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np-hardness

RAIRO - Theoretical Informatics and Applications (1)

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1 results

Packing of (0, 1)-matrices
Stéphane Vialette
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 40 / Issue 4 / October 2006

Published online by Cambridge University Press:

08 November 2006, pp. 519-535

Print publication:

October 2006
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The MATRIX PACKING DOWN problem asks to find a row permutation of a given (0,1)-matrix in such a way that the total sum of the first non-zero column indexes is maximized. We study the computational complexity of this problem. We prove that the MATRIX PACKING DOWN problem is NP-complete even when restricted to zero trace symmetric (0,1)-matrices or to (0,1)-matrices with at most two 1's per column. Also, as intermediate results, we introduce several new simple graph layout problems which are proved to be NP-complete.