Deadlock prevention by acyclic orientations
Deadlock prevention for routing messages has a central role in communication networks, since it directly influences the correctness of parallel and distributed systems. In this paper, we extend some of the computational results presented in Second Colloquium on Structural Information and Communicati...
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| Vydáno v: | Discrete Applied Mathematics Ročník 129; číslo 1; s. 31 - 47 |
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Elsevier B.V
15.06.2003
Elsevier |
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| ISSN: | 0166-218X, 1872-6771 |
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| Abstract | Deadlock prevention for routing messages has a central role in communication networks, since it directly influences the correctness of parallel and distributed systems. In this paper, we extend some of the computational results presented in Second Colloquium on Structural Information and Communication Complexity (SIROCCO), Carleton University Press, 1995, pp. 1–12 on acyclic orientations for the determination of optimal deadlock-free routing schemes. In this context, minimizing the number of buffers needed to prevent deadlocks for a set of communication requests is related to finding an acyclic orientation of the network which minimizes the maximum number of changes of orientations on the dipaths realizing the communication requests. The corresponding value is called the rank of the set of dipaths.
We first show that the problem of minimizing the rank is NP-hard if all shortest paths between the couples of nodes wishing to communicate have to be represented and even not approximable if only one shortest path between each couple has to be represented. This last result holds even if we allow an error which is any sublinear function in the number of couples to be connected.
We then improve some of the known lower and upper bounds on the rank of all possible shortest dipaths between any couple of vertices for particular topologies, such as grids and hypercubes, and we find tight results for tori. |
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| AbstractList | In this paper we consider a combinatorial problem consisting in finding an acyclic orientation of a graph which minimizes the maximum number of changes of orientations along a given set of dipaths. A change of orientation along a dipath occurs when two consecutive arcs are discordly oriented. Such maximum number of changes of orientations is called the rank of the acyclic orientation with respect to the set of dipaths and the minimum rank of all possible acyclic orientations is the rank of the graph with respect to the set of dipaths. Besides its theoretical interest, the topic has also practical applications. In fact, Deadlock prevention for routing messages has a central role in communication networks, since it directly influences the correctness of parallel and distributed systems. In this paper, we extend some of the computational results presented in Second Colloquium on Structural Information and Communication Complexity (SIROCCO), Carleton University Press, 1995, pp. 1–12 on acyclic orientations for the determination of optimal deadlock-free routing schemes. In this context, minimizing the number of buffers needed to prevent deadlocks for a set of communication requests is related to finding an acyclic orientation of the network which minimizes the maximum number of changes of orientations on the dipaths realizing the communication requests. The corresponding value is called the rank of the set of dipaths. We first show that the problem of minimizing the rank is NP-hard if all shortest paths between the couples of nodes wishing to communicate have to be represented and even not approximable if only one shortest path between each couple has to be represented. This last result holds even if we allow an error which is any sublinear function in the number of couples to be connected. We then improve some of the known lower and upper bounds on the rank of all possible shortest dipaths between any couple of vertices for particular topologies, such as grids and hypercubes, and we find tight results for tori. |
| Author | Bermond, Jean-Claude Flammini, Michele Ianni, Miriam Di Pérennès, Stéphane |
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| Cites_doi | 10.1016/0022-0000(91)90005-P 10.1145/135419.135425 10.1109/TCOM.1980.1094666 10.1109/TCOM.1981.1095021 10.1007/BFb0032940 10.1109/SPDP.1991.218233 10.1145/113379.113405 10.1145/112600.112616 10.1145/140901.140902 10.1109/TC.1987.1676939 |
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| Keywords | Computational and structural complexity Parallel algorithms Routing and communication in interconnection networks |
