Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Memoryless Worker-Task Assignment with Polylogarithmic Switching Cost   We study the basic problem of assigning memoryless workers to tasks with
dynamically changing demands. Given a set of $w$ workers and a multiset $T
\subseteq[t]$ of $|T|=w$ tasks, a memoryless worker-task assignment function is
any function $\phi$ that assigns the workers $[w]$ to the tasks $T$ based only
on the current value of $T$. The assignment function $\phi$ is said to have
switching cost at most $k$ if, for every task multiset $T$, changing the
contents of $T$ by one task changes $\phi(T)$ 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
$\operatorname{polylog} (wt)$. 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.

23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
2
The categories of this paper are: math
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn