  Auctions are widely used in exchanges to match buy and sell requests. Once
the buyers and sellers place their requests, the exchange determines how these
requests are to be matched. The two most popular objectives used while
determining the matching are maximizing volume at a uniform price and
maximizing volume with dynamic pricing. In this work, we study the algorithmic
complexity of the problems arising from these matching tasks.
  We present a linear time algorithm for uniform price matching which is an
improvement over the previous algorithms that take $O(n\log n)$ time to match
$n$ requests. For dynamic price matching, we establish a lower bound of
$\Omega(n \log n)$ on the running time, thereby proving that the currently
known best algorithm is time-optimal.
