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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Veröffentlicht in:Discrete Applied Mathematics Jg. 129; H. 1; S. 31 - 47
Hauptverfasser: Bermond, Jean-Claude, Ianni, Miriam Di, Flammini, Michele, Pérennès, Stéphane
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 15.06.2003
Elsevier
Schlagworte:
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
Computational and structural complexity
Parallel algorithms
Routing and communication in interconnection networks
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.
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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  organization: MASCOTTE Project I3S-CNRS/Université de Nice-Sophia Antipolis/INRIA, 2004 Route des Lucioles, BP93, F-06902 Sophia-Antipolis, Cedex France
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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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Issue 1
Keywords Computational and structural complexity
Parallel algorithms
Routing and communication in interconnection networks
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References J. Duato, Deadlock-free adaptive routing algorithms for multicomputers: evaluation of a new algorithm, in: Third IEEE Symposium on Parallel and Distributed Processing, 1991.
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.
Bermond, Syska (BIB3) 1992
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.
Merlin, Schweitzer (BIB12) 1980; COM-28
Ranade (BIB14) 1991; 43
Dally, Seitz (BIB5) 1987; C-36
Gunther (BIB11) 1981; COM-29
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.
Garey, Johnson (BIB10) 1977
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.
Tel (BIB15) 1994
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.
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.
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.
Merlin (10.1016/S0166-218X(02)00232-9_BIB12) 1980; COM-28
Ranade (10.1016/S0166-218X(02)00232-9_BIB14) 1991; 43
Bermond (10.1016/S0166-218X(02)00232-9_BIB3) 1992
Garey (10.1016/S0166-218X(02)00232-9_BIB10) 1977
10.1016/S0166-218X(02)00232-9_BIB2
10.1016/S0166-218X(02)00232-9_BIB4
10.1016/S0166-218X(02)00232-9_BIB1
Tel (10.1016/S0166-218X(02)00232-9_BIB15) 1994
Gunther (10.1016/S0166-218X(02)00232-9_BIB11) 1981; COM-29
Dally (10.1016/S0166-218X(02)00232-9_BIB5) 1987; C-36
10.1016/S0166-218X(02)00232-9_BIB6
10.1016/S0166-218X(02)00232-9_BIB7
10.1016/S0166-218X(02)00232-9_BIB13
10.1016/S0166-218X(02)00232-9_BIB8
10.1016/S0166-218X(02)00232-9_BIB9
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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