Partial is Full

Abstract

AbstractLink reversal is the basis of several well-known routing algorithms [1,2,3]. In these algorithms, logical directions are imposed on the communication links and a node that becomes a sink reverses some of its incident links to allow the (re)construction of paths to the destination. In the Full Reversal (FR) algorithm [1], a sink reverses all its incident links. In other schemes, a sink reverses only some of its incident links; a notable example is the Partial Reversal (PR) algorithm [1]. Prior work [4] has introduced a generalization, called LR, of link-reversal routing, including FR and PR. In this paper, we show that every execution of LR on any link-labeled input graph corresponds, in a precise sense, to an execution of FR on a transformed graph. Thus, all the link reversal schemes captured by LR can be reduced to FR, indicating that “partial is full.” The correspondence preserves the work and time complexities. As a result, we can, for the first time, obtain the exact time complexity for LR, and by specialization for PR.KeywordsTime ComplexityDirected GraphSink NodePartial ReversalRoute ProblemThese 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.