Before revision:  We demonstrate the application of local information cost by deriving a lower bound on the communication complexity of computing a (2t-1)-spanner that consists of at most O(n^{1+ \frac{1 + \epsilon})
After revision:  We demonstrate the application of_\gamma(P)/ \log\tau \log n) bits are required for solving a graph problem P with a \tau-round algorithm that errs with probability at most \gamma. Our result is the first lower bound that yields a general trade-off between communication and time for graph problems in the CONGEST-KT1 model. We demonstrate how to apply the local information cost by deriving a lower bound on the communication complexity of computing a (2t-1)-spanner that consists of at most O(n^{1+ \frac{1 + \epsilon})