The syntactic structure of a sentence can be represented as a tree where edges indicate syntactic dependencies between words. When that structure is a star, it has been demonstrated that the head should be placed in the middle of the linear arrangement according to the principle of syntactic dependency distance minimization. However, hubs of stars tend to be put at one of the ends, against that principle. Here we address two questions: (1) How difficult is it to minimize dependency distance? (2) Why anti dependency distance minimization effects have been found in star structures but not in path structures? The ease of optimization is determined by the shape of the optimization landscape. It was demonstrated that the landscape of star structures is quasiconvex (Ferrer-i-Cancho 2015, Language Dynamics and Change). As for (1), here we show that it is indeed convex (a particular case of quasiconvexity) both for star trees and quasistar trees and thus the distance-based optimization problem is simpler than previously believed. As for (2), we argue that (a) competing principles, rather than the difficulty of optimization, must be the actual reason for anti-dependency distance minimization effects and that (b) dependency distance minimization on star-like structures is less rewarding compared to other structures.

翻译：句子的句法结构可表示为树形图，其中边表示词语之间的句法依赖关系。研究表明，当该结构为星状时，根据句法依赖距离最小化原则，核心词应置于线性排列的中间位置。然而，星状结构的中心节点往往倾向于被置于端点之一，这与该原则相悖。本文探讨两个问题：(1) 最小化依赖距离的难度如何？(2) 为何星状结构中存在反依赖距离最小化效应，而路径结构中却未发现？优化的容易程度取决于优化景观的形状。已有证明表明，星状结构的景观是拟凸的（Ferrer-i-Cancho 2015，《语言动态与变化》）。针对问题(1)，本文证明星树和准星树的景观确实是凸的（拟凸性的特例），因此基于距离的优化问题比先前认为的更简单。针对问题(2)，本文提出：(a) 竞争性原则而非优化难度必须是反依赖距离最小化效应的实际原因；(b) 与其他结构相比，星状结构上的依赖距离最小化收益较低。