Push-Down Trees: Optimal Self-Adjusting Complete Trees

Chen Avin, Kaushik Mondal, Stefan Schmid

Research output: Contribution to journalArticlepeer-review


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

Original languageAmerican English
Pages (from-to)2419-2432
Number of pages14
JournalIEEE/ACM Transactions on Networking
Issue number6
StatePublished - 1 Dec 2022


  • Reconfigurable networks
  • competitive analysis
  • online algorithms
  • self-adjusting datastructures

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Science Applications
  • Computer Networks and Communications
  • Electrical and Electronic Engineering


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