Omer Egecioglu - Profile on Academia.edu (original) (raw)

Papers by Omer Egecioglu

In a recent paper we have presented a method to evaluate certain Hankel determinants as almost pr... more In a recent paper we have presented a method to evaluate certain Hankel determinants as almost products; i.e. as a sum of a small number of products. The technique to find the explicit form of the almost product relies on differential-convolution equations and trace calculations. In the trace calculations a number of intermediate nonlinear terms involving determinants occur, but only to cancel out in the end. In this paper, we introduce a class of multilinear operators \gamma acting on tuples of matrices as an alternative to the trace method. These operators do not produce extraneous nonlinear terms, and can be combined easily with differentiation. The paper is self contained. An example of an almost product evaluation using \gamma-operators is worked out in detail and tables of the \gamma-operator values on various forms of matrices are provided. We also present an explicit evaluation of a new class of Hankel determinants and conjectures.

Distributed and Parallel Databases, 2005

It is desirable to design partitioning methods that minimize the I/O time incurred during query e... more It is desirable to design partitioning methods that minimize the I/O time incurred during query execution in spatial databases. This paper explores optimal partitioning for two-dimensional data for a class of queries and develops multi-disk allocation techniques that maximize the degree of I/O parallelism obtained in each case. We show that hexagonal partitioning has optimal I/O performance for circular queries among all partitioning methods that use convex non-overlapping regions. An analysis and extension of this result to all possible partitioning techniques is also given. For rectangular queries, we show that hexagonal partitioning has overall better I/O performance for a general class of range queries, except for rectilinear queries, in which case rectangular grid partitioning is superior. By using current algorithms for rectangular grid partitioning, parallel storage and retrieval algorithms for hexagonal partitioning can be constructed. Some of these results carry over to circular partitioning of the data-which is an example of a non-convex region.

Polynomial Families Satisfying a Riemann Hypothesis

Efficient Computation of Long Similar Subsequences

Lecture Notes in Computer Science, 2002

Abstract. Given sequences X of length n and Y of length m with n ≥ m, let LAt ∗ and NLAt ∗ denote... more Abstract. Given sequences X of length n and Y of length m with n ≥ m, let LAt ∗ and NLAt ∗ denote the maximum ordinary, and max-imum length normalized scores of local alignments with length at least a given threshold value t. The alignment length is defined as the sum ...

Algorithms for Local Alignments with Length Constraints

Page 1. Algorithms For Local Alignment With Length Constraints? Abdullah N. Arslan and Omer E gec... more Page 1. Algorithms For Local Alignment With Length Constraints? Abdullah N. Arslan and Omer E gecio glu Department of Computer Science University of California, Santa Barbara CA 93106, USA farslan,omerg@cs.ucsb.edu Abstract. ...

An Improved Upper Bound on the Size of Planar Convex-Hulls

Cocoon, 2001

Page 1. An Improved Upper Bound on the Size of Planar Convex-Hulls* Abdullah N. Arslan and ¨Omer ... more Page 1. An Improved Upper Bound on the Size of Planar Convex-Hulls* Abdullah N. Arslan and ¨Omer E˘gecio˘glu Department of Computer Science University of California, Santa Barbara CA 93106, USA {arslan,omer}@cs.ucsb.edu Abstract. ...

The Bisection Width and the Isoperimetric Number of Arrays

... BibTeX. @TECHREPORT{Azizoglu00thebisection, author = {M. Cemil Azizoglu and Ömer Egecioglu}, ... more ... BibTeX. @TECHREPORT{Azizoglu00thebisection, author = {M. Cemil Azizoglu and Ömer Egecioglu}, title = {The Bisection Width and the Isoperimetric Number of Arrays}, institution = {DISCRETE APPL. ... 81, Optimal assignments of numbers to vertices - Harper - 1964. ...

A parallel algorighm for generating discrete orthogonal polynomials

Parallel Computing, 1992

Ijfcs, 2002

The local sequence alignment problem is the detection of similar subsequences in two given sequen... more The local sequence alignment problem is the detection of similar subsequences in two given sequences of lengths n m. Unfortunately the common notion of local alignment su ers from some wellknown anomalies which result from not taking into account the lengths of the aligned subsequences. We introduce the length restricted local alignment problem which includes as a constraint an upper limit T on the length of one of the subsequences to be aligned. We propose an e cient approximation algorithm using which we can nd a solution satisfying the length bound, and whose score is within di erence of the optimum score for any given positive integer in time O(nmT= ) using O(mT= ) space. We also introduce the cyclic local alignment problem and show how our idea can be applied to this case as well. This is a dual approach to the well-known cyclic edit distance problem.

