Understanding the Search Behaviour of Greedy Best-First Search

A classical result in optimal search shows that A* with an admissible and consistent heuristic expands every state whose f -value is below the optimal solution cost and no state whose f -value is above the optimal solution cost. For satisficing search algorithms, a similarly clear understanding is currently lacking. We examine the search behaviour of greedy bestfirst search (GBFS) in order to make progress towards such an understanding. We introduce the concept of high-water mark benches, which separate the search space into areas that are searched by a GBFS algorithm in sequence. High-water mark benches allow us to exactly determine the set of states that are not expanded under any GBFS tie-breaking strategy. For the remaining states, we show that some are expanded by all GBFS searches, while others are expanded only if certain conditions are met.