Abstract
The forwarding index problem is, given a connected graph G and an integer k, finding a way of connecting each ordered pair of vertices by a path so that every vertex is an internal point of at most k such paths. Such a problem arises in the design of communication networks and parallel architectures, a model of parallel computation being represented by a network of processors or machines processing and forwarding(synchronous) messages to each other and a physical constraint on the number of messages that can be processed by a single machine. In this paper, the author proves that the forwarding index problem is NP-complete even if the diameter of the graph is 2, thereby answering a question of F. Chung et al. [IEEE Trans. Inform. Theory, 33 (1987), pp. 224–232] concerning the complexity of the problem.
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