WABI '02 Proceedings of the Second International Workshop on Algorithms in Bioinformatics
Finding All Common Intervals of k Permutations
CPM '01 Proceedings of the 12th Annual Symposium on Combinatorial Pattern Matching
Identifying conserved gene clusters in the presence of orthologous groups
RECOMB '04 Proceedings of the eighth annual international conference on Resaerch in computational molecular biology
A certifying algorithm for the consecutive-ones property
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Journal of Computer and System Sciences
On the similarity of sets of permutations and its applications to genome comparison
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Perfect Sorting by Reversals Is Not Always Difficult
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Finding Nested Common Intervals Efficiently
RECOMB-CG '09 Proceedings of the International Workshop on Comparative Genomics
Ultra-perfect sorting scenarios
RECOMB-CG'10 Proceedings of the 2010 international conference on Comparative genomics
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
Gapped permutation patterns for comparative genomics
WABI'06 Proceedings of the 6th international conference on Algorithms in Bioinformatics
The reversal median problem, common intervals, and mitochondrial gene orders
CompLife'06 Proceedings of the Second international conference on Computational Life Sciences
Revisiting t. uno and m. yagiura's algorithm
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Algebraic operations on PQ trees and modular decomposition trees
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Perfect sorting by reversals is not always difficult
WABI'05 Proceedings of the 5th International conference on Algorithms in Bioinformatics
Using permutation patterns for content-based phylogeny
PRIB'06 Proceedings of the 2006 international conference on Pattern Recognition in Bioinformatics
A PQ framework for reconstructions of common ancestors and phylogeny
RCG'06 Proceedings of the RECOMB 2006 international conference on Comparative Genomics
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Permutations on strings representing gene clusters on genomes have been studied earlier in [3, 12, 14, 17, 18] and the idea of a maximal permutation pattern was introduced in [12]. In this paper, we present a new tool for representation and detection of gene clusters in multiple genomes, using PQ trees [6]: this describes the inner structure and the relations between clusters succinctly, aids in filtering meaningful from apparently meaningless clusters and also gives a natural and meaningful way of visualizing complex clusters. We identify a minimal consensus PQ tree and prove that it is equivalent to a maximal πpattern [12] and each subgraph of the PQ tree corresponds to a non-maximal permutation pattern. We present a general scheme to handle multiplicity in permutations and also give a linear time algorithm to construct the minimal consensus PQ tree. Further, we demonstrate the results on whole genome data sets. In our analysis of the whole genomes of human and rat we found about 1.5 million common gene clusters but only about 500 minimal consensus PQ trees, and, with E Coli K-12 and B Subtilis genomes we found only about 450 minimal consensus PQ trees out of about 15,000 gene clusters. Further, we show specific instances of functionally related genes in the two cases.