The reconstruction of ancestral genome architectures and gene orders from homologies between extant species is a longstanding problem, considered by both cytogeneticists and bioinformaticians. A comparison of the two approaches was recently investigated and discussed in a series of papers, sometimes with diverging points of view regarding the performance of these two approaches. We describe a general methodological framework for reconstructing ancestral genome segments from conserved syntenies in extant genomes. We show that this problem, from a computational point of view, is naturally related to physical mapping of chromosomes and benefits from using combinatorial tools developed in this scope. We develop this framework into a new reconstruction method considering conserved gene clusters with similar gene content, mimicking principles used in most cytogenetic studies, although on a different kind of data. We implement and apply it to datasets of mammalian genomes. We perform intensive theoretical and experimental comparisons with other bioinformatics methods for ancestral genome segments reconstruction. We show that the method that we propose is stable and reliable: it gives convergent results using several kinds of data at different levels of resolution, and all predicted ancestral regions are well supported. The results come eventually very close to cytogenetics studies. It suggests that the comparison of methods for ancestral genome reconstruction should include the algorithmic aspects of the methods as well

We develop a refinement of a forbidden submatrix characterization of 0/1-matrices fulfilling the Consecutive Ones Property (C1P). This novel characterization finds applications in new polynomial-time approximation algorithms and fixed-parameter tractability results for the problem to find a maximum-size submatrix of a 0/1-matrix such that the submatrix has the C1P. Moreover, we achieve a problem kernelization based on simple data reduction rules and provide several search tree algorithms. Finally, we derive inapproximability results.

We develop an algorithmically useful refinement of a forbidden submatrix characterization of 0/1-matrices fulfilling the Consecutive Ones Property (C1P). This characterization finds applications in new polynomial-time approximation algorithms and fixed-parameter tractability results for the NP-hard problem to delete a minimum number of rows or columns from a 0/1-matrix such that the remaining submatrix has the C1P.

We survey the consecutive-ones property of binary matrices. Herein, a binary matrix has the consecutive-ones property (C1P) if there is a permutation of its columns that places the 1s consecutively in every row. We provide an overview over connections to graph theory, characterizations, recognition algorithms, and applications such as integer linear programming and solving Set Cover.

Set Cover problems are of core importance in many applications. In recent research, the “red-blue variants” where blue elements all need to be covered whereas red elements add further constraints on the optimality of a covering have received considerable interest. Application scenarios range from data mining to interference reduction in cellular networks. As a rule, these problem variants are computationally at least as hard as the original set cover problem. In this work we investigate whether and how the well-known consecutive ones property, restricting the structure of the input sets, makes the red-blue covering problems feasible. We explore a sharp border between polynomial-time solvability and NP-hardness for these problems.

Abstract—Recent applications including the Semantic Web, Web ontology and XML have sparked a renewed interest on graph-structured databases. Among others, twig queries have been a popular tool for retrieving subgraphs from graphstructured databases. To optimize twig queries, selectivity estimation has been a crucial and classical step. However, the majority of existing works on selectivity estimation focuses on relational and tree data. In this paper, we investigate selectivity estimation of twig queries on possibly cyclic graph data. To facilitate selectivity estimation on cyclic graphs, we propose a matrix representation of graphs derived from prime labeling — a scheme for reachability queries on directed acyclic graphs. With this representation, we exploit the consecutive ones property (C1P) of matrices. As a consequence, a node is mapped to a point in a two-dimensional space whereas a query is mapped to multiple points. We adopt histograms for scalable selectivity estimation. We perform an extensive experimental evaluation on the proposed technique and show that our technique controls the estimationerrorunder1.3%on XMARK and DBLP,whichismore accurate than previous techniques. On TREEBANK, we produce RMSE and NRMSE 6.8 times smaller than previous techniques. I.

The polynomial-time decidable Consecutive-Ones Property (C1P) of binary matrices, formally introduced in 1965 by Fulkerson and Gross [52], has since found applications in many areas. In this thesis, we propose and study several variants of this property that are motivated by the reconstruction of ancestral species. We first propose the Gapped C1P, or the (k,δ)-Consecutive-Ones Property ((k,δ)-C1P): a binary matrix M has the (k,δ)-C1P for integers k and δ if the columns of M can be permuted such that each row contains at most k blocks of1’s and no two neighboring blocks of 1’s are separated by a gap of more than δ 0’s. The C1P is equivalent to the (1,0)-C1P. We show that for every bounded and unbounded k ≥ 2,δ ≥ 1,(k,δ)̸=(2,1), deciding the(k,δ)-C1P is NP-complete [55]. We also provide an algorithm for a relevant case of the (2,1)-C1P. We then study the(k,δ)-C1P with a bound d on the maximum number of1’s in any row (the maximum degree) of M. We show that the(d,k,δ)-Consecutive-Ones Property ((d,k,δ)-C1P) is polynomial-time decidable when all three parameters are fixed constants. Since fixing d also fixes k(k≤d), the only case left to consider

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