kdependency

Kdependency is a concept in dependency modeling used to describe the reachability of one component from another within a bound of k steps in a dependency graph. In a directed graph G=(V,E), where an edge (u,v) indicates that component u depends on component v, the kdependency relation R_k is defined as the set of pairs (u,v) such that the shortest directed path from u to v has length at most k. Equivalently, u k-depends on v if there exists a dependency path of length ≤ k from u to v. Some formulations distinguish exact k-distance, requiring the path length to be exactly k.

This notion is useful for assessing the potential impact of changes, bounding the scope of transitive analysis, and guiding optimization in build systems and data pipelines. For example, in a software build DAG, kdependency information helps identify which modules may be affected by a change in a given module within k steps, enabling faster partial rebuilds and safer change propagation policies.

Computation and variants: R_k can be computed by performing a breadth-first search from each node up to depth k, or by processing adjacency matrices to capture reachability within k steps. In large graphs, one typically combines approximate methods with centrality or sampling to keep costs manageable. The choice of k reflects a trade-off between precision and performance and may be adapted dynamically.

Limitations include cycles and weighted dependencies, which require adaptations of the distance measure, and the fact that a fixed k may not capture all relevant transitive effects in some domains.

See also: reachability, transitive closure, dependency management, graph theory.