We revisit the design of self-adjusting single-source tree networks. The problem can be seen as a generalization of the classic list update problem to trees, and finds applications in reconfigurable datacenter networks. We are given a balanced binary tree T connecting n nodes V = {v1, . . . , vn}. A source node v0, attached to the root of the tree, issues communication requests to nodes in V , in an online and adversarial manner; the access cost of a request to a node v, is given by the current depth of v in T. The online algorithm can try to reduce the access cost by performing swap operations, with which the position of a node is exchanged with the position of its parent in the tree; a swap operation costs one unit. The objective is to design an online algorithm which minimizes the total access cost plus adjustment cost (swapping). Avin et al. [10] (LATIN 2020) recently presented RANDOM-PUSH, a constant competitive online algorithm for this problem, based on random walks, together with a sophisticated analysis exploiting the working set property. This paper studies analytically and empirically, online algorithms for this problem. In particular, we explore how to derandomize RANDOM-PUSH. In the analytical part, we consider a simple derandomized algorithm which we call ROTOR-PUSH, as its behavior is reminiscent of rotor walks. Our first contribution is a proof that ROTOR-PUSH is constant competitive: its competitive ratio is 12 and hence by a factor of five lower than the best existing competitive ratio. Interestingly, in contrast to RANDOMPUSH, the algorithm does not feature the working set property, which requires a new analysis. We further present a significantly improved and simpler analysis for the randomized algorithm, showing that it is 16-competitive. In the empirical part, we compare all self-adjusting singlesource tree networks, using both synthetic and real data. In particular, we shed light on the extent to which these selfadjusting trees can exploit temporal and spatial structure in the workload. As a contribution to the research community and to ensure reproducibility, we will make available all our experimental artefacts and source codes.

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