In modern software development, software libraries play a crucial role in reducing software development effort and improving software quality. However, at the same time, the asynchronous upgrades of software libraries and client software projects often result in incompatibilities between different versions of libraries and client projects. When libraries evolve, it is often very challenging for library developers to maintain the so-called backward compatibility and keep all their external behavior untouched, and behavioral backward incompatibilities (BBIs) may occur. In practice, the regression test suites of library projects often fail to detect all BBIs. Therefore, in this paper, we propose DeBBI to detect BBIs via cross-project testing and analysis, i.e., using the test suites of various client projects to detect library BBIs. Since executing all the possible client projects can be extremely time consuming, DeBBI transforms the problem of cross-project BBI detection into a traditional information retrieval (IR) problem to execute the client projects with higher probability to detect BBIs earlier. Furthermore, DeBBI considers project diversity and test relevance information for even faster BBI detection. The experimental results show that DeBBI can reduce the end-to-end testing time for detecting the first and average unique BBIs by 99.1% and 70.8% for JDK compared to naive cross-project BBI detection. Also, DeBBI has been applied to other popular 3rd-party libraries, and detected 19 BBI bugs (with 3 already confirmed as previously unknown bugs).