The Smith-Waterman algorithm for local sequence alignment is one of the most important techniques... more The Smith-Waterman algorithm for local sequence alignment is one of the most important techniques in computational molecular biology. This ingenious dynamic programming approach was designed to reveal the highly conserved fragments by discarding poorly conserved initial and terminal segments. However, the existing notion of local similarity has a serious aw: it does not discard poorly conserved intermediate segments. The Smith-Waterman algorithm nds the local alignment with maximal score but it is unable to nd local alignment with maximum degree of similarity (e.g., maximal percent of matches). Moreover, there is still no e cient algorithm that answers the following natural question: do two sequences share a (su ciently long) fragment with more than 70% of similarity? As a result, the local alignment sometimes produces a mosaic of well-conserved fragments arti cially connected by poorly-conserved or even unrelated fragments. This may lead to problems in comparison of long genomic sequences and comparative gene prediction as recently pointed out by . In this paper we propose a new sequence comparison algorithm (normalized local alignment) that reports the regions with maximum degree of similarity. The algorithm is based on fractional programming and its running time is O(n 2 log n). In practice, normalized local alignment is only 3-5 times slower than the standard Smith-Waterman algorithm.

Proceedings of the Fifth Annual International Conference on Computational Biology, Apr 1, 2001

The Smith-Waterman algorithm for local sequence alignment is one of the most important techniques... more The Smith-Waterman algorithm for local sequence alignment is one of the most important techniques in computational molecular biology. This ingenious dynamic programming approach was designed to reveal the highly conserved fragments by discarding poorly conserved initial and terminal segments. However, the existing notion of local similarity has a serious aw: it does not discard poorly conserved intermediate segments. The Smith-Waterman algorithm nds the local alignment with maximal score but it is unable to nd local alignment with maximum degree of similarity (e.g., maximal percent of matches). Moreover, there is still no e cient algorithm that answers the following natural question: do two sequences share a (su ciently long) fragment with more than 70% of similarity? As a result, the local alignment sometimes produces a mosaic of well-conserved fragments arti cially connected by poorly-conserved or even unrelated fragments. This may lead to problems in comparison of long genomic sequences and comparative gene prediction as recently pointed out by . In this paper we propose a new sequence comparison algorithm (normalized local alignment) that reports the regions with maximum degree of similarity. The algorithm is based on fractional programming and its running time is O(n 2 log n). In practice, normalized local alignment is only 3-5 times slower than the standard Smith-Waterman algorithm.

In the directed acyclic graph (dag) model of algorithms, consider the following problem for prece... more In the directed acyclic graph (dag) model of algorithms, consider the following problem for precedence-constrained multiprocessor schedules for array computations: Given a sequence of dags and linear schedules parameterized by Ò, compute a lower bound on the number of processors required by the schedule as a function of Ò. This problem is formulated so that the number of tasks that are scheduled for execution during any fixed time step is the number of non-negative integer solutions Ò to a set of parametric linear Diophantine equations. Generating function methods are then used for constructing a formula for the numbers Ò . We implemented this algorithm as a Mathematica program. This paper is an overview of the techniques involved and their applications to well-known schedules for Matrix-Vector Product, Triangular Matrix Product, and Gaussian Elimination dags. Some example runs and automatically produced symbolic formulas for processor lower bounds by the algorithm are given.

The Edge-isoperimetric Number of Generalized Cylinders

How to Approximate the Inner-Product: Fast Dynamic Algorithms for Similarity

CiteSeerX - Document Details (Isaac Councill, Lee Giles): We develop dynamic dimensionality reduc... more CiteSeerX - Document Details (Isaac Councill, Lee Giles): We develop dynamic dimensionality reduction based on the approximation of the standard inner-product. This results in a family of fast algorithms for checking similarity of objects whose feature representations are large ...

