Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tree exploration in dual-memory model   We study the problem of online tree exploration by a deterministic mobile
agent. Our main objective is to establish what features of the model of the
mobile agent and the environment allow linear exploration time. We study agents
that, upon entering to a node, do not receive as input the edge via which they
entered. In such a model, deterministic memoryless exploration is infeasible,
hence the agent needs to be allowed to use some memory. The memory can be
located at the agent or at each node. The existing lower bounds show that if
the memory is either only at the agent or only at the nodes, then the
exploration needs superlinear time. We show that tree exploration in
dual-memory model, with constant memory at the agent and logarithmic at each
node is possible in linear time when one of two additional features is present:
fixed initial state of the memory at each node (so called clean memory) or a
single movable token. We present two algorithms working in linear time for
arbitrary trees in these two models. On the other hand, in our lower bound we
show that if the agent has a single bit of memory and one bit is present at
each node, then exploration may require quadratic time on paths, if the initial
memory at nodes could be set arbitrarily (so called dirty memory). This shows
that having clean node memory or a token allows linear exploration of trees in
the model with two types of memory, but having neither of those features may
lead to quadratic exploration time even on a simple path.

9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th