Nonserial Dynamic Programming and Tree Decomposition in Discrete Optimization

Shcherbina, Oleg

doi:10.1007/978-3-540-69995-8_26

Cited by 19 publications

(12 citation statements)

References 9 publications

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“…An dependency graph contains a vertex for each variable and an edge is added between vertices if they appear in the same constraint or component of the objective function. NSDP is a process which eliminates variables in such a way that adjacent variables can be merged together [30]. The first step in applying NSDP is identifying weakly connected components of interaction graph.…”

Section: Non-serial Dynamic Programmingmentioning

confidence: 99%

“…However, solving the scaffolding ILP directly for very large problem instances is often impractical. To achieve scalability we take advantage of the sparsity of the underlying scaffolding graph by independently scaffolding its tri-connected components, generated in linear time using the SPQR-tree datastructure, and then optimally combining them using non-serial dynamical programming (NSDP) [30]. For cases when even tri-connected components are too large to be handled directly we adopt a hierarchical scaffolding scheme that solves multiple ILPs for increasingly denser subgraphs of G obtained by filtering low confidence edges.…”

Section: Introductionmentioning

confidence: 99%

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Scalable genome scaffolding using integer linear programming

Lindsay

Salooti

Zelikovsky

et al. 2012

Proceedings of the ACM Conference on Bioinformatics, Computational Biology and Biomedicine

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The rapidly diminishing cost of genome sequencing is driving renewed interest in large scale genome sequencing programs such as Genome 10K (G10K). Despite renewed interest the assembly of large genomes from short reads is still an extremely resource intensive process. This work presents a scalable algorithms to create scaffolds, or ordered and oriented sets of assembled contigs, which is one part of a practical assembly. This is accomplished using integer linear programming (ILP). In order to process large mammalian genomes we employ non-serial dynamic programming (NSDP) and a hierarchical strategy. Both existing and novel quantitative metrics are used to compare scaffolding tools and gain deeper insight into the challenges of scaffolding. The code is available at: https://bitbucket.org/jrl03001/silp

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Section: Non-serial Dynamic Programmingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Scalable genome scaffolding using integer linear programming

Lindsay

Salooti

Zelikovsky

et al. 2012

Proceedings of the ACM Conference on Bioinformatics, Computational Biology and Biomedicine

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“…The parallel algorithm proposed here is related to nonserial dynamic programming methods that describe the connection between variables in the problem using tree representations, see, e.g., Bertelè and Brioschi (1973); Moallemi (2007);Shcherbina (2007). Nonserial dynamic programming share the basic ideas with serial dynamic programming, see Bertsekas (2000), but can handle more general problem structures.…”

Section: Parallel Newton Step Computationmentioning

confidence: 99%

On Structure Exploiting Numerical Algorithms for Model Predictive Control

Nielsen

2015

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One of the most common advanced control strategies used in industry today is Model Predictive Control (mpc), and some reasons for its success are that it can handle multivariable systems and constraints on states and control inputs in a structured way. At each time-step in the mpc control loop the control input is computed by solving a constrained finite-time optimal control (cftoc) problem on-line. There exist several optimization methods to solve the cftoc problem, where two common types are interior-point (ip) methods and active-set (as) methods. In both these types of methods, the main computational effort is known to be the computation of the search directions, which boils down to solving a sequence of Newton-system-like equations. These systems of equations correspond to unconstrained finite-time optimal control (uftoc) problems. Hence, high-performance ip and as methods for cftoc problems rely on efficient algorithms for solving the uftoc problems.The solution to a uftoc problem is computed by solving the corresponding Karush-Kuhn-Tucker (kkt) system, which is often done using generic sparsity exploiting algorithms or Riccati recursions. When an as method is used to compute the solution to the cftoc problem, the system of equations that is solved to obtain the solution to a uftoc problem is only changed by a low-rank modification of the system of equations in the previous iteration. This structured change is often exploited in as methods to improve performance in terms of computation time. Traditionally, this has not been possible to exploit when Riccati recursions are used to solve the uftoc problems, but in this thesis, an algorithm for performing low-rank modifications of the Riccati recursion is presented.In recent years, parallel hardware has become more commonly available, and the use of parallel algorithms for solving the cftoc problem and the underlying uftoc problem has increased. Some existing parallel algorithms for computing the solution to this type of problems obtain the solution iteratively, and these methods may require many iterations to converge. Some other parallel algorithms compute the solution directly (non-iteratively) by solving parts of the system of equations in parallel, followed by a serial solution of a dense system of equations without the sparse structure of the mpc problem. In this thesis, two parallel algorithms that compute the solution directly (non-iteratively) in parallel are presented. These algorithms can be used in both ip and as methods, and they exploit the sparse structure of the mpc problem such that no dense system of equations needs to be solved serially. Furthermore, one of the proposed parallel algorithms exploits the special structure of the mpc problem even in the parallel computations, which improves performance in terms of computation time even more. By using these algorithms, it is possible to obtain logarithmic complexity growth in the prediction horizon length.v Populärvetenskaplig sammanfattningModellprediktiv reglering (eng. Model Predictive...

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“…Scalability of our algorithm, referred to as SILP2, is achieved by adopting a non-serial dynamical programming (NSDP) approach [ 27 ]. Rather than solving one large ILP, several smaller ILPs can be solved seperately and composed to find the complete and optimal solution.…”

Section: Introductionmentioning

confidence: 99%

ILP-based maximum likelihood genome scaffolding

et al. 2014

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BackgroundInterest in de novo genome assembly has been renewed in the past decade due to rapid advances in high-throughput sequencing (HTS) technologies which generate relatively short reads resulting in highly fragmented assemblies consisting of contigs. Additional long-range linkage information is typically used to orient, order, and link contigs into larger structures referred to as scaffolds. Due to library preparation artifacts and erroneous mapping of reads originating from repeats, scaffolding remains a challenging problem. In this paper, we provide a scalable scaffolding algorithm (SILP2) employing a maximum likelihood model capturing read mapping uncertainty and/or non-uniformity of contig coverage which is solved using integer linear programming. A Non-Serial Dynamic Programming (NSDP) paradigm is applied to render our algorithm useful in the processing of larger mammalian genomes. To compare scaffolding tools, we employ novel quantitative metrics in addition to the extant metrics in the field. We have also expanded the set of experiments to include scaffolding of low-complexity metagenomic samples.ResultsSILP2 achieves better scalability throughg a more efficient NSDP algorithm than previous release of SILP. The results show that SILP2 compares favorably to previous methods OPERA and MIP in both scalability and accuracy for scaffolding single genomes of up to human size, and significantly outperforms them on scaffolding low-complexity metagenomic samples.ConclusionsEquipped with NSDP, SILP2 is able to scaffold large mammalian genomes, resulting in the longest and most accurate scaffolds. The ILP formulation for the maximum likelihood model is shown to be flexible enough to handle metagenomic samples.

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Nonserial Dynamic Programming and Tree Decomposition in Discrete Optimization

Cited by 19 publications

References 9 publications

Scalable genome scaffolding using integer linear programming

Scalable genome scaffolding using integer linear programming

On Structure Exploiting Numerical Algorithms for Model Predictive Control

ILP-based maximum likelihood genome scaffolding

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