2026-07-22T21:50:42Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:16360 2024-03-06T10:57:16Z ddc:004 open_access

Memoryless Worker-Task Assignment with Polylogarithmic Switching Cost Berger, Aaron Kuszmaul, William Polak, Adam Tidor, Jonathan Wein, Nicole Distributed Task Allocation Metric Embeddings Probabilistic Method We study the basic problem of assigning memoryless workers to tasks with dynamically changing demands. Given a set of w workers and a multiset T ⊆ [t] of |T| = w tasks, a memoryless worker-task assignment function is any function ϕ that assigns the workers [w] to the tasks T based only on the current value of T. The assignment function ϕ is said to have switching cost at most k if, for every task multiset T, changing the contents of T by one task changes ϕ(T) by at most k worker assignments. The goal of memoryless worker task assignment is to construct an assignment function with the smallest possible switching cost. In past work, the problem of determining the optimal switching cost has been posed as an open question. There are no known sub-linear upper bounds, and after considerable effort, the best known lower bound remains 4 (ICALP 2020). We show that it is possible to achieve polylogarithmic switching cost. We give a construction via the probabilistic method that achieves switching cost O(log w log (wt)) and an explicit construction that achieves switching cost polylog (wt). We also prove a super-constant lower bound on switching cost: we show that for any value of w, there exists a value of t for which the optimal switching cost is w. Thus it is not possible to achieve a switching cost that is sublinear strictly as a function of w. Finally, we present an application of the worker-task assignment problem to a metric embeddings problem. In particular, we use our results to give the first low-distortion embedding from sparse binary vectors into low-dimensional Hamming space. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Aaron Berger and William Kuszmaul and Adam Polak and Jonathan Tidor and Nicole Wein 2022 Is Part Of LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2022.19 urn:nbn:de:0030-drops-163608 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.19 eng https://creativecommons.org/licenses/by/4.0/legalcode