Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Competitive Analysis for Two Variants of Online Metric Matching Problem   In this paper, we study two variants of the online metric matching problem.
The first problem is the online metric matching problem where all the servers
are placed at one of two positions in the metric space. We show that a simple
greedy algorithm achieves the competitive ratio of 3 and give a matching lower
bound. The second problem is the online facility assignment problem on a line,
where servers have capacities, servers and requests are placed on 1-dimensional
line, and the distances between any two consecutive servers are the same. We
show lower bounds $1+ \sqrt{6}$ $(> 3.44948)$, $\frac{4+\sqrt{73}}{3}$
$(>4.18133)$ and $\frac{13}{3}$ $(>4.33333)$ on the competitive ratio when the
numbers of servers are 3, 4 and 5, respectively.

8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
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The categories of this paper are: nlin