Given two strings $S$ and $P$, the Episode Matching problem is to compute the length of the shortest substring of $S$ that contains $P$ as a subsequence. The best known upper bound for this problem is $\tilde O(nm)$ by Das et al. (1997), where $n,m$ are the lengths of $S$ and $P$, respectively. Although the problem is well studied and has many applications in data mining, this bound has never been improved. In this paper we show why this is the case by proving that an $O((nm)^{1-\epsilon})$ algorithm (even for binary strings) would refute the popular Strong Exponential Time Hypothesis (SETH). The proof is based on a simple reduction from Orthogonal Vectors.

翻译：以两个字符串 $S 和 $P 来计算最短的子串($S)的长度($S) 包含美元作为子序列。 这个问题最著名的上限是 Das 等人 (1997年) 的 $\ tilde O (nm) 美元, 其中, $m 美元分别为 $S 和 $P 的长度。 虽然问题研究周全,数据开采中有许多应用, 但这一界限从未改进。 在本文中, 我们通过证明 $O (nm) {1\\\\\\\ epsilon} 算法( 即使是二元字符) 将反驳流行的强显性时节( SETH) 。 证据基于来自 Othoconal 矢量器的简单缩减 。