arXiv subjects

Yoshihiko Terai

Publications and source records attributed to Yoshihiko Terai.

2 recordsLinked to original sources

arXiv2026

A Refined Analysis of the Sequential Access Theorem for Splay Trees

A splay tree is a self-adjusting binary search tree that allows access, insertion, and deletion to be performed in amortized $O(\log n)$ time, where $n$ is the number of stored elements. The sequential access theorem states that, when the elements of a splay tree are accessed in increasing order, the amortized cost per operation becomes a constant. In this paper, we show that the upper bound for this constant is at most $5.5$ by refining the existing analysis and introducing a new potential function. Furthermore, we complement our result by showing that there exists a splay tree for which the constant is lower-bounded by almost $4$.

cs.DS↗

arXiv2025

Computing Power Indices in Weighted Majority Games with Formal Power Series

In this paper, we propose fast pseudo-polynomial-time algorithms for computing power indices in weighted majority games. We show that we can compute the Banzhaf index for all players in $O(n+q\log (q))$ time, where $n$ is the number of players and $q$ is a given quota. Moreover, we prove that the Shapley--Shubik index for all players can be computed in $O(nq\log (q))$ time. Our algorithms are faster than existing algorithms when $q=2^{o(n)}$. Our algorithms exploit efficient computation techniques for formal power series.

cs.GT↗