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**Published in:** LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

We study the Traveling Salesman problem (TSP), where given a complete undirected graph G = (V,E) with n vertices and an edge cost function c:E↦R_{⩾0}, the goal is to find a minimum-cost cycle visiting every vertex exactly once. It is well-known that unless P = NP, TSP cannot be approximated in polynomial time within a factor of ρ(n) for any computable function ρ, while the metric case of TSP, that the edge cost function satisfies the △-inequality, admits a polynomial-time 1.5-approximation. We investigate TSP on general graphs from the perspective of parameterized approximability. A parameterized ρ-approximation algorithm returns a ρ-approximation solution in f(k)⋅|I|^O(1) time, where f is a computable function and k is a parameter of the input I. We introduce two parameters, which measure the distance of a given TSP-instance from the metric case, and achieve the following two results:
- A 3-approximation algorithm for TSP in O((3k₁)! 8^k₁⋅ n²+n³) time, where k₁ is the number of triangles in which the edge costs violate the △-inequality.
- A 3-approximation algorithm for TSP in O(n^O(k₂)) time and a (6k₂+9)-approximation algorithm for TSP in O(k₂^O(k₂)⋅n³) time, where k₂ is the minimum number of vertices, whose removal results in a metric graph.
To our best knowledge, the above algorithms are the first non-trivial parameterized approximation algorithms for TSP on general graphs.

Jianqi Zhou, Peihua Li, and Jiong Guo. Parameterized Approximation Algorithms for TSP. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 50:1-50:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{zhou_et_al:LIPIcs.ISAAC.2022.50, author = {Zhou, Jianqi and Li, Peihua and Guo, Jiong}, title = {{Parameterized Approximation Algorithms for TSP}}, booktitle = {33rd International Symposium on Algorithms and Computation (ISAAC 2022)}, pages = {50:1--50:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-258-7}, ISSN = {1868-8969}, year = {2022}, volume = {248}, editor = {Bae, Sang Won and Park, Heejin}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.50}, URN = {urn:nbn:de:0030-drops-173358}, doi = {10.4230/LIPIcs.ISAAC.2022.50}, annote = {Keywords: FPT-approximation algorithms, the Traveling Salesman problem, the triangle inequality, fixed-parameter tractability, metric graphs} }

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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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Complete Volume

**Published in:** LIPIcs, Volume 63, 11th International Symposium on Parameterized and Exact Computation (IPEC 2016)

LIPIcs, Volume 63, IPEC'16, Complete Volume

Jiong Guo and Danny Hermelin. LIPIcs, Volume 63, IPEC'16, Complete Volume. In 11th International Symposium on Parameterized and Exact Computation (IPEC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 63, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@Proceedings{guo_et_al:LIPIcs.IPEC.2016, title = {{LIPIcs, Volume 63, IPEC'16, Complete Volume}}, booktitle = {11th International Symposium on Parameterized and Exact Computation (IPEC 2016)}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-023-1}, ISSN = {1868-8969}, year = {2017}, volume = {63}, editor = {Guo, Jiong and Hermelin, Danny}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2016}, URN = {urn:nbn:de:0030-drops-69572}, doi = {10.4230/LIPIcs.IPEC.2016}, annote = {Keywords: Complexity Measures and Classes, Analysis of Algorithms and Problem Complexity, Discrete Mathematics} }

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Front Matter

**Published in:** LIPIcs, Volume 63, 11th International Symposium on Parameterized and Exact Computation (IPEC 2016)

Front Matter, Table of Contents, Preface, Program Committee, External Reviewers, List of Authors

Jiong Guo and Danny Hermelin. Front Matter, Table of Contents, Preface, Program Committee, External Reviewers, List of Authors. In 11th International Symposium on Parameterized and Exact Computation (IPEC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 63, pp. 0:i-0:xiv, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{guo_et_al:LIPIcs.IPEC.2016.0, author = {Guo, Jiong and Hermelin, Danny}, title = {{Front Matter, Table of Contents, Preface, Program Committee, External Reviewers, List of Authors}}, booktitle = {11th International Symposium on Parameterized and Exact Computation (IPEC 2016)}, pages = {0:i--0:xiv}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-023-1}, ISSN = {1868-8969}, year = {2017}, volume = {63}, editor = {Guo, Jiong and Hermelin, Danny}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2016.0}, URN = {urn:nbn:de:0030-drops-69180}, doi = {10.4230/LIPIcs.IPEC.2016.0}, annote = {Keywords: Front Matter, Table of Contents, Preface, Program Committee, External Reviewers, List of Authors} }

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**Published in:** OASIcs, Volume 34, German Conference on Bioinformatics 2013

Introduction: With the so-called OMICS technology the scientific community has generated huge amounts of data that allow us to reconstruct the interplay of all kinds of biological entities. The emerging interaction networks are usually modeled as graphs with thousands of nodes and tens of thousands of edges between them. In addition to sequence alignment, the comparison of biological networks has proven great potential to infer the biological function of proteins and genes. However, the corresponding network alignment problem is computationally hard and theoretically intractable for real world instances.
Results: We therefore developed GEDEVO, a novel tool for efficient graph comparison dedicated to real-world size biological networks. Underlying our approach is the so-called Graph Edit Distance (GED) model, where one graph is to be transferred into another one, with a minimal number of (or more general: minimal costs for) edge insertions and deletions. We present a novel evolutionary algorithm aiming to minimize the GED, and we compare our implementation against state of the art tools: SPINAL, GHOST, \CGRAAL, and \MIGRAAL. On a set of protein-protein interaction networks from different organisms we demonstrate that GEDEVO outperforms the current methods. It thus refines the previously suggested alignments based on topological information only.
Conclusion: With GEDEVO, we account for the constantly exploding number and size of available biological networks. The software as well as all used data sets are publicly available at http://gedevo.mpi-inf.mpg.de.

