Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal Analysis of an Online Algorithm for the Bipartite Matching
  Problem on a Line   In the online metric bipartite matching problem, we are given a set $S$ of
server locations in a metric space. Requests arrive one at a time, and on its
arrival, we need to immediately and irrevocably match it to a server at a cost
which is equal to the distance between these locations. A $\alpha$-competitive
algorithm will assign requests to servers so that the total cost is at most
$\alpha$ times the cost of $M_{OPT}$ where $M_{OPT}$ is the minimum cost
matching between $S$ and $R$.
  We consider this problem in the adversarial model for the case where $S$ and
$R$ are points on a line and $|S|=|R|=n$. We improve the analysis of the
deterministic Robust Matching Algorithm (RM-Algorithm, Nayyar and Raghvendra
FOCS'17) from $O(\log^2 n)$ to an optimal $\Theta(\log n)$. Previously, only a
randomized algorithm under a weaker oblivious adversary achieved a competitive
ratio of $O(\log n)$ (Gupta and Lewi, ICALP'12). The well-known Work Function
Algorithm (WFA) has a competitive ratio of $O(n)$ and $\Omega(\log n)$ for this
problem. Therefore, WFA cannot achieve an asymptotically better competitive
ratio than the RM-Algorithm.

10
The categories of this paper are: q-bio
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
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin