Volume
LIPIcs, Volume 214
16th International Symposium on Parameterized and Exact Computation (IPEC 2021)
Event
IPEC 2021, September 8-10, 2021, Lisbon, PortugalEditors
Publication Details
- published at: 2021-11-22
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-95977-216-7
- DBLP: db/conf/iwpec/ipec2021
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Complete Volume
LIPIcs, Volume 214, IPEC 2021, Complete Volume
Abstract
LIPIcs, Volume 214, IPEC 2021, Complete Volume
Cite as
16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 1-474, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@Proceedings{golovach_et_al:LIPIcs.IPEC.2021,
title = {{LIPIcs, Volume 214, IPEC 2021, Complete Volume}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {1--474},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021},
URN = {urn:nbn:de:0030-drops-153828},
doi = {10.4230/LIPIcs.IPEC.2021},
annote = {Keywords: LIPIcs, Volume 214, IPEC 2021, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization
Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as
16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 0:i-0:xviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{golovach_et_al:LIPIcs.IPEC.2021.0,
author = {Golovach, Petr A. and Zehavi, Meirav},
title = {{Front Matter, Table of Contents, Preface, Conference Organization}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {0:i--0:xviii},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.0},
URN = {urn:nbn:de:0030-drops-153834},
doi = {10.4230/LIPIcs.IPEC.2021.0},
annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
A Polynomial Kernel for Deletion to Ptolemaic Graphs
Abstract
For a family of graphs F, given a graph G and an integer k, the F-Deletion problem asks whether we can delete at most k vertices from G to obtain a graph in the family F. The F-Deletion problems for all non-trivial families F that satisfy the hereditary property on induced subgraphs are known to be NP-hard by a result of Yannakakis (STOC'78). Ptolemaic graphs are the graphs that satisfy the Ptolemy inequality, and they are the intersection of chordal graphs and distance-hereditary graphs. Equivalently, they form the set of graphs that do not contain any chordless cycles or a gem as an induced subgraph. (A gem is the graph on 5 vertices, where four vertices form an induced path, and the fifth vertex is adjacent to all the vertices of this induced path.) The Ptolemaic Deletion problem is the F-Deletion problem, where F is the family of Ptolemaic graphs. In this paper we study Ptolemaic Deletion from the viewpoint of Kernelization Complexity, and obtain a kernel with 𝒪(k⁶) vertices for the problem.
Cite as
Akanksha Agrawal, Aditya Anand, and Saket Saurabh. A Polynomial Kernel for Deletion to Ptolemaic Graphs. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 1:1-1:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{agrawal_et_al:LIPIcs.IPEC.2021.1,
author = {Agrawal, Akanksha and Anand, Aditya and Saurabh, Saket},
title = {{A Polynomial Kernel for Deletion to Ptolemaic Graphs}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {1:1--1:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.1},
URN = {urn:nbn:de:0030-drops-153840},
doi = {10.4230/LIPIcs.IPEC.2021.1},
annote = {Keywords: Ptolemaic Deletion, Kernelization, Parameterized Complexity, Gem-free chordal graphs}
}
Document
Refuting FPT Algorithms for Some Parameterized Problems Under Gap-ETH
Abstract
In this article we study a well-known problem, called Bipartite Token Jumping and not-so-well known problem(s), which we call, Half (Induced-) Subgraph, and show that under Gap-ETH, these problems do not admit FPT algorithms. The problem Bipartite Token Jumping takes as input a bipartite graph G and two independent sets S,T in G, where |S| = |T| = k, and the objective is to test if there is a sequence of exactly k-sized independent sets ⟨ I₀, I₁,⋯, I_𝓁 ⟩ in G, such that: i) I₀ = S and I_𝓁 = T, and ii) for every j ∈ [𝓁], I_{j} is obtained from I_{j-1} by replacing a vertex in I_{j-1} by a vertex in V(G) ⧵ I_{j-1}. We show that, assuming Gap-ETH, Bipartite Token Jumping does not admit an FPT algorithm. We note that this result resolves one of the (two) open problems posed by Bartier et al. (ISAAC 2020), under Gap-ETH. Most of the known reductions related to Token Jumping exploit the property given by triangles (i.e., C₃s), to obtain the correctness, and our results refutes FPT algorithm for Bipartite Token Jumping, where the input graph cannot have any triangles.
