Efficient dispersal of information for security, load balancing, and fault tolerance
Journal of the ACM (JACM)
Combinatorial algorithms for integrated circuit layout
Combinatorial algorithms for integrated circuit layout
A linear time algorithm for unique Horn satisfiability
Information Processing Letters
Realization of an arbitrary permutation on a hypercube
Information Processing Letters
k-Pairwise Cluster Fault Tolerant Routing in Hypercubes
IEEE Transactions on Computers
Routing a permutation in the hypercube by two sets of edge disjoint paths
Journal of Parallel and Distributed Computing
Node-to-set and set-to-set cluster fault tolerant routing in hypercubes
Parallel Computing
From Hall's matching theorem to optimal routing on hypercubes
Journal of Combinatorial Theory Series B
Complexity and approximations for multimessage multicasting
Journal of Parallel and Distributed Computing
Node-Disjoint Paths on the Mesh and a New Trade-Off in VLSI Layout
SIAM Journal on Computing
The two paths problem is polynomial
The two paths problem is polynomial
Pairwise edge disjoint shortest paths in the n-cube
Theoretical Computer Science
Optimizing two-dimensional search results presentation
Proceedings of the fourth ACM international conference on Web search and data mining
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In parallel and distributed systems many communications take place concurrently. The efficient delivery of all the messages depends on the routing algorithms as well as the underlying interconnection network topology. The grid is a planar network topology that lends itself for efficient VLSI implementation and therefore is of interest for theoretical analysis. Frequently, networks and switches achieve high performance by delivering the messages through shortest paths. In addition, network fault tolerance improves through insuring that the traversed paths are both edge and/or node disjoint. The edge disjoint criterion is useful when network links are the predominant constraint, and the node disjoint criterion becomes important when switches are the fault tolerant bottleneck. Because the latter necessarily implies the former, it is apparent that node disjointness contributes to fault tolerance and enhanced performance. In this paper, we examine the k-pairwise node and edge disjoint shortest paths problem in the undirected graph topology of the grid. Herein it is shown that the k-pairwise node as well as the k-pairwise edge disjoint shortest paths decision problems are NP-hard, and remain NP-hard even for many different restrictions on the problem. We also discuss polynomial time algorithms for restricted versions of our problems.