Proceedings Ieee Infocom, Apr 19, 2009

Deployed anonymous networks such as Tor focus on delivering messages through end-to-end paths wit... more Deployed anonymous networks such as Tor focus on delivering messages through end-to-end paths with high anonymity. Selection of routers in the anonymous path construction is either performed randomly, or relies on self-described resource availability from each router, which makes the system vulnerable to low-resource attacks. In this paper, we investigate an alternative router and path selection mechanism for constructing efficient end-to-end paths with low loss of path anonymity. We propose a novel construct called a "route mesh," and a dynamic programming algorithm that determines optimallatency paths from many random samples using only a small number of end-to-end measurements. We prove analytically that our path search algorithm finds the optimal path, and requires exponentially lower number of measurements compared to a standard measurement approach. In addition, our analysis shows that route meshes incur only a small loss in anonymity for its users. Meanwhile, experimental deployment of our anonymous routers on Planet-lab shows dramatic improvements in path selection quality using very small route meshes that incur low measurement overheads.

Parallel Algorithms for Fast Computation of Normalized Edit Distances

The authors give work-optimal and polylogarithmic time parallel algorithms for solving the normal... more The authors give work-optimal and polylogarithmic time parallel algorithms for solving the normalized edit distance problem. The normalized edit distance between two strings X and Y with lengths n⩾m is the minimum quotient of the sum of the costs of edit operations transforming X into Y by the length of the edit path corresponding to those edit operations. Marzal and

The Electronic Journal of Combinatorics, 2008

An extensive literature exists describing various techniques for the evaluation of Hankel determi... more An extensive literature exists describing various techniques for the evaluation of Hankel determinants. The prevailing methods such as Dodgson condensation, continued fraction expansion, LU decomposition, all produce product formulas when they are applicable. We mention the classic case of the Hankel determinants with binomial entries 3k+2 k and those with entries 3k k ; both of these classes of Hankel determinants have product form evaluations. The intermediate case, 3k+1 k has not been evaluated. There is a good reason for this: these latter determinants do not have product form evaluations.

Efficient Non-parametric Estimation of Probability Density Functions

CiteSeerX - Document Details (Isaac Councill, Lee Giles): Accurate and fast estimation of probabi... more CiteSeerX - Document Details (Isaac Councill, Lee Giles): Accurate and fast estimation of probability density functions is crucial for satisfactory computational performance in many scientific problems. When the type of density is known a priori, then the problem becomes statistical ...

Bessel Polynomials and the Partial Sums of the Exponential Series

Siam Journal on Discrete Mathematics, 2011

In a recent paper we have presented a method to evaluate certain Hankel determinants as almost pr... more In a recent paper we have presented a method to evaluate certain Hankel determinants as almost products; i.e. as a sum of a small number of products. The technique to find the explicit form of the almost product relies on differential-convolution equations and trace calculations. In the trace calculations a number of intermediate nonlinear terms involving determinants occur, but only to cancel out in the end. In this paper, we introduce a class of multilinear operators \gamma acting on tuples of matrices as an alternative to the trace method. These operators do not produce extraneous nonlinear terms, and can be combined easily with differentiation. The paper is self contained. An example of an almost product evaluation using \gamma-operators is worked out in detail and tables of the \gamma-operator values on various forms of matrices are provided. We also present an explicit evaluation of a new class of Hankel determinants and conjectures.

Distributed and Parallel Databases, 2005

It is desirable to design partitioning methods that minimize the I/O time incurred during query e... more It is desirable to design partitioning methods that minimize the I/O time incurred during query execution in spatial databases. This paper explores optimal partitioning for two-dimensional data for a class of queries and develops multi-disk allocation techniques that maximize the degree of I/O parallelism obtained in each case. We show that hexagonal partitioning has optimal I/O performance for circular queries among all partitioning methods that use convex non-overlapping regions. An analysis and extension of this result to all possible partitioning techniques is also given. For rectangular queries, we show that hexagonal partitioning has overall better I/O performance for a general class of range queries, except for rectilinear queries, in which case rectangular grid partitioning is superior. By using current algorithms for rectangular grid partitioning, parallel storage and retrieval algorithms for hexagonal partitioning can be constructed. Some of these results carry over to circular partitioning of the data-which is an example of a non-convex region.

Polynomial Families Satisfying a Riemann Hypothesis

Efficient Computation of Long Similar Subsequences

Lecture Notes in Computer Science, 2002

Abstract. Given sequences X of length n and Y of length m with n ≥ m, let LAt ∗ and NLAt ∗ denote... more Abstract. Given sequences X of length n and Y of length m with n ≥ m, let LAt ∗ and NLAt ∗ denote the maximum ordinary, and max-imum length normalized scores of local alignments with length at least a given threshold value t. The alignment length is defined as the sum ...

