Deadlock-free interval routing schemes

Abstract

k-Interval Labeling Schemes (k-ILS) are compact routing schemes on general networks which have been studied extensively and recently been implemented on the latest generation INMOS Transputer Router chips. In this paper we introduce an extension of the k-ILS to the 〈k, s∼>-DFILS (Deadlock-Free ILS), where k is the number of intervals and s is the number of buffers used at each node or edge to prevent deadlock. Whereas k-ILS only compactly represents shortest paths between pairs of nodes, this new extension aims to represent those particular ones that give rise also to deadlock-free routing controllers which use a low number of buffers per node or per edge. In this paper we prove new NP-hardness results on the problem of devising low occupancy schemes, also for classical k-ILS. Moreover, while space complexity results are given for 〈k, s∼>-DFILS in arbitrary networks, tight results are shown for specific topologies, such as trees, rings, grids, complete graphs and chordal rings. Finally, trade-offs are derived between the number of intervals k and the number of buffers s in Deadlock-Free Interval Routing Schemes for hypercubes, grids, tori and Cartesian products of graphs.KeywordsShort PathInterconnection NetworkSimple PathLinear IntervalDeadlock PreventionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.