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