Algorithms for Local Alignments with Length Constraints

Page 1. Algorithms For Local Alignment With Length Constraints? Abdullah N. Arslan and Omer E gec... more Page 1. Algorithms For Local Alignment With Length Constraints? Abdullah N. Arslan and Omer E gecio glu Department of Computer Science University of California, Santa Barbara CA 93106, USA farslan,omerg@cs.ucsb.edu Abstract. ...

An Improved Upper Bound on the Size of Planar Convex-Hulls

Cocoon, 2001

Page 1. An Improved Upper Bound on the Size of Planar Convex-Hulls* Abdullah N. Arslan and ¨Omer ... more Page 1. An Improved Upper Bound on the Size of Planar Convex-Hulls* Abdullah N. Arslan and ¨Omer E˘gecio˘glu Department of Computer Science University of California, Santa Barbara CA 93106, USA {arslan,omer}@cs.ucsb.edu Abstract. ...

The Bisection Width and the Isoperimetric Number of Arrays

... BibTeX. @TECHREPORT{Azizoglu00thebisection, author = {M. Cemil Azizoglu and Ömer Egecioglu}, ... more ... BibTeX. @TECHREPORT{Azizoglu00thebisection, author = {M. Cemil Azizoglu and Ömer Egecioglu}, title = {The Bisection Width and the Isoperimetric Number of Arrays}, institution = {DISCRETE APPL. ... 81, Optimal assignments of numbers to vertices - Harper - 1964. ...

A parallel algorighm for generating discrete orthogonal polynomials

Parallel Computing, 1992

Ijfcs, 2002

The local sequence alignment problem is the detection of similar subsequences in two given sequen... more The local sequence alignment problem is the detection of similar subsequences in two given sequences of lengths n m. Unfortunately the common notion of local alignment su ers from some wellknown anomalies which result from not taking into account the lengths of the aligned subsequences. We introduce the length restricted local alignment problem which includes as a constraint an upper limit T on the length of one of the subsequences to be aligned. We propose an e cient approximation algorithm using which we can nd a solution satisfying the length bound, and whose score is within di erence of the optimum score for any given positive integer in time O(nmT= ) using O(mT= ) space. We also introduce the cyclic local alignment problem and show how our idea can be applied to this case as well. This is a dual approach to the well-known cyclic edit distance problem.

The Smith-Waterman algorithm for local sequence alignment is one of the most important techniques... more The Smith-Waterman algorithm for local sequence alignment is one of the most important techniques in computational molecular biology. This ingenious dynamic programming approach was designed to reveal the highly conserved fragments by discarding poorly conserved initial and terminal segments. However, the existing notion of local similarity has a serious aw: it does not discard poorly conserved intermediate segments. The Smith-Waterman algorithm nds the local alignment with maximal score but it is unable to nd local alignment with maximum degree of similarity (e.g., maximal percent of matches). Moreover, there is still no e cient algorithm that answers the following natural question: do two sequences share a (su ciently long) fragment with more than 70% of similarity? As a result, the local alignment sometimes produces a mosaic of well-conserved fragments arti cially connected by poorly-conserved or even unrelated fragments. This may lead to problems in comparison of long genomic sequences and comparative gene prediction as recently pointed out by . In this paper we propose a new sequence comparison algorithm (normalized local alignment) that reports the regions with maximum degree of similarity. The algorithm is based on fractional programming and its running time is O(n 2 log n). In practice, normalized local alignment is only 3-5 times slower than the standard Smith-Waterman algorithm.

Proceedings of the Fifth Annual International Conference on Computational Biology, Apr 1, 2001

The Smith-Waterman algorithm for local sequence alignment is one of the most important techniques... more The Smith-Waterman algorithm for local sequence alignment is one of the most important techniques in computational molecular biology. This ingenious dynamic programming approach was designed to reveal the highly conserved fragments by discarding poorly conserved initial and terminal segments. However, the existing notion of local similarity has a serious aw: it does not discard poorly conserved intermediate segments. The Smith-Waterman algorithm nds the local alignment with maximal score but it is unable to nd local alignment with maximum degree of similarity (e.g., maximal percent of matches). Moreover, there is still no e cient algorithm that answers the following natural question: do two sequences share a (su ciently long) fragment with more than 70% of similarity? As a result, the local alignment sometimes produces a mosaic of well-conserved fragments arti cially connected by poorly-conserved or even unrelated fragments. This may lead to problems in comparison of long genomic sequences and comparative gene prediction as recently pointed out by . In this paper we propose a new sequence comparison algorithm (normalized local alignment) that reports the regions with maximum degree of similarity. The algorithm is based on fractional programming and its running time is O(n 2 log n). In practice, normalized local alignment is only 3-5 times slower than the standard Smith-Waterman algorithm.

