منابع مشابه
Generalisations of total unimodularity
In this paper we examine possible generalisations of total unimodularity. To this end, we introduce two concepts: total k-modularity and k-regularity. Total k-modularity extends the permitted values for the subdeterminants of a matrix to the powers of k, while k-regularity sets requirements on the inverses of non-singular submatrices. It is shown that the advantageous properties of totally unim...
متن کاملTotal Dual Integrality 1.1 Total Unimodularity
where A and b are rational and the associate dual program min y b s.t. A y = c (2) y ≥ 0 Definition 1 The system of inequalities by Ax ≤ b is Total Dual Integral or TDI if for all integral vectors c the dual program has an integral solution whenever the optimal value is finite. The main result for today is Theorem 1 If Ax ≤ b is TDI and b is integral then P = {x : Ax ≤ b} is integral ∗ ∗ Proof:...
متن کاملNon Total-Unimodularity Neutralized Simplicial Complexes
Given a simplicial complex K with weights on its simplices and a chain on it, the Optimal Homologous Chain Problem (OHCP) is to find a chain with minimal weight that is homologous (over Z) to the given chain. The OHCP is NP-complete, but if the boundary matrix of K is totally unimodular (TU), it becomes solvable in polynomial time when modeled as a linear program (LP). We define a condition on ...
متن کاملLecture 4 — Total Unimodularity and Total Dual Integrality
Definition 1.1. A matrix A ∈ Zm×n is totally unimodular if the determinant of every square submatrix B ∈ Zk×k equals either −1, 0, or +1. Alternatively, by Cramer’s rule, A ∈ Zm×n is totally unimodular if every nonsingular submatrix B ∈ Zk×k has an integral inverse B−1 ∈ Zk×k. Recall: B−1 = 1 det B B ∗, where B∗ is the adjugate matrix (transpose of the matrix of cofactors) of B. One important c...
متن کاملExploiting total unimodularity for classes of random network problems
Network analysis is of great interest for the study of social, biological and technological networks, with applications, among others, in business, marketing, epidemiology and telecommunications. Researchers are often interested in assessing whether an observed feature in some particular network is expected to be found within families of networks under some hypothesis (named conditional random ...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1980
ISSN: 0024-3795
DOI: 10.1016/0024-3795(80)90183-4