Lower Bounds in Minimum Rank Problems

Lower bounds for Minimum Interference Frequency Assignment Problems

In this paper we describe a new lower bound procedure for the minimum interference frequency assignment problem (MI-FAP). In the MI-FAP we have to assign frequencies to transmitter-receiver pairs in such a way that the cumulative interference in the communication network is minimized. Mainly due to the fairly large number of available frequencies, exact methods fail to solve the more di cult in...

Minimum Rank Problems

A graph describes the zero-nonzero pattern of a family of matrices, with the type of graph (undirected or directed, simple or allowing loops) determining what type of matrices (symmetric or not necessarily symmetric, diagonal entries free or constrained) are described by the graph. The minimum rank problem of the graph is to determine the minimum among the ranks of the matrices in this family; ...

Equations for Lower Bounds on Border Rank

We present new methods for determining polynomials in the ideal of the variety of bilinear maps of border rank at most r. We apply these methods to several cases including the case r = 6 in the space of bilinear maps C × C → C. This space of bilinear maps includes the matrix multiplication operator M2 for two by two matrices. We show these newly obtained polynomials do not vanish on the matrix ...

Decorous Lower Bounds for Minimum Linear Arrangement

Alberto Caprara DEIS, Università di Bologna, Viale Risorgimento 2, I-40136 Bologna, Italy, [email protected] Adam N. Letchford Department of Management Science, Lancaster University, Lancaster LA1 4YX, Great Britain, [email protected] Juan-José Salazar-González DEIOC, Universidad de La Laguna, c/ Astrof́ısico Francisco Sánchez, s/n E-38271 La Laguna, Tenerife, Spain, jjsalaza@...

Lower Bounds for Covering Problems