Automated Evaluation of OCR Zoning
IEEE Transactions on Pattern Analysis and Machine Intelligence
Sorting by bounded permutations
Sorting by bounded permutations
SIAM Journal on Discrete Mathematics
A 2-approximation algorithm for genome rearrangements by reversals and transpositions
Theoretical Computer Science - Special issue: Genome informatics
Discrete Mathematics
Genome Rearrangements and Sorting by Reversals
SIAM Journal on Computing
(1 + ɛ)-Approximation of sorting by reversals and transpositions
Theoretical Computer Science
A simpler and faster 1.5-approximation algorithm for sorting by transpositions
Information and Computation
A 1.375-Approximation Algorithm for Sorting by Transpositions
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
A simpler 1.5-approximation algorithm for sorting by transpositions
CPM'03 Proceedings of the 14th annual conference on Combinatorial pattern matching
A 1.375-approximation algorithm for sorting by transpositions
WABI'05 Proceedings of the 5th International conference on Algorithms in Bioinformatics
A faster and simpler 2-approximation algorithm for block sorting
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
A quadratic time 2-approximation algorithm for block sorting
Theoretical Computer Science
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Given a permutation π, the block sorting problem is to find a shortest series of block moves which, when applied in succession, sorts π. Here a block is a maximal substring of successive integers in order, and a block move is the displacement of a block to a location where it merges with another block, block sorting is an NP-hard optimization problem and has a factor 2 approximation algorithm. In this paper, we present a combinatorial characterization of optimal solutions of block sorting and use it to prove various computationally important properties of the problem. In particular, we identify certain block moves that are provably optimal. We also establish the equivalence of block sorting and a combinatorial puzzle. We consider several polynomial-time heuristics for block sorting that are inspired either by the above-mentioned combinatorial characterization, or by the approach that was based on the block merging problem, or both. Although these heuristics seem to be promising candidates for improving the approximation ratio (their approximation ratios are provably at most 2), we show that none of them leads to a better approximation ratio than 2.