Online weighted matching problem is a fundamental problem in machine learning
due to its numerous applications. Despite many efforts in this area, existing
algorithms are either too slow or don't take deadline (the longest
time a node can be matched) into account. In this paper, we introduce a market
model with deadline first. Next, we present our two optimized
algorithms (\textsc{FastGreedy} and \textsc{FastPostponedGreedy}) and offer
theoretical proof of the time complexity and correctness of our algorithms. In
\textsc{FastGreedy} algorithm, we have already known if a node is a buyer or a
seller. But in \textsc{FastPostponedGreedy} algorithm, the status of each node
is unknown at first. Then, we generalize a sketching matrix to run the original
and our algorithms on both real data sets and synthetic data sets. Let
Ο΅β(0,0.1) denote the relative error of the real weight of each
edge. The competitive ratio of original \textsc{Greedy} and
\textsc{PostponedGreedy} is 21β and 41β respectively. Based
on these two original algorithms, we proposed \textsc{FastGreedy} and
\textsc{FastPostponedGreedy} algorithms and the competitive ratio of them is
21βΟ΅β and 41βΟ΅β respectively. At the same
time, our algorithms run faster than the original two algorithms. Given n
nodes in Rd, we decrease the time complexity from O(nd) to
O(Ο΅β2β (n+d))