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On the Construction of Classes of Suffix Trees for Square Matrices: Algorithms and Applications

Raffaele Giancarlo, Roberto Grossi
1996 Information and Computation  
Such an algorithm improves in various respects the algorithms for the construction of the PAT tree and the Lsuffix tree. The framework and the algorithm easily generalize to d>2 dimensions.  ...  An index for TEXT can be informally seen as the two-dimensional analog of the suffix tree for a string.  ...  However, we need novel algorithmic techniques that are improvements and generalizations of the ones that have been devised for the construction of suffix tree data structures for strings and square matrices  ... 
doi:10.1006/inco.1996.0087 fatcat:3hpis6csqfedxnwrwc4ndweyde

Submatrix Maximum Queries in Monge Matrices and Partial Monge Matrices, and Their Applications

Haim Kaplan, Shay Mozes, Yahav Nussbaum, Micha Sharir
2017 ACM Transactions on Algorithms  
For partial Monge matrices the space and preprocessing grow by α(n) (the inverse Ackermann function), and the query remains O(log 2 n).  ...  We describe a data structure for submatrix maximum queries in Monge matrices or partial Monge matrices, where a query seeks the maximum element in a contiguous submatrix of the given matrix.  ...  For a survey on Monge matrices and their uses in combinatorial optimization see [12] . A particularly famous result with many applications is an algorithm by Aggarwal et al.  ... 
doi:10.1145/3039873 fatcat:e6mgjx6a3jecxbj7am4pob6rem

Semi-local string comparison: algorithmic techniques and applications [article]

Alexander Tiskin
2013 arXiv   pre-print
The semi-local LCS problem asks for the LCS scores for each of the input strings against every substring of the other input string, and for every prefix of each input string against every suffix of the  ...  This work is devoted to exploring the structure of the semi-local LCS problem, its efficient solutions, and its applications in string comparison and other related areas, including computational molecular  ...  Michal Ziv-Ukelson for fruitful discussions, and many anonymous referees for their comments that helped to improve this work.  ... 
arXiv:0707.3619v21 fatcat:ufmpjbkmsvbvhf6l6zxugdcyc4

Parallel Construction and Query of Index Data Structures for Pattern Matching on Square Matrices

Raffaele Giancarlo, Roberto Grossi
1999 Journal of Complexity  
The main data structure is the Lsuffix tree, which is a generalization of the classical suffix tree for strings.  ...  The query algorithms are work optimal while the construction algorithm is work optimal only for arbitrary and large alphabets.  ...  We give some efficient algorithms for the construction and query of index data structures on the text, the main one being the Lsuffix tree of a square matrix [23] .  ... 
doi:10.1006/jcom.1998.0496 fatcat:li3m4yo2s5hcxnm5nmaafy35iq

Generalizations of suffix arrays to multi-dimensional matrices

Dong Kyue Kim, Yoo Ah Kim, Kunsoo Park
2003 Theoretical Computer Science  
However, the construction algorithm for Lsu x trees maintains complicated data structures and uses a large amount of space.  ...  Our contributions are the ÿrst e cient algorithms for constructing two-dimensional and three-dimensional su x arrays directly.  ...  Acknowledgements We are grateful to the referee for his valuable comments to improve the presentation of this paper.  ... 
doi:10.1016/s0304-3975(02)00861-7 fatcat:5qo5yrfg4fc53h3v5qwtrjhg3i

Generalizations of suffix arrays to multi-dimensional matrices

Dong Kyue Kim, Yoo Ah Kim, Kunsoo Park
2003 Theoretical Computer Science  
However, the construction algorithm for Lsu x trees maintains complicated data structures and uses a large amount of space.  ...  Our contributions are the ÿrst e cient algorithms for constructing two-dimensional and three-dimensional su x arrays directly.  ...  Acknowledgements We are grateful to the referee for his valuable comments to improve the presentation of this paper.  ... 
doi:10.1016/s0304-3975(02)00828-9 fatcat:mrh7eii66jfmpebyt44emocugm

Cycle bases in graphs characterization, algorithms, complexity, and applications

Telikepalli Kavitha, Christian Liebchen, Kurt Mehlhorn, Dimitrios Michail, Romeo Rizzi, Torsten Ueckerdt, Katharina A. Zweig
2009 Computer Science Review  
We provide polynomial algorithms for the minimum cycle basis problem for some of the classes and prove APX -hardness for others.  ...  In this paper, we survey the state of knowledge on cycle bases and also derive some new results.  ...  A Acknowledgement: The third author, KM, based part of a recent course on "Selected Topics in Algorithms" on this survey. He wants to thank the students of the course for numerous comments.  ... 
doi:10.1016/j.cosrev.2009.08.001 fatcat:zjz5byapyfcz3jbytxf2f7ijwi

