The goal of cryptocurrencies is decentralization. In principle, all
currencies have equal status. Unlike traditional stock markets, there is no
default currency of denomination (fiat), thus the trading pairs can be set
freely. However, it is impractical to set up a trading market between every two
currencies. In order to control management costs and ensure sufficient
liquidity, we must give priority to covering those large-volume trading pairs
and ensure that all coins are reachable. We note that this is an optimization
problem. Its particularity lies in: 1) the trading volume between most (>99.5%)
possible trading pairs cannot be directly observed. 2) It satisfies the
connectivity constraint, that is, all currencies are guaranteed to be tradable.
To solve this problem, we use a two-stage process: 1) Fill in missing values
based on a regularized, truncated eigenvalue decomposition, where the
regularization term is used to control what extent missing values should be
limited to zero. 2) Search for the optimal trading pairs, based on a branch and
bound process, with heuristic search and pruning strategies.
The experimental results show that: 1) If the number of denominated coins is
not limited, we will get a more decentralized trading pair settings, which
advocates the establishment of trading pairs directly between large currency
pairs. 2) There is a certain room for optimization in all exchanges. The
setting of inappropriate trading pairs is mainly caused by subjectively setting
small coins to quote, or failing to track emerging big coins in time. 3) Too
few trading pairs will lead to low coverage; too many trading pairs will need
to be adjusted with markets frequently. Exchanges should consider striking an
appropriate balance between them.

加密货币交易对最优化问题的解决方法：使用基于正则化截断特征值分解的方法填补缺失值，然后使用启发式搜索和修剪策略的分支限界过程来搜索最优交易对，实验结果显示应在交易对数量、涵盖面与频繁调整间权衡取得合适平衡。