From the post:
Application Integration is the biggest cost driver of corporate IT. While it has been popular to emphasise the business process integration aspects of EAI, it remains true that data integration is a huge part of the problem, responsible for much of the cost of EAI. You cannot begin to do process integration without some data integration.
Data integration is an N-squared problem. If you have N different systems or sources of data to integrate, you may need to build as many as N(N -1) different data exchange interfaces between them – near enough to N2. For large companies, where N may run into the hundreds, and N2 may be more than 100,000, this looks an impossible problem.
In practice, the figures are not quite that huge. In our experience, a typical system may interface to between 5 and 30 other systems – so the total number of interfaces is between 5N and 30N. Even this makes a prohibitive number of data interfaces to build and maintain. Many IT managers quietly admit that they just cannot maintain the necessary number of data interfaces, because the cost would be prohibitive. Then business users are forced to live with un-integrated, inconsistent data and fragmented processes, at great cost to the business.
The bad news is that N just got bigger. New commercial imperatives, the rise of e-commerce, XML and web services require companies of all sizes to integrate data and processes with their business partners’ data and processes. If you make an unsolved problem bigger, it generally remains unsolved.
I was searching for N-squared references when I encountered this paper. You can see what I think is the topic map answer to the N-squared problem at: Semantic Integration: N-Squared to N+1 (and decentralized).