Data Access Complexity: Monotonicity and Proportionality.

Computational complexity characterizes a program's resource requirements, most commonly time and space. Locality complexity characterizes the asymptotic behavior of cache memory as program inputs and cache sizes vary. This paper presents two properties of locality complexity. First, Monotonicity: complexity is non-decreasing with input size, a property proven for fully associative LRU and working-set caches. Second, Proportionality: with optimal cache management, performance improves at least linearly with cache size. This property is universal, holding for all programs and inputs.