Graph edit distance (GED) is an important similarity measure adopted in a similarity-based analysis between two graphs, and computing GED is a primitive operator in graph database analysis. Partially due to the NP-hardness, the existing techniques for computing GED are only able to process very small graphs with less than 30 vertices. Motivated by this, in this paper we systematically study the problems of both GED computation, and GED verification (i.e., verify whether the GED between two graphs is no larger than a user-given threshold). Firstly, we develop a unified framework that can be instantiated into either a best-first search approach AStar+ or a depth-first search approach DFS+. Secondly, we design anchor-aware lower bound estimation techniques to compute tighter lower bounds for intermediate search states, which significantly reduce the search spaces of both AStar+ and DFS+. We also propose efficient techniques to compute the lower bounds. Thirdly, based on our unified framework, we contrast AStar+ with DFS+ regarding their time and space complexities, and recommend that AStar+ is better than DFS+ by having a much smaller search space. Extensive empirical studies validate that AStar+ performs better than DFS+, and show that our AStar+-BMa approach outperforms the state-of-the-art technique by more than four orders of magnitude.