Slabicedepends

Slabicedepends is a conceptual framework for describing how dependencies are managed in slab-based computations. The idea applies when a large problem is partitioned into slabs, which are processed in sequence or concurrently depending on data availability. Slabs represent the unit of work, and dependencies capture the requirement that some slabs must complete or produce data before others can begin.

Core concepts include preparation of slab units, directed dependency relations among slabs, a readiness condition that a slab can start, and a scheduling policy that orders slabs to maximize parallelism while ensuring correctness.

Implementation often uses a dependency graph (often a directed acyclic graph). A topological sort or dynamic scheduler determines an execution order; in streaming or online scenarios, readiness can be detected on the fly. While slabicedepends treats the graph as mostly static, it allows for limited updates if data changes require recomputation of downstream slabs; cycles are generally avoided or resolved with a stabilization step.

Applications include numerical simulations with layered meshes (for example, layered finite element or finite difference methods), image or volume processing pipelines that operate on slab partitions, and data analytics workflows that partition inputs into slabs for parallel processing.

Limitations include the overhead of maintaining dependency information, potential scheduling complexity, and diminishing returns when slabs have low computation-to-communication ratios. The concept is primarily theoretical and used to inform designs for parallelization strategies.

See also: dependency graph, DAG scheduling, task-based parallelism, slab decomposition.