Generating and counting Hamilton cycles in random regular graphs
Journal of Algorithms
Sperner theory
Algorithms for computing and integrating physical maps using unique probes
RECOMB '97 Proceedings of the first annual international conference on Computational molecular biology
Approximately Counting Hamilton Paths and Cycles in Dense Graphs
SIAM Journal on Computing
On the consecutive ones property
Discrete Applied Mathematics - Special volume on computational molecular biology DAM-CMB series volume 2
Theoretical Computer Science
File organization: the consecutive retrieval property
Communications of the ACM
Approximation algorithms
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
Finding All Common Intervals of k Permutations
CPM '01 Proceedings of the 12th Annual Symposium on Combinatorial Pattern Matching
PQ-tree algorithms.
Efficient text fingerprinting via Parikh mapping
Journal of Discrete Algorithms
Consecutive block minimization is 1.5-approximable
Information Processing Letters
Computational Complexity: A Modern Approach
Computational Complexity: A Modern Approach
Journal of Computer and System Sciences
Counting the orderings for multisets in consecutive ones property and PQ-trees
DLT'11 Proceedings of the 15th international conference on Developments in language theory
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A binary matrix satisfies the consecutive ones property (c1p) if its columns can be permuted such that the 1s in each row of the resulting matrix are consecutive. Equivalently, a family of setsF={Q"1,...,Q"m}, where Q"i@?R for some universe R, satisfies the c1p if the symbols in R can be permuted such that the elements of each set Q"i@?F occur consecutively, as a contiguous segment of the permutation of R@?s symbols. Motivated by combinatorial problems on sequences with repeated symbols, we consider the c1p version on multisets and prove that counting the orderings (permutations) thus generated is #P-complete. We prove completeness results also for counting the permutations generated by PQ-trees (which are related to the c1p), thus showing that a polynomial-time algorithm is unlikely to exist when dealing with multisets and sequences with repeated symbols. To prove our results, we use a combinatorial approach based on parsimonious reductions from the Hamiltonian path problem, which enables us to prove also the hardness of approximation for these counting problems.