A Unified Approach for Reconstructing Ancient Gene Clusters
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Minimal Conflicting Sets for the Consecutive Ones Property in Ancestral Genome Reconstruction
RECOMB-CG '09 Proceedings of the International Workshop on Comparative Genomics
A faster algorithm for finding minimum tucker submatrices
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
A polynomial-time algorithm for finding a minimal conflicting set containing a given row
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Faster and simpler minimal conflicting set identification
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Faster and simpler minimal conflicting set identification
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
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Let ${\cal C}$ be a finite set of n elements and ${\cal R}=\{r_1,r_2, \ldots , r_m\}$ a family of m subsets of ${\cal C}$. A subset ${\cal X}$ of ${\cal R}$ satisfies the Consecutive Ones Property (C1P) if there exists a permutation P of ${\cal C}$ such that each ri in ${\cal X}$ is an interval of P. A Minimal Conflicting Set (MCS)${\cal S} \subseteq{\cal R}$ is a subset of ${\cal R}$ that does not satisfy the C1P, but such that any of its proper subsets does. In this paper, we present a new simpler and faster algorithm to decide if a given element $r \in{\cal R}$ belongs to at least one MCS. Our algorithm runs in O(n2m2+nm7), largely improving the current O(m6n5 (m+n)2 log(m+n)) fastest algorithm of [Blin et al, CSR 2011]. The new algorithm is based on an alternative approach considering minimal forbidden induced subgraphs of interval graphs instead of Tucker matrices.