Deadlock-Free Message Routing in Multiprocessor Interconnection Networks
IEEE Transactions on Computers
Journal of Computer and System Sciences
On the design of deadlock-free adaptive routing algorithms for multicomputers: theoretical aspects
EDMCC2 Proceedings of the 2nd European conference on Distributed memory computing
Efficient deadlock-free routing
PODC '91 Proceedings of the tenth annual ACM symposium on Principles of distributed computing
Fully-adaptive minimal deadlock-free packet routing in hypercubes, meshes, and other networks
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
Requirements for deadlock-free, adaptive packet routing
PODC '92 Proceedings of the eleventh annual ACM symposium on Principles of distributed computing
Adaptive deadlock- and livelock-free routing with all minimal paths in Torus networks
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
Introduction to distributed algorithms
Introduction to distributed algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Ranks of graphs: The size of acyclic orientation cover for deadlock-free packet routing
Theoretical Computer Science
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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.