Counting linear extensions is #P-complete
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Mining association rules between sets of items in large databases
SIGMOD '93 Proceedings of the 1993 ACM SIGMOD international conference on Management of data
A Spectral Algorithm for Seriation and the Consecutive Ones Problem
SIAM Journal on Computing
Physical mapping of chromosomes using unique probes
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Global partial orders from sequential data
Proceedings of the sixth ACM SIGKDD international conference on Knowledge discovery and data mining
An open graph visualization system and its applications to software engineering
Software—Practice & Experience - Special issue on discrete algorithm engineering
A simple test for the consecutive ones property
Journal of Algorithms
Spectral partitioning works: planar graphs and finite element meshes
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
Algorithms for discovering bucket orders from data
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Discovering bucket orders from full rankings
Proceedings of the 2008 ACM SIGMOD international conference on Management of data
Finding Total and Partial Orders from Data for Seriation
DS '08 Proceedings of the 11th International Conference on Discovery Science
Proceedings of the sixth ACM international conference on Web search and data mining
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In applications such as paleontology and medical genetics the 0-1 data has an underlying unknown order (the ages of the fossil sites, the locations of markers in the genome). The order might be total or partial: for example, two sites in different parts of the globe might be ecologically incomparable, or the ordering of certain markers might be different in different subgroups of the data. We consider the following problem. Given a table over a set of 0-1 variables, find a partial order for the rows minimizing a score function and being as specific as possible. The score function can be, e.g., the number of changes from 1 to 0 in a column (for paleontology) or the likelihood of the marker sequence (for genomic data). Our solution for this task first constructs small totally ordered fragments of the partial order, then finds good orientations for the fragments, and finally uses a simple and efficient heuristic method for finding a partial order that corresponds well with the collection of fragments. We describe the method, discuss its properties, and give empirical results on paleontological data demonstrating the usefulness of the method. In the application the use of the method highlighted some previously unknown properties of the data and pointed out probable errors in the data.