Self-Stabilizing Task Allocation in Spite of Noise

Anna Dornhaus, Nancy Lynch, Frederik Mallmann-Trenn, Dominik Pajak, Tsvetomira Radeva

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study the problem of distributed task allocation by workers in an ant colony in a setting of limited capabilities and noisy environment feedback. We assume that each task has a demand that should be satisfied but not exceeded, i.e., there is an optimal number of ants that should be working on this task at a given time. The goal is to assign a near-optimal number of workers to each task in a distributed manner without explicit access to the value of the demand nor to the number of ants working on the task. We seek to answer the question of how the quality of task allocation depends on the accuracy of assessing by the ants whether too many (overload) or not enough (lack) ants are currently working on a given task. In our model, each ant receives a binary feedback that depends on the deficit, defined as the difference between the demand and the current number of workers in the task. The feedback is modeled as a random variable that takes values lack or overload with probability given by a sigmoid function of the deficit. The higher the overload or lack of workers for a task, the more likely it is that an ant receives the correct feedback from this task; the closer the deficit is to zero, the less reliable the feedback becomes. Each ant receives the feedback independently about one chosen task. We measure the performance of task allocation algorithms using the notion of inaccuracy, defined as the number of steps in which the deficit of some task is beyond certain threshold. We propose a simple, constant-memory, self-stabilizing, distributed algorithm that converges from any initial assignment to a near-optimal assignment under noisy feedback and keeps the deficit small for all tasks in almost every step. We also prove a lower bound for any constant-memory algorithm, which matches, up to a constant factor, the accuracy achieved by our algorithm.

Original languageEnglish (US)
Title of host publicationSPAA 2020 - Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures
PublisherAssociation for Computing Machinery
Pages201-211
Number of pages11
ISBN (Electronic)9781450369350
DOIs
StatePublished - Jul 6 2020
Event32nd ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2020 - Virtual, Online, United States
Duration: Jul 15 2020Jul 17 2020

Publication series

NameAnnual ACM Symposium on Parallelism in Algorithms and Architectures

Conference

Conference32nd ACM Symposium on Parallelism in Algorithms and Architectures, SPAA 2020
Country/TerritoryUnited States
CityVirtual, Online
Period7/15/207/17/20

Keywords

  • ants
  • biologically inspired algorithms
  • noise
  • task-allocation

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture

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