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**Published in:** LIPIcs, Volume 128, 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)

The Maximal Strip Recovery problem (MSR) and its complementary (CMSR) are well-studied NP-hard problems in computational genomics. The input of these dual problems are two signed permutations. The goal is to delete some gene markers from both permutations, such that, in the remaining permutations, each gene marker has at least one common neighbor. Equivalently, the resulting permutations could be partitioned into common strips of length at least two. Then MSR is to maximize the number of remaining genes, while the objective of CMSR is to delete the minimum number of gene markers. In this paper, we present a new approximation algorithm for the Complementary Maximal Strip Recovery (CMSR) problem. Our approximation factor is 2, improving the currently best 7/3-approximation algorithm. Although the improvement on the factor is not huge, the analysis is greatly simplified by a compensating method, commonly referred to as the non-oblivious local search technique. In such a method a substitution may not always increase the value of the current solution (it sometimes may even decrease the solution value), though it always improves the value of another function seemingly unrelated to the objective function.

Haitao Jiang, Jiong Guo, Daming Zhu, and Binhai Zhu. A 2-Approximation Algorithm for the Complementary Maximal Strip Recovery Problem. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, pp. 5:1-5:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@InProceedings{jiang_et_al:LIPIcs.CPM.2019.5, author = {Jiang, Haitao and Guo, Jiong and Zhu, Daming and Zhu, Binhai}, title = {{A 2-Approximation Algorithm for the Complementary Maximal Strip Recovery Problem}}, booktitle = {30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)}, pages = {5:1--5:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-103-0}, ISSN = {1868-8969}, year = {2019}, volume = {128}, editor = {Pisanti, Nadia and P. Pissis, Solon}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2019.5}, URN = {urn:nbn:de:0030-drops-104769}, doi = {10.4230/LIPIcs.CPM.2019.5}, annote = {Keywords: Maximal strip recovery, complementary maximal strip recovery, computational genomics, approximation algorithm, local search} }

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**Published in:** LIPIcs, Volume 105, 29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018)

A short swap switches two elements with at most one element caught between them. Sorting permutation by short swaps asks to find a shortest short swap sequence to transform a permutation into another. A short swap can eliminate at most three inversions. It is still open for whether a permutation can be sorted by short swaps each of which can eliminate three inversions. In this paper, we present a polynomial time algorithm to solve the problem, which can decide whether a permutation can be sorted by short swaps each of which can eliminate 3 inversions in O(n) time, and if so, sort the permutation by such short swaps in O(n^2) time, where n is the number of elements in the permutation.
A short swap can cause the total length of two element vectors to decrease by at most 4. We further propose an algorithm to recognize a permutation which can be sorted by short swaps each of which can cause the element vector length sum to decrease by 4 in O(n) time, and if so, sort the permutation by such short swaps in O(n^2) time. This improves upon the O(n^2) algorithm proposed by Heath and Vergara to decide whether a permutation is so called lucky.

Shu Zhang, Daming Zhu, Haitao Jiang, Jingjing Ma, Jiong Guo, and Haodi Feng. Can a permutation be sorted by best short swaps?. In 29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 105, pp. 14:1-14:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{zhang_et_al:LIPIcs.CPM.2018.14, author = {Zhang, Shu and Zhu, Daming and Jiang, Haitao and Ma, Jingjing and Guo, Jiong and Feng, Haodi}, title = {{Can a permutation be sorted by best short swaps?}}, booktitle = {29th Annual Symposium on Combinatorial Pattern Matching (CPM 2018)}, pages = {14:1--14:12}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-074-3}, ISSN = {1868-8969}, year = {2018}, volume = {105}, editor = {Navarro, Gonzalo and Sankoff, David and Zhu, Binhai}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2018.14}, URN = {urn:nbn:de:0030-drops-86957}, doi = {10.4230/LIPIcs.CPM.2018.14}, annote = {Keywords: Algorithm, Complexity, Short Swap, Permutation, Reversal} }

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**Published in:** LIPIcs, Volume 54, 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)

The genomic scaffold filling problem has attracted a lot of attention recently. The problem is on filling an incomplete sequence (scaffold) I into I', with respect to a complete reference genome G, such that the number of adjacencies between G and I' is maximized. The problem is NP-complete and APX-hard, and admits a 1.2-approximation. However, the sequence input I is not quite practical and does not fit most of the real datasets (where a scaffold is more often given as a list of contigs). In this paper, we revisit the genomic scaffold filling problem by considering this important case when, (1) a scaffold S is given, the missing genes X = c(G) - c(S) can only be inserted in between the contigs, and the objective is to maximize the number of adjacencies between G and the filled S' and (2) a scaffold S is given, a subset of the missing genes X' subset X = c(G) - c(S) can only be inserted in between the contigs, and the objective is still to maximize the number of adjacencies between G and the filled S''. For problem (1), we present a simple NP-completeness proof, we then present a factor-2 greedy approximation algorithm, and finally we show that the problem is FPT when each gene appears at most d times in G. For problem (2), we prove that the problem is W[1]-hard and then we present a factor-2 FPT-approximation for the case when each gene appears at most d times in G.

Haitao Jiang, Chenglin Fan, Boting Yang, Farong Zhong, Daming Zhu, and Binhai Zhu. Genomic Scaffold Filling Revisited. In 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 54, pp. 15:1-15:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)

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@InProceedings{jiang_et_al:LIPIcs.CPM.2016.15, author = {Jiang, Haitao and Fan, Chenglin and Yang, Boting and Zhong, Farong and Zhu, Daming and Zhu, Binhai}, title = {{Genomic Scaffold Filling Revisited}}, booktitle = {27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)}, pages = {15:1--15:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-012-5}, ISSN = {1868-8969}, year = {2016}, volume = {54}, editor = {Grossi, Roberto and Lewenstein, Moshe}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2016.15}, URN = {urn:nbn:de:0030-drops-60791}, doi = {10.4230/LIPIcs.CPM.2016.15}, annote = {Keywords: Computational biology, Approximation algorithms, FPT algorithms, NP- completeness} }

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