Topological graph theory
Theory of 2-structures. Part I: clans, basic subclasses, and morphisms
Theoretical Computer Science
Finite metric spaces: combinatorics, geometry and algorithms
Proceedings of the eighteenth annual symposium on Computational geometry
Geometry of Cuts and Metrics
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Let g: D × D → R be a symmetric function on a finite set D satisfying g(x, x) = 0 for all x ∈ D. A switch gσ of g w.r.t. a local valuation σ: D → R is defined by gσ(x, y) = σ(x) + g(x, y) + σ(y) for x ≠ y and gσ(x, x) = 0 for all x. We show that every symmetric function g has a unique minimal semimetric switch, and, moreover, there is a switch of g that is isometric to a finite Manhattan metric. Also, for each metric on D, we associate an extension metric on the set of all nonempty subsets of D, and we show that this extended metric inherits the switching classes on D.