Everyone puts things off sometimes. How can we combat this tendency to procrastinate? A well-known technique used by instructors is to break up a large project into more manageable chunks. But how should this be done best? Here we study the process of chunking using the graph-theoretic model of present bias introduced by Kleinberg and Oren (2014). We first analyze how to optimally chunk single edges within a task graph, given a limited number of chunks. We show that for edges on the shortest path, the optimal chunking makes initial chunks easy and later chunks progressively harder. For edges not on the shortest path, optimal chunking is significantly more complex, but we provide an efficient algorithm that chunks the edge optimally. We then use our optimal edge-chunking algorithm to optimally chunk task graphs. We show that with a linear number of chunks on each edge, the biased agent's cost can be exponentially lowered, to within a constant factor of the true cheapest path. Finally, we extend our model to the case where a task designer must chunk a graph for multiple types of agents simultaneously. The problem grows significantly more complex with even two types of agents, but we provide optimal graph chunking algorithms for two types. Our work highlights the efficacy of chunking as a means to combat present bias.

翻译：人人皆有拖延之时。如何克服这种拖延倾向？教育者常用的一种有效方法是把大型任务分解成更易于管理的小块。然而，如何实现最优分块？本文利用Kleinberg与Oren（2014）提出的基于图论的当下偏好模型，系统研究了任务分块过程。首先，我们分析了在给定分块数量限制下，如何对任务图中的单条边进行最优分块。研究表明，对于最短路径上的边，最优分块策略应使初始分块难度较低，后续分块逐步递增。对于非最短路径上的边，最优分块显著复杂，但我们提出了高效算法实现边的最优分块。在此基础上，我们利用该边级最优分块算法实现了任务图的整体最优分块。证明表明，若每条边设置线性数量的分块，有当下偏好的主体所产生的成本可呈指数级降低，直至接近真实最短路径成本的常数倍。最后，我们将模型扩展至任务设计者需同时为多种类型主体进行图分块的情形。即使仅涉及两类主体，问题复杂度已大幅提升，但我们仍为两类主体情形提供了最优图分块算法。本研究凸显了分块策略作为对抗当下偏好的有效手段的显著价值。