We present a novel deterministic dependency parsing algorithm that attempts to create the easiest arcs in the dependency structure first in a non-directional manner. Traditional deterministic parsing algorithms are based on a shift-reduce framework: they traverse the sentence from left-to-right and, at each step, perform one of a possible set of actions, until a complete tree is built. A drawback of this approach is that it is extremely local: while decisions can be based on complex structures on the left, they can look only at a few words to the right. In contrast, our algorithm builds a dependency tree by iteratively selecting the best pair of neighbours to connect at each parsing step. This allows incorporation of features from already built structures both to the left and to the right of the attachment point. The parser learns both the attachment preferences and the order in which they should be performed. The result is a deterministic, best-first, O(nlogn) parser, which is signif...