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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Zusammenfassung: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.
ISSN:0166-218X
1872-6771
DOI:10.1016/S0166-218X(02)00232-9