Rashid Ibragimov, Maximilian Malek, Jiong Guo, and Jan Baumbach. GEDEVO: An Evolutionary Graph Edit Distance Algorithm for Biological Network Alignment. In German Conference on Bioinformatics 2013. Open Access Series in Informatics (OASIcs), Volume 34, pp. 68-79, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)

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@InProceedings{ibragimov_et_al:OASIcs.GCB.2013.68, author = {Ibragimov, Rashid and Malek, Maximilian and Guo, Jiong and Baumbach, Jan}, title = {{GEDEVO: An Evolutionary Graph Edit Distance Algorithm for Biological Network Alignment}}, booktitle = {German Conference on Bioinformatics 2013}, pages = {68--79}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-939897-59-0}, ISSN = {2190-6807}, year = {2013}, volume = {34}, editor = {Bei{\ss}barth, Tim and Kollmar, Martin and Leha, Andreas and Morgenstern, Burkhard and Schultz, Anne-Kathrin and Waack, Stephan and Wingender, Edgar}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.GCB.2013.68}, URN = {urn:nbn:de:0030-drops-42298}, doi = {10.4230/OASIcs.GCB.2013.68}, annote = {Keywords: Network Alignment, Graph Edit Distance, Evolutionary Algorithm, Protein-Protein Interactions} }

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**Published in:** Dagstuhl Reports, Volume 2, Issue 6 (2012)

This report documents the program and the outcomes of Dagstuhl Seminar 12241 ``Data Reduction and Problem Kernels''. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available.

Michael R. Fellows, Jiong Guo, Dániel Marx, and Saket Saurabh. Data Reduction and Problem Kernels (Dagstuhl Seminar 12241). In Dagstuhl Reports, Volume 2, Issue 6, pp. 26-50, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2012)

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@Article{fellows_et_al:DagRep.2.6.26, author = {Fellows, Michael R. and Guo, Jiong and Marx, D\'{a}niel and Saurabh, Saket}, title = {{Data Reduction and Problem Kernels (Dagstuhl Seminar 12241)}}, pages = {26--50}, journal = {Dagstuhl Reports}, ISSN = {2192-5283}, year = {2012}, volume = {2}, number = {6}, editor = {Fellows, Michael R. and Guo, Jiong and Marx, D\'{a}niel and Saurabh, Saket}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagRep.2.6.26}, URN = {urn:nbn:de:0030-drops-37297}, doi = {10.4230/DagRep.2.6.26}, annote = {Keywords: Preprocessing, Fixed-parameter tractability, Parameterized algorithmics} }

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**Published in:** LIPIcs, Volume 3, 26th International Symposium on Theoretical Aspects of Computer Science (2009)

The Nemhauser-Trotter local optimization theorem applies to the NP-hard \textsc{Vertex Cover} problem and has applications in approximation as well as parameterized algorithmics. We present a framework that generalizes Nemhauser and Trotter's result to vertex deletion and graph packing problems, introducing novel algorithmic strategies based on purely combinatorial arguments (not referring to linear programming as the Nemhauser-Trotter result originally did).
We exhibit our framework using a generalization of \textsc{Vertex Cover}, called \textrm{\sc Bounded-Degree Deletion}, that has promise to become an important tool in the analysis of gene and other biological networks. For some fixed~$d\geq 0$, \textrm{\sc Bounded-Degree Deletion} asks to delete as few vertices as possible from a graph in order to transform it into a graph with maximum vertex degree at most~$d$. \textsc{Vertex Cover} is the special case of $d=0$. Our generalization of the Nemhauser-Trotter theorem implies that \textrm{\sc Bounded-Degree Deletion} has a problem kernel with a linear number of vertices for every constant~$d$. We also outline an application of our extremal combinatorial approach to the problem of packing stars with a bounded number of leaves. Finally, charting the border between (parameterized) tractability and intractability for \textrm{\sc Bounded-Degree Deletion}, we provide a W[2]-hardness result for \textrm{\sc Bounded-Degree Deletion} in case of unbounded $d$-values.

Michael R. Fellows, Jiong Guo, Hannes Moser, and Rolf Niedermeier. A Generalization of Nemhauser and Trotter's Local Optimization Theorem. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 409-420, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2009)

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@InProceedings{fellows_et_al:LIPIcs.STACS.2009.1820, author = {Fellows, Michael R. and Guo, Jiong and Moser, Hannes and Niedermeier, Rolf}, title = {{A Generalization of Nemhauser and Trotter's Local Optimization Theorem}}, booktitle = {26th International Symposium on Theoretical Aspects of Computer Science}, pages = {409--420}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-09-5}, ISSN = {1868-8969}, year = {2009}, volume = {3}, editor = {Albers, Susanne and Marion, Jean-Yves}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1820}, URN = {urn:nbn:de:0030-drops-18200}, doi = {10.4230/LIPIcs.STACS.2009.1820}, annote = {Keywords: Algorithms, Computational complexity, NP-hard problems, W\lbrack2\rbrack-completeness, Graph problems, Combinatorial optimization, Fixed-parameter tractability, K} }

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