Visualizing the Intellectual Structure with Paper-Reference Matrices

Jian Zhang, Chaomei Chen, Jiexun Li
2009 IEEE Transactions on Visualization and Computer Graphics  
Instead of using a reference-reference matrix, we directly use the original paper-reference matrix as the information source, and transform the paper-reference matrix into an FP-tree and visualize it in  ...  Visualizing the intellectual structure of scientific domains using co-cited units such as references or authors has become a routine for domain analysis.  ...  Vogeley, Danny Pan and John Parejko for their constructive suggestions on the SDSS case study. Funding for the SDSS and SDSS-II has been provided by the Alfred P.  ... 
doi:10.1109/tvcg.2009.202 pmid:19834184 fatcat:noirwbzehrfuvjpm5pddejtjyy

Submatrix Maximum Queries in Monge Matrices are Equivalent to Predecessor Search [article]

Pawel Gawrychowski, Shay Mozes, Oren Weimann
2017 arXiv   pre-print
We present an optimal data structure for submatrix maximum queries in n x n Monge matrices.  ...  Our result is a two-way reduction showing that the problem is equivalent to the classical predecessor problem in a universe of polynomial size.  ...  Now either we have already found the maximum, or it belongs to one of the staircase matrices fully contained in the query range.  ... 
arXiv:1502.07663v3 fatcat:ldvo7bphxfemhbpeqtaytmezaq

New Acyclic and Star Coloring Algorithms with Application to Computing Hessians

Assefaw H. Gebremedhin, Arijit Tarafdar, Fredrik Manne, Alex Pothen
2007 SIAM Journal on Scientific Computing  
For a graph G on n vertices and m edges, the time complexity of our star coloring algorithm is O(nd 2 ), where d k , a generalization of vertex degree, denotes the average number of distinct paths of length  ...  To the best of our knowledge, our work is the first practical algorithm for the acyclic coloring problem.  ...  Our sincere thanks go to the anonymous referees for their valuable comments on the content and presentation of this paper and for bringing related works in the literature to our attention.  ... 
doi:10.1137/050639879 fatcat:my5gpzch4vb35flx534hisffly

Heuristic algorithms and learning techniques: applications to the graph coloring problem

Daniel Cosmin Porumbel
2011 4OR  
Toward applications for other combinatorial problems By carefully investigating the source code of the guided algorithms-see Algorithm 4.2 (p. 55) and Algorithm 4.3 (p. 59)-one observes that TS-Div and  ...  The rest of the assignment can be constructed by applying the Hungarian algorithm on the remaining rows and columns.  ...  This situation typically appears for dense graphs, for which one needs a large number of colors k and the average class size (i.e. |V | k ) becomes very low.  ... 
doi:10.1007/s10288-011-0193-5 fatcat:nihv44ivizh3fgo7vwo2kynwka

A scalable sparse Cholesky based approach for learning high-dimensional covariance matrices in ordered data

Kshitij Khare, Sang-Yun Oh, Syed Rahman, Bala Rajaratnam
2019 Machine Learning  
Acknowledgment We have been fortunate to have our colleagues and collaborators give us their impressions and contributions toward the contents of this book. We would like to  ...  We can categorize these structures into three algorithms: (1) hash table-based algorithms, (2) suffix tree-based algorithms and (3) algorithms based on merge sorting.  ...  the suffix-based trees for alignment of sequences are MUMmer and REPuter (Paszkiewicz and Studholme 2010 ).  ... 
doi:10.1007/s10994-019-05810-5 fatcat:nulmjvxvwjgojfoe2ywv3pjrpu

Submatrix Maximum Queries in Monge Matrices Are Equivalent to Predecessor Search [chapter]

Paweł Gawrychowski, Shay Mozes, Oren Weimann
2015 Lecture Notes in Computer Science  
Our result settles the problem, improving on the O(log 2 n) query-time in SODA'12, and on the O(log n) query-time in ICALP'14.  ...  . 8 We consider m × n matrices, but for simplicity we sometimes state the results for n × n matrices.  ...  Now either we have already found the maximum, or it belongs to one of the staircase matrices fully contained in the query range.  ... 
doi:10.1007/978-3-662-47672-7_47 fatcat:rzxs4qvqbvajrnsqwlrceemtja

Jensen-Bregman LogDet Divergence with Application to Efficient Similarity Search for Covariance Matrices

A. Cherian, S. Sra, A. Banerjee, N. Papanikolopoulos
2013 IEEE Transactions on Pattern Analysis and Machine Intelligence  
Utilizing the fact that the square-root of JBLD is a metric, we address the problem of efficient nearest neighbor retrieval on large covariance datasets via a metric tree data structure.  ...  An important task in all of these applications is to compare two covariance matrices using a (dis)similarity function, for which the common choice is the Riemannian metric on the manifold inhabited by  ...  the metric tree is constructed optimally, the search time for AIRM and J ℓd are comparable, and (iii) (which is the most important) the metric tree construction for AIRM almost increases quadratically  ... 
doi:10.1109/tpami.2012.259 pmid:23868777 fatcat:3fgogwtie5genex5ohziish2ka

Page 7892 of Mathematical Reviews Vol. , Issue 99k [page]

1999 Mathematical Reviews  
Giancarlo proposed a two-dimensional index data structure, the Lsuffix tree, that generalizes suffix trees to square matrices.  ...  However, the construction algorithm for Lsuffix trees maintains complicated data structures and uses a large amount of space.  ... 
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