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| References_xml | – start-page: 149 year: 1992 end-page: 158 ident: BIB3 article-title: Routage wormhole et canaux virtuel publication-title: Algorithmique Parallèle – volume: COM-29 start-page: 512 year: 1981 end-page: 514 ident: BIB11 article-title: Prevention of deadlock in packet-switched data transport system publication-title: IEEE Trans. Commun. – year: 1977 ident: BIB10 publication-title: Computers and Intractability. A Guide to the Theory of NP-completeness – reference: B. Awerbuch, S. Kutten, D. Peleg, Efficient deadlock-free routing, in: 10th Annual ACM Symposium on Principles of Distributed Computing (PODC), Montreal, Canada, 1991, pp. 177–188. – reference: R. Cypher, L. Gravano, Requirements for deadlock-free, adaptive packet routing, in: 11th Annual ACM Symposium on Principles of Distributed Computing (PODC), 1992, pp. 25–33. – reference: M. Di Ianni, M. Flammini, R. Flammini, S. Salomone, Systolic acyclic orientations for deadlock prevention, in: Second Colloquium on Structural Information and Communication Complexity (SIROCCO), Carleton University Press, 1995, pp. 1–12. – reference: P.E. Berman, L. Gravano, G.D. Pifarré, J.L.C. Sanz, Adaptive deadlock and livelock-free routing with all minimal paths in torus networks, in: Fourth Symposium on Parallel Algorithms and Architectures (SPAA), June 1992, pp. 3–12. – volume: C-36 start-page: 547 year: 1987 end-page: 553 ident: BIB5 article-title: Deadlock-free message routing in multiprocessor interconnection networks publication-title: IEEE Trans. Comput. – reference: G.D. Pifarré, L. Gravano, S.A. Felperin, J.L.C. Sanz, Fully-adaptive minimal deadlock-free packet routing in hypercube, meshes, and other networks, in: Third Symposium on Parallel Algorithms and Architectures (SPAA), 1991, pp. 278–290. – reference: J. Duato, On the design of deadlock-free adaptive routing algorithms for multicomputers: theoretical aspects, in: Second European Conference on Distributed Memory Computing, Lecture Notes in Computer Science, Vol. 487, Springer, Berlin, 1991, pp. 234–243. – volume: 43 start-page: 307 year: 1991 end-page: 326 ident: BIB14 article-title: How to emulate shared memory publication-title: J. Comput. Syst. Sci. – reference: J. Duato, Deadlock-free adaptive routing algorithms for multicomputers: evaluation of a new algorithm, in: Third IEEE Symposium on Parallel and Distributed Processing, 1991. – year: 1994 ident: BIB15 publication-title: Introduction to Distributed Algorithms – reference: E. Fleury, P. Fraigniaud, Deadlocks in adaptive wormhole routing, Research Report, Laboratoire de l'Informatique du Parallélisme, LIP, École Normale Supérieure de Lyon, 69364 Lyon, Cedex 07, France, March 1994. – volume: COM-28 start-page: 345 year: 1980 end-page: 352 ident: BIB12 article-title: Deadlock avoidance in store-and-forward networks: store and forward deadlock publication-title: IEEE Trans. Comm. – year: 1977 ident: 10.1016/S0166-218X(02)00232-9_BIB10 – ident: 10.1016/S0166-218X(02)00232-9_BIB9 – volume: 43 start-page: 307 year: 1991 ident: 10.1016/S0166-218X(02)00232-9_BIB14 article-title: How to emulate shared memory publication-title: J. Comput. Syst. Sci. doi: 10.1016/0022-0000(91)90005-P – ident: 10.1016/S0166-218X(02)00232-9_BIB4 doi: 10.1145/135419.135425 – volume: COM-28 start-page: 345 year: 1980 ident: 10.1016/S0166-218X(02)00232-9_BIB12 article-title: Deadlock avoidance in store-and-forward networks: store and forward deadlock publication-title: IEEE Trans. Comm. doi: 10.1109/TCOM.1980.1094666 – volume: COM-29 start-page: 512 year: 1981 ident: 10.1016/S0166-218X(02)00232-9_BIB11 article-title: Prevention of deadlock in packet-switched data transport system publication-title: IEEE Trans. Commun. doi: 10.1109/TCOM.1981.1095021 – ident: 10.1016/S0166-218X(02)00232-9_BIB6 – ident: 10.1016/S0166-218X(02)00232-9_BIB8 doi: 10.1007/BFb0032940 – year: 1994 ident: 10.1016/S0166-218X(02)00232-9_BIB15 – ident: 10.1016/S0166-218X(02)00232-9_BIB7 doi: 10.1109/SPDP.1991.218233 – ident: 10.1016/S0166-218X(02)00232-9_BIB13 doi: 10.1145/113379.113405 – start-page: 149 year: 1992 ident: 10.1016/S0166-218X(02)00232-9_BIB3 article-title: Routage wormhole et canaux virtuel – ident: 10.1016/S0166-218X(02)00232-9_BIB1 doi: 10.1145/112600.112616 – ident: 10.1016/S0166-218X(02)00232-9_BIB2 doi: 10.1145/140901.140902 – volume: C-36 start-page: 547 issue: 5 year: 1987 ident: 10.1016/S0166-218X(02)00232-9_BIB5 article-title: Deadlock-free message routing in multiprocessor interconnection networks publication-title: IEEE Trans. Comput. doi: 10.1109/TC.1987.1676939 |
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| Snippet | Deadlock prevention for routing messages has a central role in communication networks, since it directly influences the correctness of parallel and distributed... In this paper we consider a combinatorial problem consisting in finding an acyclic orientation of a graph which minimizes the maximum number of changes of... |
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| SubjectTerms | Computational and structural complexity Computer Science Data Structures and Algorithms Discrete Mathematics Networking and Internet Architecture Operations Research Parallel algorithms Routing and communication in interconnection networks Social and Information Networks |
| Title | Deadlock prevention by acyclic orientations |
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