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Tiling has long been used to improve cache performance. Recursion has recently been used as a cache-oblivious method of improving cache performance. Both of these techniques are normally applied to dense linear algebra problems. We develop new implementations by means of these two techniques for the fundamental graph problem of Transitive Closure, namely the Floyd-Warshall Algorithm, and prove their optimality with respect to processor-memory traffic. Using these implementations we show up todoi:10.1109/tpds.2004.44 fatcat:knegwttiirgzbon755jkezo3ni