The discretizable molecular distance geometry problem

Lavor, Carlile; Liberti, Leo; Maculan, Nelson; Mucherino, Antonio

doi:10.1007/s10589-011-9402-6

Cited by 111 publications

(198 citation statements)

References 58 publications

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“…Because the DDGP contains the DMDGP (see [26] for the definition of the DDGP in 3D and for a comparison between DDGP and DMDGP), the proof of NP-hardness of the DMDGP given in [15,17] also holds for the DDGP. The DMDGP and DDGP can both be solved (approximately for a given ε > 0) using a recursive binary exploration following the order < on V : at each rank i, use the already known positions of the adjacent predecessors in Uv to find at most two positions for the i-th vertex, and recurse the search over each of them.…”

Section: ⊓ ⊔mentioning

confidence: 99%

“…The DMDGP and DDGP can both be solved (approximately for a given ε > 0) using a recursive binary exploration following the order < on V : at each rank i, use the already known positions of the adjacent predecessors in Uv to find at most two positions for the i-th vertex, and recurse the search over each of them. Such an algorithm, called Branch-and-Prune (BP), was described in [21], further discussed in [17], and used in several papers [27,19,18,28,29,25,20] to solve different DMDGP variants. Similar algorithms were proposed in [35,3].…”

Section: ⊓ ⊔mentioning

confidence: 99%

“…Similar algorithms were proposed in [35,3]. Discrete search algorithms such as BP solve DDGP instances much faster than continuous (and SDP-based) searches (see [22,17]); most importantly, and uniquely among other distance geometry methods, they can be configured to find all incongruent solutions to a given instance.…”

Section: ⊓ ⊔mentioning

confidence: 99%

“…Search methods based on this principle were proposed in [21,35,3]. The same vertex order for the problem restricted to K = 3 was discussed within the context of the Discretizable Molecular Distance Geometry Problem (DMDGP), see [15], and an application to real proteins discussed in [27,19].…”

Section: Introductionmentioning

confidence: 99%

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Discretization orders for distance geometry problems

et al. 2011

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Given a weighted, undirected simple graph G = (V, E, d) (where d : E → R + ), the Distance Geometry Problem (DGP) is to determine an embeddingAlthough, in general, the DGP is solved using continuous methods, under certain conditions the search is reduced to a discrete set of points. We give one such condition as a particular order on V . We formalize the decision problem of determining whether such an order exists for a given graph and show that this problem is NP-complete in general and polynomial for fixed dimension K. We present results of computational experiments on a set of protein backbones whose natural atomic order does not satisfy the order requirements and compare our approach with some available continuous space searches.

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Section: ⊓ ⊔mentioning

confidence: 99%

Section: ⊓ ⊔mentioning

confidence: 99%

Section: ⊓ ⊔mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Discretization orders for distance geometry problems

et al. 2011

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“…In this way, the search domain is reduced to a discrete set. Computational experiments presented, for example, in [12,[14][15][16][17][18]25], showed that the combinatorial approach to the MDGP is more efficient than the continuous one. We refer to this combinatorial reformulation of the MDGP as the Discretizable Molecular Distance Geometry Problem (DMDGP).…”

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confidence: 99%

On the computation of protein backbones by using artificial backbones of hydrogens

2010

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NMR experiments provide information from which some of the distances between pairs of hydrogen atoms of a protein molecule can be estimated. Such distances can be exploited in order to identify the three-dimensional conformation of the molecule: this problem is known in the literature as the Molecular Distance Geometry Problem (MDGP). In this paper, we show how an artificial backbone of hydrogens can be defined which allows the reformulation of the MDGP as a combinatorial problem. This is done with the aim of solving the problem by the Branch and Prune (BP) algorithm, which is able to solve it efficiently. Moreover, we show how the real backbone of a protein conformation can be computed by using the coordinates of the hydrogens found by the BP algorithm. Formal proofs of the presented results are provided, as well as computational experiences on a set of instances whose size ranges from 60 to 6000 atoms.

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An autonomic parallel strategy for exhaustive search tree algorithms on shared or heterogeneous systems

Passos,

Rebello

2023

Concurrency and Computation

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SummaryBacktracking branch‐and‐prune (BP) algorithms and their variants are exhaustive search tree techniques widely employed to solve optimization problems in many scientific areas. However, they characteristically often demand significant amounts of computing power for problem sizes representative of real‐world scenarios. Given that their search domains can often be partitioned, these algorithms are frequently designed to execute in parallel by harnessing distributed computing systems. However, to achieve efficient parallel execution times, an effective strategy is required to balance the nonuniform partition workloads across the available resources. Furthermore, with the increasing integration of servers with heterogeneous resources and the adoption of resource sharing, balancing workloads is becoming complex. This paper proposes a strategy to execute parallel BP algorithms more efficiently on even shared or heterogeneous distributed systems. The approach integrates a self‐adjusting dynamic partitioning method in the BP algorithm with a dynamic scheduler, provided by an application middleware, which manages the parallel execution while addressing any issues of imbalance. Empirical results indicate better scalability with efficiencies above 90% for instances of an application case study for the discretizable molecular distance geometry problem (DMDGP). Improvements of up to 38% were obtained in execution speed‐ups compared to a more traditional parallel BP implementation for DMDGP.

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The discretizable molecular distance geometry problem

Cited by 111 publications

References 58 publications

Discretization orders for distance geometry problems

Discretization orders for distance geometry problems

On the computation of protein backbones by using artificial backbones of hydrogens

An autonomic parallel strategy for exhaustive search tree algorithms on shared or heterogeneous systems

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