54 citations · 123 across the 39 of their papers we have counts for
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A Nonpositive Curvature Property of Modular Semilattices
Hiroshi Hirai
The orthoscheme complex of a graded poset is a metrization of its order complex such that the simplex of each maximal chain is isometric to the Euclidean simplex of vertices $0, e_…
Weakly modular graphs and nonpositive curvature
Jérémie Chalopin, Victor Chepoi, Hiroshi Hirai +1
This article investigates structural, geometrical, and topological characterizations and properties of weakly modular graphs and of cell complexes derived from them. The unifying t…
Discrete Convexity and Polynomial Solvability in Minimum 0-Extension Problems
Hiroshi Hirai
For a graph G and a set V containing the vertex set of G, a 0-extension of G is a metric d on V such that d extends the shortest path metric of G and for all x in V there exists a…
On tight spans and tropical polytopes for directed distances
Hiroshi Hirai, Shungo Koichi
An extension of a metric space is a metric space with and , and is said to be tight if there is no other extension of wit…