Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing Minimum Spanning Trees with Uncertainty   We consider the minimum spanning tree problem in a setting where information
about the edge weights of the given graph is uncertain. Initially, for each
edge $e$ of the graph only a set $A_e$, called an uncertainty area, that
contains the actual edge weight $w_e$ is known. The algorithm can `update' $e$
to obtain the edge weight $w_e \in A_e$. The task is to output the edge set of
a minimum spanning tree after a minimum number of updates. An algorithm is
$k$-update competitive if it makes at most $k$ times as many updates as the
optimum. We present a 2-update competitive algorithm if all areas $A_e$ are
open or trivial, which is the best possible among deterministic algorithms. The
condition on the areas $A_e$ is to exclude degenerate inputs for which no
constant update competitive algorithm can exist. Next, we consider a setting
where the vertices of the graph correspond to points in Euclidean space and the
weight of an edge is equal to the distance of its endpoints. The location of
each point is initially given as an uncertainty area, and an update reveals the
exact location of the point. We give a general relation between the edge
uncertainty and the vertex uncertainty versions of a problem and use it to
derive a 4-update competitive algorithm for the minimum spanning tree problem
in the vertex uncertainty model. Again, we show that this is best possible
among deterministic algorithms.

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The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex