54 citations · 123 across the 39 of their papers we have counts for
7 papers · 1 filter
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…
Minimum 0-Extension Problems on Directed Metrics
Hiroshi Hirai, Ryuhei Mizutani
For a metric on a finite set , the minimum 0-extension problem 0-Ext is defined as follows: Given and , minimi…
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 combinatorial algorithm for computing the rank of a generic partitioned matrix with submatrices
Hiroshi Hirai, Yuni Iwamasa
In this paper, we consider the problem of computing the rank of a block-structured symbolic matrix (a generic partitioned matrix) , where is a $2 \tim…
Helly groups
Jérémie Chalopin, Victor Chepoi, Anthony Genevois +2
Helly graphs are graphs in which every family of pairwise intersecting balls has a non-empty intersection. This is a classical and widely studied class of graphs. In this article w…