THE UNIFORM MINIMUM-ONES 2SAT PROBLEM AND ITS APPLICATION TO HAPLOTYPE CLASSIFICATION

作     者：Boeckenhauer, Hans-Joachim Forisek, Michal Oravec, Jan Steffen, Bjoern Steinhoefel, Kathleen Steinova, Monika 

作者机构：ETH Dept Comp Sci Zurich Switzerland Comenius Univ Dept Comp Sci Bratislava 81806 Slovakia Kings Coll London Dept Comp Sci London England 

出 版 物：《RAIRO-THEORETICAL INFORMATICS AND APPLICATIONS》 (法国自动化、信息与运筹学；理论与应用信息)

年 卷 期：2010年第44卷第3期

页      面：363-377页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 08[工学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：SNF [200021-109252/1] 

主　　题：Exact algorithms fixed-parameter algorithms minimum-ones 2SAT haplotypes 

摘      要：Analyzing genomic data for finding those gene variations which are responsible for hereditary diseases is one of the great challenges in modern bioinformatics. In many living beings (including the human), every gene is present in two copies, inherited from the two parents, the so-called haplotypes. In this paper, we propose a simple combinatorial model for classifying the set of haplotypes in a population according to their responsibility for a certain genetic disease. This model is based on the minimum-ones 2SAT problem with uniform clauses. The minimum-ones 2SAT problem asks for a satisfying assignment to a satisfiable formula in 2CNF which sets a minimum number of variables to true. This problem is well-known to be NP-hard, even in the case where all clauses are uniform, i.e., do not contain a positive and a negative literal. We analyze the approximability and present the first non-trivial exact algorithm for the uniform minimum-ones 2SAT problem with a running time of O(1.21061(n)) on a 2SAT formula with n variables. We also show that the problem is fixed-parameter tractable by showing that our algorithm can be adapted to verify in O*(2(k)) time whether an assignment with at most k true variables exists.