EEMCS EPrints Service

Education

Research

Prospective Students

Jobs

Publications

Intranet (internal)

Nederlands

Contact

Sitemap

Organisation

19049 Recognizing sparse perfect elimination bipartite graphs

Home Policy Brochure Browse Search User Area Contact Help

Bomhoff, M.J. (2010) Recognizing sparse perfect elimination bipartite graphs. Memorandum 1931, Department of Applied Mathematics, University of Twente, Enschede. ISSN 1874-4850

There is a more recent version of this eprint available. Click here to view it.

Full text available as:

PDF

- Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
139 Kb

Official URL: http://www.math.utwente.nl/publications

Abstract

When applying Gaussian elimination to a sparse matrix, it is desirable to avoid turning zeros into non-zeros to preserve the sparsity. The class of perfect elimination bipartite graphs is closely related to square matrices that Gaussian elimination can be applied to without turning any zero into a non-zero. Existing literature on the recognition of this class and finding suitable pivots mainly focusses on time complexity. For $n \times n$ matrices with m non-zero elements, the currently best known algorithm has a time complexity of $O(n^3/\log n)$ . However, when viewed from a practical perspective, the space complexity also deserves attention: it may not be worthwhile to look for a suitable set of pivots for a sparse matrix if this requires $\Omega(n^2)$ space. We present two new algorithms for the recognition of sparse instances: one with a $O(n m)$ time complexity in $\Theta(n^2)$ space and one with a $O(m^2)$ time complexity in $\Theta(m)$ space. Furthermore, if we allow only pivots on the diagonal, our second algorithm can easily be adapted to run in time $O(n m)$ .

Item Type:	Internal Report (Memorandum)
Research Group:	EWI-DMMP: Discrete Mathematics and Mathematical Programming
Research Program:	CTIT-IE&ICT: Industrial Engineering and ICT
Research Project:	SST: Smart Synthesis Tools
ID Code:	19049
Deposited On:	13 December 2010
More Information:	statistics metis

Available Versions of this Item

Recognizing sparse perfect elimination bipartite graphs (deposited 13 December 2010)
[Currently Displayed]
- Recognizing sparse perfect elimination bipartite graphs (deposited 03 January 2012)

Export this item as:

To correct this item please ask your editor

Repository Staff Only: edit this item