Deterministic Self-Adjusting Tree Networks Using Rotor Walks

Chen Avin, Marcin Bienkowski, Iosif Salem, Robert Sama, Stefan Schmid, Pawel Schmidt

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

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. [12] (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 RANDOM-PUSH, 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 single-source tree networks, using both synthetic and real data. In particular, we shed light on the extent to which these self-adjusting trees can exploit temporal and spatial structure in the workload. Our experimental artefacts and source codes are publicly available.

Original languageEnglish
Title of host publicationProceedings - 2022 IEEE 42nd International Conference on Distributed Computing Systems, ICDCS 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages67-77
Number of pages11
ISBN (Electronic)9781665471770
DOIs
StatePublished - 1 Jan 2022
Event42nd IEEE International Conference on Distributed Computing Systems, ICDCS 2022 - Bologna, Italy
Duration: 10 Jul 202213 Jul 2022

Publication series

NameProceedings - International Conference on Distributed Computing Systems
Volume2022-July

Conference

Conference42nd IEEE International Conference on Distributed Computing Systems, ICDCS 2022
Country/TerritoryItaly
CityBologna
Period10/07/2213/07/22

Keywords

  • competitive analysis
  • list update
  • online algorithms
  • rotor walks
  • self adjusting networks

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Networks and Communications

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