To tackle the exponentiality associated with NP-hard problems, two paradigms have been proposed. First, Branch & Bound, like Dynamic Programming, achieve efficient exact inference but requires extensive information and analysis about the problem at hand. Second, meta-heuristics are easier to implement but comparatively inefficient. As a result, a number of problems have been left unoptimized and plain greedy solutions are used. We introduce a theoretical framework and propose a powerful yet simple search method called Dilemma First Search (DFS). DFS exploits the decision heuristic needed for the greedy solution for further optimization. DFS is useful when it is hard to design efficient exact inference. We evaluate DFS on two problems: First, the Knapsack problem, for which efficient algorithms exist, serves as a toy example. Second, Decision Tree inference, where state-of-the-art algorithms rely on the greedy or randomness-based solutions. We further show that decision trees benefit from optimizations that are performed in a fraction of the iterations required by a random-based search.

Urban models are key to navigation, architecture and entertainment. Apart from visualizing facades, a number of tedious tasks remain largely manual (e.g. compression, generating new facade designs and structurally comparing facades for classification, retrieval and clustering). We propose a novel procedural modelling method to automatically learn a grammar from a set of facades, generate new facade instances and compare facades. To deal with the difficulty of grammatical inference, we reformulate the problem. Instead of inferring a compromising, one-size-fits-all, single grammar for all tasks, we infer a model whose successive refinements are production rules tailored for each task. We demonstrate our automatic rule inference on datasets of two different architectural styles. Our method supercedes manual expert work and cuts the time required to build a procedural model of a facade from several days to a few milliseconds.