Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: One Tree Suffices: A Simultaneous O(1)-Approximation for Single-Sink
  Buy-at-Bulk   We study the single-sink buy-at-bulk problem with an unknown cost function.
We wish to route flow from a set of demand nodes to a root node, where the cost
of routing x total flow along an edge is proportional to f(x) for some concave,
non-decreasing function f satisfying f(0)=0. We present a simple, fast,
combinatorial algorithm that takes a set of demands and constructs a single
tree T such that for all f the cost f(T) is a 47.45-approximation of the
optimal cost for that f. This is within a factor of 2.33 of the best
approximation ratio currently achievable when the tree can be optimized for a
specific function. Trees achieving simultaneous O(1)-approximations for all
concave functions were previously not known to exist regardless of computation
time.

18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat