在密度约束下定位序列中的区域
Locating regions in a sequence under density constraints
摘要：
一些生物学问题需要识别序列中的区域，其中一些特征出现在目标密度范围内：例如，包括富含GC的区域的位置，CpG岛的识别和序列匹配。从数学上讲，这相当于在一个0和1组成的字符串中搜索一个1的相对比例介于给定下限和上限之间的子串。我们考虑的算法问题定位最长的这样的子串，以及其他相关的问题（如寻找最短的子串或最大的不相交的子串）。为了找到最长的这样的子串，我们开发了一个算法，运行在O（n）的时间，改善了以前最著名的O（n log n）的结果。对于相关的问题，我们开发O（n log log n）的算法，再次改善最有名的O（n log n）的结果。实际测试验证了我们的新算法享有显着更小的时间和内存足迹，并可以处理的序列，数量级更长的结果。
英文摘要：
Several biological problems require the identification of regions in a sequence where some feature occurs within a target density range: examples including the location of GC-rich regions, identification of CpG islands, and sequence matching. Mathematically, this corresponds to searching a string of 0s and 1s for a substring whose relative proportion of 1s lies between given lower and upper bounds. We consider the algorithmic problem of locating the longest such substring, as well as other related problems (such as finding the shortest substring or a maximal set of disjoint substrings). For locating the longest such substring, we develop an algorithm that runs in O(n) time, improving upon the previous best-known O(n log n) result. For the related problems we develop O(n log log n) algorithms, again improving upon the best-known O(n log n) results. Practical testing verifies that our new algorithms enjoy significantly smaller time and memory footprints, and can process sequences that are orders of magnitude longer as a result.
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