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- Ali Çivril, Malik Magdon-Ismail
- Theor. Comput. Sci.
- 2009

Given a matrix A ∈ Rm×n (n vectors in m dimensions), we consider the problem of selecting a subset of its columns such that its elements are as linearly independent as possible. This notion turned out to be important in low-rank approximations to matrices and rank revealing QR factorizations which have been investigated in the linear algebra community and… (More)

- Ali Çivril, Malik Magdon-Ismail
- Theor. Comput. Sci.
- 2012

Given a real matrix A ∈ Rm×n of rank r, and an integer k < r, the sum of the outer products of top k singular vectors scaled by the corresponding singular values provide the best rank-k approximation Ak to A. When the columns of A have specific meaning, it might be desirable to find good approximations to Ak which use a small number of columns of A. This… (More)

- Ali Çivril, Malik Magdon-Ismail, Eli Bocek-Rivele
- Graph Drawing
- 2005

We present a novel graph drawing algorithm which uses a spectral decomposition of the distance matrix to approximate the graph theoretical distances. The algorithm preserves symmetry and node densities, i.e., the drawings are aesthetically pleasing. The runtime for typical 20, 000 node graphs ranges from 100 to 150 seconds.

- Ali Çivril, Malik Magdon-Ismail
- Algorithmica
- 2011

Given a matrix A∈ℝ m×n (n vectors in m dimensions), and a positive integer k<n, we consider the problem of selecting k column vectors from A such that the volume of the parallelepiped they define is maximum over all possible choices. We prove that there exists δ<1 and c>0 such that this problem is not approximable within 2−ck for k=δn, unless P=NP.

- Yehuda Koren, Ali Çivril
- Graph Drawing
- 2008

We introduce a new force-directed model for computing graph layout. The model bridges the two more popular force directed approaches – the stress and the electrical-spring models – through the binary stress cost function, which is a carefully defined energy function with low descriptive complexity allowing fast computation via a Barnes-Hut scheme. This… (More)

- Ali Çivril
- J. Comput. Syst. Sci.
- 2014

- Ugur Dogrusöz, Erhan Giral, Ahmet Cetintas, Ali Çivril, Emek Demir
- Inf. Sci.
- 2009

We present an algorithm for the layout of undirected compound graphs, relaxing restrictions of previously known algorithms in regards to topology and geometry. The algorithm is based on the traditional force-directed layout scheme with extensions to handle multilevel nesting, edges between nodes of arbitrary nesting levels, varying node sizes, and other… (More)

- Ali Çivril, Malik Magdon-Ismail, Eli Bocek-Rivele
- Graph Drawing
- 2006

We present a fast spectral graph drawing algorithm for drawing undirected connected graphs. Classical Multi-Dimensional Scaling yields a quadratictime spectral algorithm, which approximates the real distances of the nodes in the final drawing with their graph theoretical distances. We build from this idea to develop the linear-time spectral graph drawing… (More)

- Ali Çivril, Malik Magdon-Ismail
- ISAAC
- 2008

Given a matrix A ∈ Rm×n of rank r, and an integer k < r, the top k singular vectors provide the best rank-k approximation to A. When the columns of A have specific meaning, it is desirable to find (provably) “good” approximations to Ak which use only a small number of columns in A. Proposed solutions to this problem have thus far focused on randomized… (More)

- Ugur Dogrusöz, Erhan Giral, Ahmet Cetintas, Ali Çivril, Emek Demir
- Graph Drawing
- 2004