Integral Boundary Points of Convex Polyhedra
By A. Hoffman, Joseph B. Kruskal. 50 Years of Integer Programming, 2010
331 citations recorded by the source corpus.
Subfields: Applied Mathematics, Electrical and Electronic Engineering, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/937e2e35497e162723fd6e76f87d2d37cd6f40ee
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In Applied Mathematics
In Electrical and Electronic Engineering
In Geometry and Topology
Citations in the corpus
- Designing Random Allocation Mechanisms: Theory and Applications (2013, background): “Hoffman and Kruskal (1956) show that the vertices of (2.1) are integer-valued if and only if the incidence matrix M = [m(i,a),S], (i, a) ∈ N ×O, S ∈ H, where m(i,a),S = 1 if (i, a) ∈ S and m(i,a),S = 0 if (i, a) 6∈ S, is totally unimodular.10 The total unimodularity of matrix M in turn follows from…”
- Nonlinear Discrete Optimization (2010, background): “It is well known [54] that the matrix defining the system of inequalities in (1.”
- Multiple Object Tracking Using K-Shortest Paths Optimization (2011, neutral): “The following two theorems hold for such matrices, as shown in [43] and [44] respectively.”
- Decomposing random mechanisms (2015, methodology): “By Hoffman and Kruskal (1956), the set of all vectors with this property is an integral polyhedron: that is, it is a polyhedron with integer-valued extreme points.”
- A Systematic Approach to Developing and Evaluating Website Fingerprinting Defenses (2014, background): “Linear programs with Totally Unimodular (TU) constraint matrices and integral objective functions have integral solutions [7].”