In the directed acyclic graph (dag) model of algorithms, consider the following problem for prece... more In the directed acyclic graph (dag) model of algorithms, consider the following problem for precedence-constrained multiprocessor schedules for array computations: Given a sequence of dags and linear schedules parameterized by Ò, compute a lower bound on the number of processors required by the schedule as a function of Ò. This problem is formulated so that the number of tasks that are scheduled for execution during any fixed time step is the number of non-negative integer solutions Ò to a set of parametric linear Diophantine equations. Generating function methods are then used for constructing a formula for the numbers Ò . We implemented this algorithm as a Mathematica program. This paper is an overview of the techniques involved and their applications to well-known schedules for Matrix-Vector Product, Triangular Matrix Product, and Gaussian Elimination dags. Some example runs and automatically produced symbolic formulas for processor lower bounds by the algorithm are given.

The Edge-isoperimetric Number of Generalized Cylinders

How to Approximate the Inner-Product: Fast Dynamic Algorithms for Similarity

CiteSeerX - Document Details (Isaac Councill, Lee Giles): We develop dynamic dimensionality reduc... more CiteSeerX - Document Details (Isaac Councill, Lee Giles): We develop dynamic dimensionality reduction based on the approximation of the standard inner-product. This results in a family of fast algorithms for checking similarity of objects whose feature representations are large ...

Proceedings Ieee Infocom, Apr 19, 2009

Deployed anonymous networks such as Tor focus on delivering messages through end-to-end paths wit... more Deployed anonymous networks such as Tor focus on delivering messages through end-to-end paths with high anonymity. Selection of routers in the anonymous path construction is either performed randomly, or relies on self-described resource availability from each router, which makes the system vulnerable to low-resource attacks. In this paper, we investigate an alternative router and path selection mechanism for constructing efficient end-to-end paths with low loss of path anonymity. We propose a novel construct called a "route mesh," and a dynamic programming algorithm that determines optimallatency paths from many random samples using only a small number of end-to-end measurements. We prove analytically that our path search algorithm finds the optimal path, and requires exponentially lower number of measurements compared to a standard measurement approach. In addition, our analysis shows that route meshes incur only a small loss in anonymity for its users. Meanwhile, experimental deployment of our anonymous routers on Planet-lab shows dramatic improvements in path selection quality using very small route meshes that incur low measurement overheads.

Parallel Algorithms for Fast Computation of Normalized Edit Distances

The authors give work-optimal and polylogarithmic time parallel algorithms for solving the normal... more The authors give work-optimal and polylogarithmic time parallel algorithms for solving the normalized edit distance problem. The normalized edit distance between two strings X and Y with lengths n⩾m is the minimum quotient of the sum of the costs of edit operations transforming X into Y by the length of the edit path corresponding to those edit operations. Marzal and

The Electronic Journal of Combinatorics, 2008

An extensive literature exists describing various techniques for the evaluation of Hankel determi... more An extensive literature exists describing various techniques for the evaluation of Hankel determinants. The prevailing methods such as Dodgson condensation, continued fraction expansion, LU decomposition, all produce product formulas when they are applicable. We mention the classic case of the Hankel determinants with binomial entries 3k+2 k and those with entries 3k k ; both of these classes of Hankel determinants have product form evaluations. The intermediate case, 3k+1 k has not been evaluated. There is a good reason for this: these latter determinants do not have product form evaluations.

Efficient Non-parametric Estimation of Probability Density Functions

CiteSeerX - Document Details (Isaac Councill, Lee Giles): Accurate and fast estimation of probabi... more CiteSeerX - Document Details (Isaac Councill, Lee Giles): Accurate and fast estimation of probability density functions is crucial for satisfactory computational performance in many scientific problems. When the type of density is known a priori, then the problem becomes statistical ...

Bessel Polynomials and the Partial Sums of the Exponential Series

Siam Journal on Discrete Mathematics, 2011