Testing for the Consecutive Ones Property and Interval Graphs on Noisy Data─ Application to Physical Mapping and Sequence Assembly

• Main Authors: Wei-Fu Lu, 呂威甫
• Other Authors: Ruei-Chuan Chang
• Format: Others
• Language: en_US
• Published: 2003
• Online Access: http://ndltd.ncl.edu.tw/handle/61974029553973019649

博士 === 國立交通大學 === 資訊科學系 === 91 === The consecutive ones property and interval graph are two fundamental mathematical models for physical mapping and clone assembly. A (0,1)-matrix satisfies the consecutive ones property (COP) for the rows if there exists a column permutation such that the ones in each row of the resultant matrix are consecutive. An interval graph is the intersection graph of a collection of intervals. Booth and Lueker (1976) used PQ-trees to test the consecutive ones property and recognize interval graphs in linear time. The linear time algorithm by Booth and Lueker (1976) has a serious drawback: the data must be error-free. However, laboratory work is never flawless. Because a single error might cause map construction to fail, traditional recognition algorithms can hardly be applied on noisy data. Moreover, no straightforward extension of traditional algorithm can overcome the drawbacks. To solve these problems, a different philosophy toward algorithm design is necessary. In this thesis, we opt to maintain a stable local structure of consecutive ones matrices and interval graphs through clustering techniques to deal with errors. We do not set any “global” objective to optimize. Rather, our algorithms try to maintain the local monotone structure, namely, to minimize the deviation from the local monotone property as much as possible. Under moderate assumptions, the algorithm can accommodate the following four types of errors: false negatives, false positives, non-unique probes and chimeric clones. In case some local data is too noisy, our algorithm could likely discover that and suggest additional lab work to reduce the degree of ambiguity in that part. A unique feature of our algorithm is that, rather than forcing all probes or clones to be included and ordered in the final arrangement, our algorithm would delete some noisy information. Thus, it could produce more than one contig. The gaps are created mostly by noisy data.