The region connection calculus ($RCC$) and Allen's interval algebra ($IA$) are two well-known NP-hard spatial-temporal qualitative reasoning problems. They are solvable in $2^{O(n \log n)}$ time, where $n$ is the number of variables, and $IA$ is additionally known to be solvable in $o(n)^n$ time. However, no improvement over exhaustive search is known for $RCC$, and if they are also solvable in single exponential time $2^{O(n)}$ is unknown. We investigate multiple avenues towards reaching such bounds. First, we show that branching is insufficient since there are too many non-redundant constraints. Concretely, we classify the maximum number of non-redundant constraints in $RCC$ and $IA$. Algorithmically, we make two significant contributions based on dynamic programming (DP). The first algorithm runs in $4^n$ time and is applicable to a non-trivial, NP-hard fragment of $IA$, which includes the well-known interval graph sandwich problem of Golumbic and Shamir (1993). For the richer $RCC$ problem with 8 basic relations we use a more sophisticated approach which asymptotically matches the $o(n)^n$ bound for $IA$.

翻译：区域连接演算（$RCC$）和Allen区间代数（$IA$）是两种著名的NP难时空定性推理问题。它们可在$2^{O(n \log n)}$时间内求解（其中$n$为变量数），且已知$IA$还可在$o(n)^n$时间内求解。然而，$RCC$目前尚无优于穷举搜索的改进方法，且其是否可在单一指数时间$2^{O(n)}$内求解仍属未知。我们探索了实现此类时间界的多种途径。首先，我们证明分支法不可行，因为非冗余约束数量过多。具体而言，我们分类了$RCC$与$IA$中非冗余约束的最大数目。在算法层面，我们基于动态规划（DP）做出了两项重要贡献。第一个算法运行时间为$4^n$，适用于$IA$中一个包含Golumbic和Shamir（1993）著名区间图夹心问题的非平凡NP难子集。对于包含8种基本关系的更复杂的$RCC$问题，我们采用了一种更精巧的方法，其渐近复杂度与$IA$的$o(n)^n$界相匹配。