3 citations · 5 across the 8 of their papers we have counts for
14 papers
Two flags in a semimodular lattice generate an antimatroid
Koyo Hayashi, Hiroshi Hirai
A basic property in a modular lattice is that any two flags generate a distributive sublattice. It is shown (Abels 1991, Herscovic 1998) that two flags in a semimodular lattice no…
Computing the nc-rank via discrete convex optimization on CAT(0) spaces
Masaki Hamada, Hiroshi Hirai
In this paper, we address the noncommutative rank (nc-rank) computation of a linear symbolic matrix \[ A = A_1 x_1 + A_2 x_2 + \cdots + A_m x_m, \] where each is an $n \times…
Node-Connectivity Terminal Backup, Separately-Capacitated Multiflow, and Discrete Convexity
Hiroshi Hirai, Motoki Ikeda
The terminal backup problems (Anshelevich and Karagiozova (2011)) form a class of network design problems: Given an undirected graph with a requirement on terminals, the goal is to…
A cost-scaling algorithm for computing the degree of determinants
Hiroshi Hirai, Motoki Ikeda
In this paper, we address computation of the degree of Dieudonné determinant of \[ A = \sum_{k=1}^m A_k x_k t^{c_k}, \] where ar…
Compression of M-convex Functions -- Flag Matroids and Valuated Permutohedra
Satoru Fujishige, Hiroshi Hirai
Murota (1998) and Murota and Shioura (1999) introduced concepts of M-convex function and M-convex function as discrete convex functions, which are generalizations of v…
A Cost-Scaling Algorithm for Minimum-Cost Node-Capacitated Multiflow Problem
Hiroshi Hirai, Motoki Ikeda
In this paper, we address the minimum-cost node-capacitated multiflow problem in an undirected network. For this problem, Babenko and Karzanov (2012) showed strongly polynomial-tim…