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On-chip interconnect structures become much more complicated and dominate system performance in multicore system-on-chips. Oscillation ring (OR) test is an efficient test method for most types of faults in the interconnect structures, and previous studies show that both 100% fault coverage and the optimum diagnosis resolution for various fault models are achievable. The cost of OR test is decided by the number of test sessions required to form all the rings. Previous ring generation algorithm tries to generate long rings that usually cannot be put into the same test session, and thus the number of test sessions is not necessarily smaller. In this brief, we study techniques to generate rings that can be tested concurrently, so that the overall test time can be reduced significantly.