Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Trade-offs between Selection Complexity and Performance when Searching
  the Plane without Communication   We consider the ANTS problem [Feinerman et al.] in which a group of agents
collaboratively search for a target in a two-dimensional plane. Because this
problem is inspired by the behavior of biological species, we argue that in
addition to studying the {\em time complexity} of solutions it is also
important to study the {\em selection complexity}, a measure of how likely a
given algorithmic strategy is to arise in nature due to selective pressures. In
more detail, we propose a new selection complexity metric $\chi$, defined for
algorithm ${\cal A}$ such that $\chi({\cal A}) = b + \log \ell$, where $b$ is
the number of memory bits used by each agent and $\ell$ bounds the fineness of
available probabilities (agents use probabilities of at least $1/2^\ell$). In
this paper, we study the trade-off between the standard performance metric of
speed-up, which measures how the expected time to find the target improves with
$n$, and our new selection metric.
  In particular, consider $n$ agents searching for a treasure located at
(unknown) distance $D$ from the origin (where $n$ is sub-exponential in $D$).
For this problem, we identify $\log \log D$ as a crucial threshold for our
selection complexity metric. We first prove a new upper bound that achieves a
near-optimal speed-up of $(D^2/n +D) \cdot 2^{O(\ell)}$ for $\chi({\cal A})
\leq 3 \log \log D + O(1)$. In particular, for $\ell \in O(1)$, the speed-up is
asymptotically optimal. By comparison, the existing results for this problem
[Feinerman et al.] that achieve similar speed-up require $\chi({\cal A}) =
\Omega(\log D)$. We then show that this threshold is tight by describing a
lower bound showing that if $\chi({\cal A}) < \log \log D - \omega(1)$, then
with high probability the target is not found within $D^{2-o(1)}$ moves per
agent. Hence, there is a sizable gap to the straightforward $\Omega(D^2/n + D)$
lower bound in this setting.

27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
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The categories of this paper are: nlin