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Vertex Deletion Parameterized by Elimination Distance and Even Less [article]

Bart M. P. Jansen, Jari J. H. de Kroon, Michał Włodarczyk
2022 arXiv   pre-print
We study the parameterized complexity of various classic vertex-deletion problems such as Odd cycle transversal, Vertex planarization, and Chordal vertex deletion under hybrid parameterizations.  ...  Secondly, we exploit the constructed decompositions for solving vertex-deletion problems by extending ideas from algorithms using iterative compression and the finite state property.  ...  The family H of K 2 -free graphs is simply the class of edge-less graphs, and the elimination distance to an edge-less graph is not a smaller parameter than treedepth or treewidth.  ... 
arXiv:2103.09715v4 fatcat:vv3kluwdtjhqdhaflntr6msvdi

Elimination Distances, Blocking Sets, and Kernels for Vertex Cover [article]

Eva-Maria C. Hols, Stefan Kratsch, Astrid Pieterse
2019 arXiv   pre-print
These bounds allow us to derive polynomial kernels for Vertex Cover parameterized by the size of a deletion set to graphs of bounded elimination distance to, e.g., forest, bipartite, or C_LP graphs.  ...  Motivated by the great variety of positive and negative results for kernelization for Vertex Cover subject to different parameters and graph classes, we seek to unify and generalize them using so-called  ...  Cover parameterized by deletion distance to C to O(|X| d ) (Section 3.3).  ... 
arXiv:1905.03631v1 fatcat:ixl6ksuc5vghpgvsscrbbddov4

On 2-Clubs in Graph-Based Data Clustering: Theory and Algorithm Engineering [article]

Aleksander Figiel, Anne-Sophie Himmel, André Nichterlein, Rolf Niedermeier
2020 arXiv   pre-print
kernel when parameterized by the number of vertex deletions.  ...  are vertex deletions).  ...  Denote by r the number of P 4 's in P that contain v, which means deleting v eliminates r P 4 's in P. The cost of deleting v is w(v) ≥ r.  ... 
arXiv:2006.14972v1 fatcat:pdshakcombchlcmjmxnwnn4s7e

Optimal Surveillance of Covert Networks by Minimizing Inverse Geodesic Length

Serge Gaspers, Kamran Najeebullah
2019 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
We also provide FPT algorithms parameterized by twin cover and neighborhood diversity combined with the deletion budget k.  ...  We show that MINIGL-ED is fixed-parameter tractable for parameter T and vertex cover by modeling the problem as an integer quadratic program.  ...  Kamran Najeebullah is supported by the Australian Government Research Training Program Scholarship.  ... 
doi:10.1609/aaai.v33i01.3301533 fatcat:uw7x4544znertcvf5igreqrgai

Kernel Bounds for Structural Parameterizations of Pathwidth [chapter]

Hans L. Bodlaender, Bart M. P. Jansen, Stefan Kratsch
2012 Lecture Notes in Computer Science  
Our main result is that, unless NP is in coNP/poly, Pathwidth admits no polynomial kernelization even when parameterized by the vertex deletion distance to a clique, by giving a cross-composition from  ...  each connected component is a star, and the vertex deletion distance to a graph where each connected component has at most c vertices.  ...  Let G be obtained by deleting v and by adding a vertex v p,q with neighbors p and q for any p, q ∈ N G (v) with p = q.  ... 
doi:10.1007/978-3-642-31155-0_31 fatcat:ym5erltrtzerdkjp2sahp6b67u

Towards fully multivariate algorithmics: Parameter ecology and the deconstruction of computational complexity

Michael R. Fellows, Bart M.P. Jansen, Frances Rosamond
2013 European journal of combinatorics (Print)  
We call for a new type of race in parameterized analysis, with the purpose of uncovering the boundaries of tractability by finding the smallest possible parameterizations which admit FPT-algorithms or  ...  An extensive overview of recent advances on this front is presented for the Vertex Cover problem.  ...  the parameterization by a promised bound on the vertex-deletion distance to a perfect graph.  ... 
doi:10.1016/j.ejc.2012.04.008 fatcat:uzjyjuxec5hvlcep3jsf3mcupu

A Structural View on Parameterizing Problems: Distance from Triviality [chapter]

Jiong Guo, Falk Hüffner, Rolf Niedermeier
2004 Lecture Notes in Computer Science  
In this paper we present several case studies of distance from triviality parameterizations (concerning Clique, Power Dominating Set, Set Cover, and Longest Common Subsequence) that exhibit the versatility  ...  Based on a series of known and new examples, we propose the generalized setting of "distance from triviality" measurement as a reasonable and prospective way of determining useful structural problem parameters  ...  In each of the less than (deg v) 2 branches we can eliminate the joint.  ... 
doi:10.1007/978-3-540-28639-4_15 fatcat:2oemfxdjpre35b4fou62izyxgu

Kernelization for Feedback Vertex Set via Elimination Distance to a Forest [article]

David Dekker, Bart M. P. Jansen
2022 arXiv   pre-print
kernel if and only if 𝒢 has bounded elimination distance to a forest.  ...  The answer turns out to be negative; the existence of polynomial kernels for structural parameterizations for Feedback Vertex Set is governed by the elimination distance to a forest.  ...  Other FPT algorithms include parameterizations by deletion distance to a chordal graph, by cliquewidth and by the number of vertices of degree at least 4 [30, 29, 10, 37] .  ... 
arXiv:2206.04387v1 fatcat:y76eq7d3j5eejiysi6woxkcp64

