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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.
We prove a lower bound on the space complexity of two-pass semi-streaming algorithms that approximate the maximum matching problem. The lower bound is parameterized by the density of Ruzsa-Szemeredi graphs: * Any two-pass semi-streaming algorithm f
For even $k$, the matchings connectivity matrix $mathbf{M}_k$ encodes which pairs of perfect matchings on $k$ vertices form a single cycle. Cygan et al. (STOC 2013) showed that the rank of $mathbf{M}_k$ over $mathbb{Z}_2$ is $Theta(sqrt 2^k)$ and use
The minimum degree algorithm is one of the most widely-used heuristics for reducing the cost of solving large sparse systems of linear equations. It has been studied for nearly half a century and has a rich history of bridging techniques from data st
For online matching with the line metric, we present a lower bound of $Omega(log n)$ on the approximation ratio of any online (possibly randomized) algorithm. This beats the previous best lower bound of $Omega(sqrt{log n})$ and matches the known upper bound of $O(log n)$.
We show that an improvement to the best known quantum lower bound for GRAPH-COLLISION problem implies an improvement to the best known lower bound for TRIANGLE problem in the quantum query complexity model. In GRAPH-COLLISION we are given free access