Soh Kumabe

Soh Kumabe, Shinya Shiroshita, Takanori Hayashi et al.

Inventory management in warehouses directly affects profits made by manufacturers. Particularly, large manufacturers produce a very large variety of products that are handled by a significantly large number of retailers. In such a case, the computational complexity of classical inventory management algorithms is inordinately large. In recent years, learning-based approaches have become popular for addressing such problems. However, previous studies have not been managed systems where both the number of products and retailers are large. This study proposes a reinforcement learning-based warehouse inventory management algorithm that can be used for supply chain systems where both the number of products and retailers are large. To solve the computational problem of handling large systems, we provide a means of approximate simulation of the system in the training phase. Our experiments on both real and artificial data demonstrate that our algorithm with approximated simulation can successfully handle large supply chain networks.

Soh Kumabe, Yuya Uezato

ReDoS is a well-known type of algorithmic complexity attack, where an adversary supplies maliciously crafted strings to a regular expression matching engine, aiming to exhaust computational resources of systems. Even quadratic-time behavior in matching engines has been exploited in successful attacks, as exemplified by major outages at Stack Overflow (2016) and Cloudflare (2019). These incidents motivate a fundamental question: Is it possible to construct matching engines that are provably efficient, running in (near-)linear time in the length of the input string? For classical regular expressions (REGEX), Thompson's construction yields a linear-time algorithm. However, practical engines support powerful features such as backreferences, which strictly extend the expressive power of REGEX but unfortunately increase the risk of ReDoS attacks. This paper investigates the fine-grained complexity of the string matching problem for regular expressions with backreferences (REWBs). Specifically, we consider $r$-use $k$-REWBs. On the hardness side, we show that the string matching problem for $k$-REWBs cannot be solved in $O(n^{2k-ε})$ time for any $ε> 0$ under SETH. We also prove that this problem is \textbf{W[2]}-hard when parameterized by the length of the REWB expression, strengthening the previous \textbf{W[1]}-hardness. Moreover, we prove that this problem for $2$-use $2$-REWBs cannot be solved in $n^{1+o(1)}$ time unless the triangle detection problem can be solved in that time. On the algorithmic side, we present an $O(n \log^2 n)$-time algorithm for $1$-use REWBs, which significantly improves upon the recent $O(n^2)$-time algorithm by Nogami and Terauchi (MFCS, 2025). Our algorithm employs several techniques including suffix trees, transition monoids of REGEXes, factorization forest data structures, and periodicity of strings.