Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Improved Local Search Algorithm for k-Median   We present a new local-search algorithm for the $k$-median clustering
problem. We show that local optima for this algorithm give a
$(2.836+\epsilon)$-approximation; our result improves upon the
$(3+\epsilon)$-approximate local-search algorithm of Arya et al. [STOC 01].
Moreover, a computer-aided analysis of a natural extension suggests that this
approach may lead to an improvement over the best-known approximation guarantee
for the problem. The new ingredient in our algorithm is the use of a potential
function based on both the closest and second-closest facilities to each
client. Specifically, the potential is the sum over all clients, of the
distance of the client to its closest facility, plus (a small constant times)
the truncated distance to its second-closest facility. We move from one
solution to another only if the latter can be obtained by swapping a constant
number of facilities, and has a smaller potential than the former. This refined
potential allows us to avoid the bad local optima given by Arya et al. for the
local-search algorithm based only on the cost of the solution.

36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
2
The categories of this paper are: math
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas