Quickest Path Distances on Context-Free Labeled Graphs∗

Given σ units of data and a digraph G = (V,E) whose edges have delays, bandwidth constraints, and are labeled by terminals from a CFG (context-free grammar) G. A path p adheres to G’s path constraints iff the concatenation of all terminals along p forms a word of the language generated by G. The all-pairs quickest CFG labeled-path distance problem is: for all pairs of vertices, find the minimum path-cost to send σ data units accounting for edge delays while adhering to labeled path and bandwidth constraints. This paper iteratively applies dynamic programming-based labeled path algorithms to CFG-labeled bandwidth-stratified induced subgraphs of an input graph. More precisely, we use Rosen, Sun and Xue’s quickest-path algorithm [13] as a framework giving bandwidth-stratified induced subgraphs. This approach is far more efficient than naively applying dynamic programming-based labeled path algorithms to bandwidth-augmented CFG-labeled graphs. Key–Words: quickest path, context-free grammar, labeled graph, dynamic programming, algorithm design.