Push-Down Trees: Optimal Self-Adjusting Complete Trees

Chen Avin, Kaushik Mondal, Stefan Schmid

Research output: Contribution to journalArticlepeer-review

Abstract

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 \ONRAND 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 \ONDET 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 languageEnglish
Pages (from-to)1-14
Number of pages14
JournalIEEE/ACM Transactions on Networking
DOIs
StateAccepted/In press - 1 Jan 2022

Keywords

  • Approximation algorithms
  • competitive analysis.
  • Costs
  • Heuristic algorithms
  • Network topology
  • online algorithms
  • Reconfigurable networks
  • Routing
  • self-adjusting datastructures
  • Servers
  • Topology

ASJC Scopus subject areas

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

Fingerprint

Dive into the research topics of 'Push-Down Trees: Optimal Self-Adjusting Complete Trees'. Together they form a unique fingerprint.

Cite this