scholarly journals Minimum decomposition into convex binary matrices

2012 ◽  
Vol 160 (7-8) ◽  
pp. 1164-1175 ◽  
Author(s):  
Fethi Jarray ◽  
Christophe Picouleau
Keyword(s):  
Binary Matrices ◽  
Minimum Decomposition

scholarly journals Reconstruction of hv-convex binary matrices from their absorbed projections

2004 ◽  
Vol 139 (1-3) ◽  
pp. 137-148 ◽  
Author(s):  
Attila Kuba ◽  
Antal Nagy ◽  
Emese Balogh
Keyword(s):  
Binary Matrices

scholarly journals Partitioning Graph Drawings and Triangulated Simple Polygons into Greedily Routable Regions

2017 ◽  
Vol 27 (01n02) ◽  
pp. 121-158 ◽  
Author(s):  
Martin Nöllenburg ◽  
Roman Prutkin ◽  
Ignaz Rutter
Keyword(s):  
Routing Protocol ◽  
Graph Drawing ◽  
Geographic Routing ◽  
Np Hard ◽  
Line Drawings ◽  
Simple Polygons ◽  
Straight Line ◽  
Starting Point ◽  
Minimum Decomposition ◽  
Geographic Routing Protocol

A greedily routable region (GRR) is a closed subset of [Formula: see text], in which any destination point can be reached from any starting point by always moving in the direction with maximum reduction of the distance to the destination in each point of the path. Recently, Tan and Kermarrec proposed a geographic routing protocol for dense wireless sensor networks based on decomposing the network area into a small number of interior-disjoint GRRs. They showed that minimum decomposition is NP-hard for polygonal regions with holes. We consider minimum GRR decomposition for plane straight-line drawings of graphs. Here, GRRs coincide with self-approaching drawings of trees, a drawing style which has become a popular research topic in graph drawing. We show that minimum decomposition is still NP-hard for graphs with cycles and even for trees, but can be solved optimally for trees in polynomial time, if we allow only certain types of GRR contacts. Additionally, we give a 2-approximation for simple polygons, if a given triangulation has to be respected.

scholarly journals Nonexistence of Almost Moore Digraphs of Diameter Three

10.37236/811 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
J. Conde ◽  
J. Gimbert ◽  
J. Gonzàlez ◽  
J. M. Miret ◽  
R. Moreno
Keyword(s):  
Number Theory ◽  
Graph Theory ◽  
Algebraic Number ◽  
Directed Graphs ◽  
Algebraic Number Theory ◽  
Cycle Structure ◽  
Spectral Techniques ◽  
Binary Matrices ◽  
Algebraic Multiplicities ◽  
Big Pieces

Almost Moore digraphs appear in the context of the degree/diameter problem as a class of extremal directed graphs, in the sense that their order is one less than the unattainable Moore bound $M(d,k)=1+d+\cdots +d^k$, where $d>1$ and $k>1$ denote the maximum out-degree and diameter, respectively. So far, the problem of their existence has only been solved when $d=2,3$ or $k=2$. In this paper, we prove that almost Moore digraphs of diameter $k=3$ do not exist for any degree $d$. The enumeration of almost Moore digraphs of degree $d$ and diameter $k=3$ turns out to be equivalent to the search of binary matrices $A$ fulfilling that $AJ=dJ$ and $I+A+A^2+A^3=J+P$, where $J$ denotes the all-one matrix and $P$ is a permutation matrix. We use spectral techniques in order to show that such equation has no $(0,1)$-matrix solutions. More precisely, we obtain the factorization in ${\Bbb Q}[x]$ of the characteristic polynomial of $A$, in terms of the cycle structure of $P$, we compute the trace of $A$ and we derive a contradiction on some algebraic multiplicities of the eigenvalues of $A$. In order to get the factorization of $\det(xI-A)$ we determine when the polynomials $F_n(x)=\Phi_n(1+x+x^2+x^3)$ are irreducible in ${\Bbb Q}[x]$, where $\Phi_n(x)$ denotes the $n$-th cyclotomic polynomial, since in such case they become 'big pieces' of $\det(xI-A)$. By using concepts and techniques from algebraic number theory, we prove that $F_n(x)$ is always irreducible in ${\Bbb Q}[x]$, unless $n=1,10$. So, by combining tools from matrix and number theory we have been able to solve a problem of graph theory.

scholarly journals Theoretical Aspects of the Territorial Approach to Region and Supply Chain Management

2021 ◽  
pp. 40-60
Author(s):  
A. P. Tyapukhin
Keyword(s):  
Supply Chain ◽  
Supply Chain Management ◽  
Supply Chains ◽  
Point Of View ◽  
Chain Management ◽  
Analysis And Synthesis ◽  
Binary Matrices ◽  
Territorial Approach ◽  
Regional Authorities ◽  
The Relationship

The territorial approach is the basic approach to a region management. At the same time, the “territory” component is the basis of the logistics complex used in Supply Chain Management. In this regard, a need is to clarify and supplement the theory and methodology of the territorial approach to the management of both the region and the supply chains.The subject of this study is the relationship between the regional authorities and the focus enterprise of the supply chain regarding the development of the territories and resources of the region on a mutually beneficial basis.The research methods are methods of analysis and synthesis, induction and deduction, as well as classification, and the tools are binary matrices that provide for the joint use of two classification attributes of the object under study and their dichotomies.The results of this study are the management principles by the competitiveness and sustainability of the management object; classifications of approaches to the management by the region and supply chains; of territories from the point of view of the focus enterprise of the supply chain and the region; the management decisions in the interaction of regions with the links of supply chains; the sequence of the formation of supply chains and the development of territories and resources of the region on the basis of the territorial approach and the relationship between them.The obtained results allow to reduce the costs and time for the development of territories and resources of the region by reducing the lost profits of the supply chain links due to their rational placement and increasing sustainability by achieving a synergistic effect both by the region and by the supply chains.

scholarly journals Invertible binary matrices with maximum number of2-by-2invertible submatrices

2017 ◽  
Vol 340 (2) ◽  
pp. 201-208 ◽  
Author(s):  
Yiwei Zhang ◽  
Tao Zhang ◽  
Xin Wang ◽  
Gennian Ge
Keyword(s):  
Binary Matrices

Choice of Binary Matrices under Restrictions with Application to Controlled Sampling

1988 ◽  
Vol 37 (3-4) ◽  
pp. 215-226
Author(s):  
Anup Kumar De ◽  
Bimal Kumar Roy
Keyword(s):  
Sampling Scheme ◽  
Binary Matrices

A population with rc units is represented by an r× c two way array in which each row (each column) represents a group w. r. t. some characteristic. We look for a sampling scheme to select n units, so that from any group at most k units are selected and π ij ⩽ π i π j all i, j. In this paper we partly solve the problem when r = c.

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