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Solving the sensor cover energy problem via integer linear programming

Pingke Li (2021)

Kybernetika

This paper demonstrates that the sensor cover energy problem in wireless communication can be transformed into a linear programming problem with max-plus linear inequality constraints. Consequently, by a well-developed preprocessing procedure, it can be further reformulated as a 0-1 integer linear programming problem and hence tackled by the routine techniques developed in linear and integer optimization. The performance of this two-stage solution approach is evaluated on a set of randomly generated...

Some decision problems on integer matrices

Christian Choffrut, Juhani Karhumäki (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Given a finite set of matrices with integer entries, consider the question of determining whether the semigroup they generated 1) is free; 2) contains the identity matrix; 3) contains the null matrix or 4) is a group. Even for matrices of dimension 3 , questions 1) and 3) are undecidable. For dimension 2 , they are still open as far as we know. Here we prove that problems 2) and 4) are decidable by proving more generally that it is recursively decidable whether or not a given non singular matrix belongs...

Some decision problems on integer matrices

Christian Choffrut, Juhani Karhumäki (2010)

RAIRO - Theoretical Informatics and Applications

Given a finite set of matrices with integer entries, consider the question of determining whether the semigroup they generated 1) is free; 2) contains the identity matrix; 3) contains the null matrix or 4) is a group. Even for matrices of dimension 3, questions 1) and 3) are undecidable. For dimension 2, they are still open as far as we know. Here we prove that problems 2) and 4) are decidable by proving more generally that it is recursively decidable whether or not a given non singular matrix belongs...

Some equalities for generalized inverses of matrix sums and block circulant matrices

Yong Ge Tian (2001)

Archivum Mathematicum

Let A 1 , A 2 , ⋯ , A n be complex matrices of the same size. We show in this note that the Moore-Penrose inverse, the Drazin inverse and the weighted Moore-Penrose inverse of the sum ∑ t = 1 n A t can all be determined by the block circulant matrix generated by A 1 , A 2 , ⋯ , A n . In addition, some equalities are also presented for the Moore-Penrose inverse and the Drazin inverse of a quaternionic matrix.

Some Examples of Rigid Representations

Kostov, Vladimir (2000)

Serdica Mathematical Journal

*Research partially supported by INTAS grant 97-1644.Consider the Deligne-Simpson problem: give necessary and sufficient conditions for the choice of the conjugacy classes Cj ⊂ GL(n,C) (resp. cj ⊂ gl(n,C)) so that there exist irreducible (p+1)-tuples of matrices Mj ∈ Cj (resp. Aj ∈ cj) satisfying the equality M1 . . .Mp+1 = I (resp. A1+. . .+Ap+1 = 0). The matrices Mj and Aj are interpreted as monodromy operators and as matrices-residua of fuchsian systems on Riemann’s sphere. We give new examples...

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