The minimum Manhattan distance and minimum jump of permutations

Approximating Minimum Manhattan Networks

Given a set S of n points in the plane, we deene a Manhattan Network on S as a rectilinear network G with the property that for every pair of points in S, the network G contains the shortest rectilinear path between them. A Minimum Manhattan Network on S is a Manhattan network of minimum possible length. A Manhattan network can be thought of as a graph G = (V; E), where the vertex set V corresp...

Bidirected minimum Manhattan network problem

In the bidirected minimum Manhattan network problem, given a set T of n terminals in the plane, we need to construct a network N (T) of minimum total length with the property that the edges of N (T) are axis-parallel and oriented in a such a way that every ordered pair of terminals is connected in N (T) by a directed Manhattan path. In this paper, we present a polynomial factor 2 approximation ...

Approximating a Minimum Manhattan Network

Minimum distance and the minimum weight codewords of Schubert codes

We consider linear codes associated to Schubert varieties in Grassmannians. A formula for the minimum distance of these codes was conjectured in 2000 and after having been established in various special cases, it was proved in 2008 by Xiang. We give an alternative proof of this formula. Further, we propose a characterization of the minimum weight codewords of Schubert codes by introducing the n...

The minimum barrier distance

In this paper we introduce a minimum barrier distance, MBD, defined for the (graphs of) real-valued bounded functions fA, whose domain D is a compact subsets of the Euclidean space R. The formulation of MBD is presented in the continuous setting, where D is a simply connected region in R, as well as in the case where D is a digital scene. The MBD is defined as the minimal value of the barrier s...