We present EWLR (Entropy-Weighted Lazy Restructuring), a self-organizing data structure that minimizes unnecessary restructuring operations by combining two orthogonal signals: regional access frequency (heat) and local structural disorder (entropy). Traditional adaptive structures, such as Splay Trees, restructure on every access; learned indexes such as ALEX restructure when their distribution model drifts. EWLR introduces a joint trigger: restructure region B only when H(B) × E(B) > τ, where H is exponentially-decayed access heat, E is a two-component disorder score, and τ is a threshold learned online via exponential moving average. We prove formally that EWLR is the first data structure where the restructuring predicate is a simultaneous function of both H and E. We derive a closed-form cost model showing EWLR achieves lower total system cost than RB Tree when the per-restructure cost exceeds R* = (q · ΔS)/ΔR, and lower cost than ALEX when R > 0.23 μs — below the latency of any storage device. On real S&P 500 market price data across 30 independent runs, EWLR reduces restructuring operations by 99.4% compared to RB Trees and 90–95% compared to ALEX, with a measured crossover of R* = −0.69 μs on the S&P 500 workload. Our C implementation achieves O(log n) insert, search, and delete via a bucket index, yielding a 31.58× speedup over the O(n) baseline, thread safety via per-bucket locking with a lock-free read path, and a Bayesian cold-start predictor that eliminates the circular pre-warming problem. EWLR is positioned as complementary to learned indexes: it excels where distribution shift makes model-based approaches stale.
Aniruddha Ravindrakumar Tayade (Tue,) studied this question.