Cache-Oblivious Algorithms are algorithms designed to achieve near-optimal cache performance across all levels of the memory hierarchy without requiring knowledge of cache sizes, line sizes, or the number of cache levels — achieving this universality through recursive divide-and-conquer structures that naturally adapt to any cache configuration.

Theoretical Foundation:

• Ideal Cache Model: analysis assumes a two-level memory hierarchy with cache size M and line size B; an algorithm is cache-oblivious if it achieves optimal cache complexity Q(N;M,B) without M or B as parameters — the performance automatically extends to all levels (L1, L2, L3, DRAM, disk)
• Tall Cache Assumption: analysis requires M = Ω(B²) — cache is big enough to hold at least B cache lines; satisfied by all practical caches (L1: 32KB with 64B lines → B²=4KB ≪ M)
• Optimal Bounds: cache-oblivious matrix multiply achieves Q = O(N³/(B√M)), matching cache-aware lower bound; cache-oblivious sorting achieves Q = O((N/B) log_{M/B}(N/B)), matching external-memory sorting bound
• Universality: since the algorithm doesn't use M or B parameters, the same binary achieves near-optimal performance on machines with different cache sizes — no tuning, no recompilation, no architecture-specific parameters

Core Algorithmic Patterns:

• Recursive Matrix Multiply: divide each matrix into 4 quadrants recursively until base case fits in cache; multiply quadrants using 8 recursive multiplications and additions; cache complexity emerges from the recursion naturally matching cache line size at the appropriate depth
• Cache-Oblivious Stencil: space-time tiling using trapezoidal decomposition — divide 1D stencil computation into space-time trapezoids that recurse until fitting in cache; generalizes to 2D/3D stencils with hyperplane cuts
• Funnel Sort: K-way merge using a funnelsort tree; K-funnel recursively merges K^(1/2) sorted sequences using K^(1/2) sub-funnels; achieves optimal O((N/B) log_{M/B}(N/B)) I/O complexity
• Van Emde Boas Layout: stores a binary tree in memory using recursive decomposition — top half of tree stored contiguously, then bottom subtrees stored recursively; achieves O(log_B N) cache misses per search

Practical Considerations:

• Constant Factors: cache-oblivious algorithms often have 2-5× larger constant factors than cache-aware counterparts due to recursive overhead and suboptimal base cases — matters for small-to-medium problem sizes
• Base Case Optimization: switching from recursion to iterative, cache-aware kernels at small sizes (fitting in L1) hybridizes the approach — cache-oblivious for outer levels, tuned kernels for inner
• Prefetch Interaction: hardware prefetchers optimized for sequential/strided patterns may perform poorly with recursive access patterns — software prefetch hints can help bridge the gap
• TLB Effects: recursive decomposition can increase TLB pressure if working sets span many virtual pages — huge pages (2MB/1GB) mitigate TLB miss penalties

Cache-oblivious algorithms represent a profound theoretical contribution showing that explicit cache management is unnecessary for achieving optimal memory hierarchy utilization — though in practice they are most valuable for portable library code and multi-level cache hierarchies where manual tuning of architecture-specific parameters is infeasible.