Here, the dilemma between high computational costs and comprehensive reaction exploration was addressed by combining an ultra-low cost reaction prediction program, the Yet Another Reaction Program (YARP), with an efficient modified Dijkstra algorithm for exploring kinetically relevant reactions. Dijkstra's algorithm is formally the most efficient single-source exploration method for finding minimum cost pathways on directed graphs. The algorithm is based on the simple rule of always exploring off of the lowest cost node that has been discovered up to that point. The algorithm can also be run in a parallel multi-source fashion from both the starting and ending nodes (if they are known) until finding a point at which the minimum cost pathways overlap. Considering the unimolecular glucose pyrolysis network as a directed graph, applying the single-source Dijkstra's algorithm is the equivalent of recursively exploring the reactivity of the products most likely form from glucose in the network at each stage of exploration. The activation energy of the rate-limiting step for forming each product was used as the "cost" function for the algorithm and YARP was used to characterize the reactions the lowest-cost products could undergo.