Push-Down Trees: Optimal Self-Adjusting Complete Trees

This paper studies a fundamental algorithmic problem related to the design of demand-aware networks: networks whose topologies adjust toward traffic patterns they serve, in an online manner. The goal is strike tradeoff between benefits such adjustments (shorter routes) and their costs (reconfigurations). In particular, we consider designing self-adjusting tree network which serves single-source, multi-destination communication. central building block for more general designs has interesting connections datastructures. We present two constant-competitive algorithms this problem, one randomized deterministic. Our approach based on natural notion Most Recently Used (MRU) tree, maintaining working set. prove that set cost lower bound any algorithm, then algorithm RANDOM- PUSH approximates MRU at low cost, by pushing less recently used communication partners down along random walk. deterministic Move-Half does not directly maintain but its still proportional also matches bound.