Variants of the Consecutive Ones property: Algorithms, Complexity and Applications in Genomics

The Consecutive Ones property (C1P) is a well studied structural property concerning binary matrices, with important applications in genome assembly. While the original decision problem of detecting C1P matrices is solvable in polynomial time, decision and optimization problems on generalizations of the property are usually intractable. These generalizations are extremely important concepts used as models in genomics, and the limits of tractability of both decision and optimization problems concerning them is a pivotal question. The following document examines generalizations of the C1P and tractability results for the same. These include fixed-parameter tractability, optimization problems on these variants, and some proposed new approaches to the original C1P problem, which we hope may lead to interesting results. It also discusses the application of the algorithms developed to genomic data sets.