منابع مشابه
Linear Discrepancy of Basic Totally Unimodular Matrices
We show that the linear discrepancy of a basic totally unimodular matrix A ∈ Rm×n is at most 1− 1 n+1 . This extends a result of Peng and Yan. AMS Subject Classification: Primary 11K38.
متن کاملLinear Discrepancy of Totally Unimodular Matrices
Let p ∈ [1,∞[ and cp = maxa∈[0,1]((1 − a)ap + a(1 − a)p)1/p. We prove that the known upper bound lindiscp(A) ≤ cp for the Lp linear discrepancy of a totally unimodular matrix A is asymptotically sharp, i.e., sup A lindiscp(A) = cp. We estimate cp = p p+1 ( 1 p+1 )1/p (1+εp) for some εp ∈ [0, 2−p+2], hence cp = 1− ln p p (1+ o(1)). We also show that an improvement for smaller matrices as in the ...
متن کاملOn the representability of totally unimodular matrices on bidirected graphs
Seymour’s famous decomposition theorem for regular matroids states that any totally unimodular (TU) matrix can be constructed through a series of composition operations called k-sums starting from network matrices and their transposes and two compact representation matrices B1, B2 of a certain ten element matroid. Given that B1, B2 are binet matrices we examine the k-sums of network and binet m...
متن کاملOn Padberg's conjecture about almost totally unimodular matrices
We consider Padberg’s conjecture about almost totally unimodular matrices proposed in 1988 in Operations Research Letters. We show that it is not correct as stated and give a modi ed version of the conjecture. c © 2000 Published by Elsevier Science B.V. All rights reserved.
متن کاملA generalization of totally unimodular and network matrices
In this thesis we discuss possible generalizations of totally unimodular and network matrices. Our purpose is to introduce new classes of matrices that preserve the advantageous properties of these well-known matrices. In particular, our focus is on the polyhedral consequences of totally unimod ular matrices, namely we look for matrices that can ensure vertices that are scalable to an integral...
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ژورنال
عنوان ژورنال: Networks
سال: 1976
ISSN: 0028-3045,1097-0037
DOI: 10.1002/net.3230060406