In this work, we study the cost efficient data versioning problem, where the goal is to optimize the storage and reconstruction (retrieval) costs of data versions, given a graph of datasets as nodes and edges capturing edit/delta information. One central variant we study is MinSum Retrieval (MSR) where the goal is to minimize the total retrieval costs, while keeping the storage costs bounded. This problem (along with its variants) was introduced by Bhattacherjee et al. [VLDB'15]. While such problems are frequently encountered in collaborative tools (e.g., version control systems and data analysis pipelines), to the best of our knowledge, no existing research studies the theoretical aspects of these problems. We establish that the currently best-known heuristic, LMG, can perform arbitrarily badly in a simple worst case. Moreover, we show that it is hard to get $o(n)$-approximation for MSR on general graphs even if we relax the storage constraints by an $O(\log n)$ factor. Similar hardness results are shown for other variants. Meanwhile, we propose poly-time approximation schemes for tree-like graphs, motivated by the fact that the graphs arising in practice from typical edit operations are often not arbitrary. As version graphs typically have low treewidth, we further develop new algorithms for bounded treewidth graphs. Furthermore, we propose two new heuristics and evaluate them empirically. First, we extend LMG by considering more potential ``moves'', to propose a new heuristic LMG-All. LMG-All consistently outperforms LMG while having comparable run time on a wide variety of datasets, i.e., version graphs. Secondly, we apply our tree algorithms on the minimum-storage arborescence of an instance, yielding algorithms that are qualitatively better than all previous heuristics for MSR, as well as for another variant BoundedMin Retrieval (BMR).

翻译：本文研究成本高效的数据版本化问题，目标是在给定数据集节点图与捕获编辑/差异信息的边条件下，优化数据版本的存储与重建（检索）成本。我们研究的一个核心变体是最小和检索（MSR）问题，其目标是在控制存储成本的同时最小化总检索成本。该问题（及其变体）由Bhattacherjee等人[VLDB'15]首次提出。尽管此类问题在协作工具（如版本控制系统和数据分析流水线）中频繁出现，但据我们所知，现有研究尚未涉及其理论层面。我们证明，当前最优启发式算法LMG在最坏简单情况下可能表现极差。此外，我们证明即使在放宽$O(\log n)$因子的存储约束条件下，对一般图上的MSR问题实现$o(n)$近似也是困难的。其他变体也展示了类似的困难结果。同时，针对实践中典型编辑操作产生的图通常非任意的特点，我们为树状图提出了多项式时间近似方案。鉴于版本图通常具有低树宽，我们进一步为有界树宽图开发了新算法。此外，我们提出两种新启发式算法并进行了实证评估。首先，通过考虑更多潜在"移动"扩展LMG，提出了新启发式算法LMG-All。LMG-All在各类数据集（即版本图）上始终优于LMG，且运行时间相当。其次，我们将树算法应用于实例的最小存储树形结构，产生了在MSR及另一变体有界最小检索（BMR）问题上质量上优于所有先前启发式算法的算法。