Preprocessing for Treewidth: A Combinatorial Analysis through Kernelization [chapter]

Hans L. Bodlaender, Bart M. P. Jansen, Stefan Kratsch
2011 Lecture Notes in Computer Science  
In contrast we show that Treewidth parameterized by the vertex-deletion distance to a single clique, and Weighted Treewidth parameterized by the size of a vertex cover, do not admit polynomial kernelizations  ...  Phrased in the language of parameterized complexity, we show that Treewidth has a polynomial kernel when parameterized by the size of a given feedback vertex set, and also by the size of a vertex cover  ...  We prove that even the larger parameterization by deletion distance to a single clique, fails to admit a polynomial kernel unless NP ⊆ coNP/poly.  ... 
doi:10.1007/978-3-642-22006-7_37 fatcat:7rpf4gak2fh77evipr2fv5hlsy

Parameterized Dynamic Cluster Editing

Junjie Luo, Hendrik Molter, André Nichterlein, Rolf Niedermeier, Michael Wagner
2018 Foundations of Software Technology and Theoretical Computer Science  
landscape under the perhaps two most natural parameterizations: the distance of the new "similar" cluster graph to (i) the second input graph and to (ii) the input cluster graph.  ...  We thoroughly study six problem variants (edge editing, edge deletion, edge insertion; each combined with two distance measures between cluster graphs).  ...  First, we left open the parameterized complexity of Dynamic Cluster Editing (deletion variant and completion variant) with matching-based distance when parameterized by the budget k, see Table 1 in Section  ... 
doi:10.4230/lipics.fsttcs.2018.46 dblp:conf/fsttcs/LuoMNN18 fatcat:orl6v37o3ngdjh5haidoklv5g4

Parameterized Dynamic Cluster Editing [article]

Junjie Luo, Hendrik Molter, André Nichterlein, Rolf Niedermeier
2018 arXiv   pre-print
landscape under the two perhaps most natural parameterizations: the distance of the new "similar" cluster graph to (i) the second input graph and to (ii) the input cluster graph.  ...  We thoroughly study six problem variants (edge editing, edge deletion, edge insertion; each combined with two distance measures between cluster graphs).  ...  DCCompletion (Matching Dist) and DCCompletion (Edge Dist) are in FPT when parameterized by the distance d.  ... 
arXiv:1810.06625v2 fatcat:lquysl3qx5djppf5v4674dlr2i

Parameterized Dynamic Cluster Editing

Junjie Luo, Hendrik Molter, André Nichterlein, Rolf Niedermeier
2020 Algorithmica  
landscape under the two perhaps most natural parameterizations: the distances of the new "similar" cluster graph to (1) the second input graph and to (2) the input cluster graph.  ...  We thoroughly study six problem variants (three modification scenarios edge editing, edge deletion, edge insertion; each combined with two distance measures between cluster graphs).  ...  Acknowledgements Open Access funding provided by Projekt DEAL. We are grateful to two anony-  ... 
doi:10.1007/s00453-020-00746-y fatcat:twhfim6bmrdjrjnahilw5goyfa

Editing graphs to satisfy degree constraints: A parameterized approach

Luke Mathieson, Stefan Szeider
2012 Journal of computer and system sciences (Print)  
In particular we consider the editing operations vertex deletion (denoted v), edge deletion (denoted e), and edge addition (denoted a). • Each vertex v of the given graph has assigned a list δ(v) of numbers  ...  By allowing arbitrary lists we can express variants of the General Factor problem introduced and studied by Lovász [19, 20] . • Vertices and edges can have positive integer weights, giving each edit operation  ...  For example, one can try to obtain polynomially-sized kernels for the case where all degree lists are intervals and the operations of vertex deletion and edge deletion are both included.  ... 
doi:10.1016/j.jcss.2011.02.001 fatcat:fljdtrsj4jfpfidlwcekot7zuu

Rank Aggregation Using Scoring Rules [article]

Niclas Boehmer, Robert Bredereck, Dominik Peters
2022 arXiv   pre-print
We distinguish three types of methods: ranking by score, ranking by repeatedly choosing a winner that we delete and rank at the top, and ranking by repeatedly choosing a loser that we delete and rank at  ...  For different rules in our classes, we then study the (parameterized) computational complexity of deciding in which positions a given candidate can appear in the chosen ranking.  ...  Thus, the Borda score of a candidate also changes less drastically in case some candidate is deleted.  ... 
arXiv:2209.08856v1 fatcat:knot4gcndvcuhhonxa5ym6rxju

Towards exact structural thresholds for parameterized complexity [article]

Falko Hegerfeld, Stefan Kratsch
2021 arXiv   pre-print
There are further results on Vertex Cover, Dominating Set and Maximum Cut. All lower bounds are matched by existing and newly designed algorithms.  ...  We rule out algorithms running in time O^*((r+1-ϵ)^k) for Deletion to r-Colorable parameterized by k=|X|.  ...  deletion distance to a single path has the same complexity as when parameterized by treewidth.  ... 
arXiv:2107.06111v1 fatcat:if7kfrfzsjfudchcbzphxchjpq
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