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Tiling has long been used to improve cache performance. Recursion hers 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 to 10× improvement in execution time. We also address Dijkstra's algorithm for the single-source shortest path problem and Prim's algorithm for Minimum Spanning Tree, for which neither tiling nor recursion can be directly applied. For these algorithms, we demonstrate up to a 2× improvement by using a cache friendly graph representation. Experimental results are shown for the Pentium Ill, UltraSPARC Ill, Alpha 21264, and MIPS R12000 machines using problem sizes between 1024 and 4096 vertices. We demonstrate improved cache performance using the Simplescalar simulator.