The fundamental inverse problem in distance geometry is the one of finding positions from inter-point distances. The Discretizable Molecular Distance Geometry Problem (DMDGP) is a subclass of the Distance Geometry Problem (DGP) whose search space can be discretized and represented by a binary tree, which can be explored by a Branch-and-Prune (BP) algorithm. It turns out that this combinatorial search space possesses many interesting symmetry properties that were studied in the last decade. In this paper, we present a new algorithm for this subclass of the DGP, which exploits DMDGP symmetries more effectively than its predecessors. Computational results show that the speedup, with respect to the classic BP algorithm, is considerable for sparse DMDGP instances related to protein conformation.

中文翻译：

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距离几何问题的 $^K$DMDGP 子类的新算法

距离几何中的基本逆问题是从点间距离找到位置之一。可离散分子距离几何问题 (DMDGP) 是距离几何问题 (DGP) 的子类，其搜索空间可以离散化并由二叉树表示，可以通过分支修剪 (BP) 算法进行探索。事实证明，这个组合搜索空间具有许多有趣的对称特性，这些特性在过去十年中得到了研究。在本文中，我们为 DGP 的这个子类提出了一种新算法，它比其前辈更有效地利用 DMDGP 对称性。计算结果表明，对于与蛋白质构象相关的稀疏 DMDGP 实例，相对于经典 BP 算法的加速是相当可观的。