The alternating decision tree brings comprehensibility to the performance enhancing capabilities of boosting. A single interpretable tree is induced wherein knowledge is distributed across the nodes and multiple paths are traversed to form predictions. The complexity of the algorithm is quadratic in the number of boosting iterations and this makes it unsuitable for larger knowledge discovery in database tasks. In this paper we explore various heuristic methods for reducing this complexity while maintaining the performance characteristics of the original algorithm. In experiments using standard, artificial and knowledge discovery datasets we show that a range of heuristic methods with log linear complexity are capable of achieving similar performance to the original method. Of these methods, the random walk heuristic is seen to out-perform all others as the number of boosting iterations increases. The average case complexity of this method is linear.