• Corpus ID: 115171597

A Combinatorial Result on Block Matrices

  title={A Combinatorial Result on Block Matrices},
  author={S. M. Sadegh Tabatabaei Yazdi and Serap A. Savari},
  journal={arXiv: Combinatorics},
Given a matrix with partitions of its rows and columns and entries from a field, we give the necessary and sufficient conditions that it has a non--singular submatrix with certain number of rows from each row partition and certain number of columns from each column partition. 

A combinatorial study of linear deterministic relay networks

  • S. M. T. YazdiS. Savari
  • Computer Science
    2010 IEEE Information Theory Workshop on Information Theory (ITW 2010, Cairo)
  • 2010
This work studies the unicast problem for this linear deterministic network model using results from matroid theory and submodular optimization, and provides deterministic and polynomial-time coding schemes that can achieve the capacity.

A max-flow/min-cut algorithm for a class of wireless networks

It is shown that the max-flow/min-cut theorem for linear deterministic relay networks is connected to a two-dimensional transversal theorem for block matrices which is a new application of the Rado-Hall theorem and a combinatorial result on sequences of block matrix which is obtained through results in submodular optimization.

A Max-Flow/Min-Cut Algorithm for Linear Deterministic Relay Networks

In the special case of a unicast session, a simple capacity-achieving transmission scheme for LDRN which codes over one symbol of information at each use of the network is obtained by a connection to the submodular flow problem and through the application of tools from matroid theory and sub modular optimization theory.