Existing exact methods for 4-connected grid pathfinding reduce online search, but often either retain fine-grained search states or require substantial preprocessing. This paper presents Key-Interval A* (KIA*), an optimal pathfinding algorithm that uses lightweight preprocessing to construct and search over a compact interval-level abstraction of free space. KIA* represents free space using intervals: maximal contiguous runs of traversable cells. It extracts key intervals that capture structural boundary changes and connects them through contiguous non-key regions. KIA* then performs A*-style search on the resulting key-interval graph and constructively reconstructs grid paths from interval chains, without cell-level local search. We prove the completeness and optimality of KIA* on 4-connected grids. Experiments on standard benchmarks show that KIA* preserves exact shortest-path lengths and achieves the fastest runtime on seven of eight benchmark groups, with the largest gains on structured and game maps.
Sachin Dev Duggal, Pradyumna Swarnalatha Ramanna, Alexandros Vassiliadescs.AI
This paper proposes a theoretical framework for understanding intelligence as a process of atomic compression and compositional reuse. We argue that cognitive, biological, computational, and organizational systems achieve scalable intelligence by decomposing complex phenomena into reusable atomic units that can be recombined into higher-order structures. Drawing on evidence from cognitive science, information theory, evolutionary biology, software engineering, medicine, legal reasoning, education, music, and artificial intelligence, the paper develops the concept of atomic units as fundamental compression layers that support efficiency, transfer, interpretability, and evolvability. The central contribution is the Compression Calculus, a formal framework for comparing surface-level representations with atomic representations and for describing how compression gains compound across abstraction layers. We introduce the Compounding Cascade thesis, according to which each additional layer of abstraction multiplicatively increases representational efficiency rather than merely adding incremental savings. The paper further argues that contemporary AI systems often operate at suboptimal levels of representation, relying on token-level processing or document-level retrieval rather than stable, concept-level atomic structures. In this view, large language models are best understood not as complete knowledge architectures, but as dynamic fusion engines capable of navigating, sequencing, and recombining atomic units. The framework provides a foundation for designing self-evolving knowledge systems that can discover, refine, and compose new primitives over time. By reframing intelligence as compression through compositional abstraction, the paper offers a unifying perspective on expertise, knowledge representation, explainable AI, and the future architecture of adaptive intelligent systems.