基于代价约束的置换排序
Sorting of Permutations by Cost-Constrained Transpositions
摘要：
我们解决的问题，找到一个置换的最小分解与非均匀成本的换位。对于任意非负成本函数，我们描述多项式时间，常数近似分解算法。对于度量路径成本，我们描述了精确的多项式时间分解算法。我们的算法代表了维特比型算法和图形搜索技术的组合，用于最大限度地减少个别换位的成本，并找到最小成本循环分解的动态规划算法。所提出的算法在信息论、生物信息学和代数学中有应用。
英文摘要：
We address the problem of finding the minimum decomposition of a permutation in terms of transpositions with non-uniform cost. For arbitrary non-negative cost functions, we describe polynomial-time, constant-approximation decomposition algorithms. For metric-path costs, we describe exact polynomial-time decomposition algorithms. Our algorithms represent a combination of Viterbi-type algorithms and graph-search techniques for minimizing the cost of individual transpositions, and dynamic programing algorithms for finding minimum cost cycle decompositions. The presented algorithms have applications in information theory, bioinformatics, and algebra.
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