Equity markets have exploded in recent years, not just in share and order volumes but also in the number of trading venues. ­That’s a mixed blessing for the institutional investors that have supported the formation of dozens of alternative sites now challenging the dominance of traditional, established exchanges: The competition puts downward pressure on the costs of executing big institutional trades but has vastly complicated the process of deciding where to go for the fastest and cheapest ­transaction.

For the better part of a decade, technology has solved that “best execution” puzzle — and with ever-­increasing effectiveness. Sophisticated algorithms now require mere micro­seconds to size up conditions and identify market centers ripe for a trade. Then they set a series of transactions in motion through high-speed order-­routing and exe­cution management systems to exchanges and ­other trading platforms the world over; these in turn continually upgrade their...