A fast exact sequential algorithm for the partial digest problem

Abbas, Mostafa M.; Bahig, Hazem M.

doi:10.1186/s12859-016-1365-2

Cited by 15 publications

(10 citation statements)

References 18 publications

(19 reference statements)

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“…However, there exist examples with exponential runtime [4,26]. Abbas and Bahig [27] later demonstrated that some of the worst-case scenarios could be avoided by performing a breadth-first search instead. An alternative to clever combinatorial search is to formulate the problem as a binary integer program [28][29][30], and then relax it to obtain a convex semidefinite program [5].…”

Section: Related Workmentioning

confidence: 99%

Reconstructing Point Sets from Distance Distributions

Huang,

Dokmanić

2018

Preprint

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We address the problem of reconstructing a set of points on a line or a loop from their unassigned noisy pairwise distances. When the points lie on a line, the problem is known as the turnpike problem; when they are on a loop, it is known as the beltway problem. We approximate the problem by discretizing the domain and representing the N points via an N -hot encoding, which is a density supported on the discretized domain. We show how the distance distribution is then simply a collection of quadratic functionals of this density and propose to recover the point locations so that the estimated distance distribution matches the measured distance distribution. This can be cast as a constrained nonconvex optimization problem which we solve using projected gradient descent with a suitable spectral initializer. We derive conditions under which the proposed approach locally converges to a global optimizer with a linear convergence rate. Compared to the conventional backtracking approach, our method jointly reconstructs all the point locations and is robust to noise in the measurements. We substantiate these claims with state-of-the-art performance across a number of numerical experiments. Our method is the first practical approach to solve the large-scale noisy beltway problem where the points lie on a loop.

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Section: Related Workmentioning

confidence: 99%

Reconstructing Point Sets from Distance Distributions

Huang,

Dokmanić

2018

Preprint

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“…Abbas and Bahig [1] introduced two exact sequential algorithms for PD problem. The first algorithm, BBb, is based on traverse the solution tree by using the breadth-first strategy from level 1 to n. The running time for the BBb algorithm is less than Skiena, Smith and Lemke algorithm.…”

Section: Best Known Exact Algorithmmentioning

confidence: 99%

“…Different algorithms are proposed to find the exact solution of PD problem [1, 2, 4-7, 9, 11-13, 15, 18]. Some of these algorithms are impractical algorithms, while the other algorithms are practical such as [1,9,18]. The first practical algorithm was designed by Skiena, Smith and Lemke [18] and ran in n 2 log n in the average case.…”

Section: Introductionmentioning

confidence: 99%

“…In the case of Zhang instances, Skiena, Smith and Lemke algorithm is faster than Formin's algorithm, while in some other case Formin's algorithm is faster than the Skiena, Smith and Lemke algorithm. The third practical algorithm was presented by Abbas and Bahig [1]. The algorithm was compared with the first practical algorithm and the results show that the proposed algorithm is more efficient than Skiena, Smith, and Lemke algorithm.…”

Section: Introductionmentioning

confidence: 99%

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Speeding Up the Partial Digest Algorithm

Bahig¹,

Abbas²

2018

Jour. Inform. Math. Sci.

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We consider the partial digest problem, which aims to find the setIn bioinformatics, the lengths of DNA fragments represents the multiset D, while the set of restriction site locations represents the set X = {x 0 , x 1 , . . . , x n }. In this paper, we study experimentally the effect of increasing and decreasing the number of levels on the breadth-breadth algorithm which is the best practical algorithm for the partial digest problem. The experimental study shows that the running time of breadth-breadth method is not the minimum time. Also, we obtained the number of levels that is used in the breadth-breadth algorithm to reduce the running time.

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“…Abbas and Bahig [4] investigated the partial digestion problem by proposing two algorithm "branch and bound based on breadth" (BBb) and "branch and bound based on breadth two times" (BBb2). The latter requires less memory than BBb as the partial digestion problem is solved in two stages in breadth-first mode.…”

Section: Sequence Analysis and Ontologiesmentioning

confidence: 99%