For an integer k ∈ ℕ, the half graph S_{k,k} is the graph with vertex set V(S_{k,k}) = A_k ∪ B_k, where A_k = {a₁,a₂,⋯, a_k} and B_k = {b₁,b₂,⋯, b_k}, and for i,j ∈ [k], {a_i,b_j} ∈ E(T_{k,k}) if and only if j ≥ i. We also study the Half (Induced-)Subgraph problem where we are given a graph G and an integer k, and the goal is to check if G contains S_{k,k} as an (induced-)subgraph. Again under Gap-ETH, we show that Half (Induced-)Subgraph does not admit an FPT algorithm, even when the input is a bipartite graph. We believe that the above problem (and its negative) result maybe of independent interest and could be useful obtaining new fixed parameter intractability results.
There are very few reductions known in the literature which refute FPT algorithms for a parameterized problem based on assumptions like Gap-ETH. Thus our technique (and simple reductions) exhibits the potential of such conjectures in obtaining new (and possibly easier) proofs for refuting FPT algorithms for parameterized problems.
Cite as
Akanksha Agrawal, Ravi Kiran Allumalla, and Varun Teja Dhanekula. Refuting FPT Algorithms for Some Parameterized Problems Under Gap-ETH. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 2:1-2:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{agrawal_et_al:LIPIcs.IPEC.2021.2,
author = {Agrawal, Akanksha and Allumalla, Ravi Kiran and Dhanekula, Varun Teja},
title = {{Refuting FPT Algorithms for Some Parameterized Problems Under Gap-ETH}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {2:1--2:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.2},
URN = {urn:nbn:de:0030-drops-153851},
doi = {10.4230/LIPIcs.IPEC.2021.2},
annote = {Keywords: Token Jumping, Bipartite Graphs, Fixed Parameter Intractability, Half Graphs, Gap-Exponential Time Hypothesis}
}
Document
The Fine-Grained Complexity of Multi-Dimensional Ordering Properties
Abstract
We define a class of problems whose input is an n-sized set of d-dimensional vectors, and where the problem is first-order definable using comparisons between coordinates. This class captures a wide variety of tasks, such as complex types of orthogonal range search, model-checking first-order properties on geometric intersection graphs, and elementary questions on multidimensional data like verifying Pareto optimality of a choice of data points.
Focusing on constant dimension d, we show that any k-quantifier, d-dimensional such problem is solvable in O(n^{k-1} log^{d-1} n) time. Furthermore, this algorithm is conditionally tight up to subpolynomial factors: we show that assuming the 3-uniform hyperclique hypothesis, there is a k-quantifier, (3k-3)-dimensional problem in this class that requires time Ω(n^{k-1-o(1)}).
Towards identifying a single representative problem for this class, we study the existence of complete problems for the 3-quantifier setting (since 2-quantifier problems can already be solved in near-linear time O(nlog^{d-1} n), and k-quantifier problems with k > 3 reduce to the 3-quantifier case). We define a problem Vector Concatenated Non-Domination VCND_d (Given three sets of vectors X,Y and Z of dimension d,d and 2d, respectively, is there an x ∈ X and a y ∈ Y so that their concatenation x∘y is not dominated by any z ∈ Z, where vector u is dominated by vector v if u_i ≤ v_i for each coordinate 1 ≤ i ≤ d), and determine it as the "unique" candidate to be complete for this class (under fine-grained assumptions).
Cite as
Haozhe An, Mohit Gurumukhani, Russell Impagliazzo, Michael Jaber, Marvin Künnemann, and Maria Paula Parga Nina. The Fine-Grained Complexity of Multi-Dimensional Ordering Properties. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{an_et_al:LIPIcs.IPEC.2021.3,
author = {An, Haozhe and Gurumukhani, Mohit and Impagliazzo, Russell and Jaber, Michael and K\"{u}nnemann, Marvin and Nina, Maria Paula Parga},
title = {{The Fine-Grained Complexity of Multi-Dimensional Ordering Properties}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {3:1--3:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.3},
URN = {urn:nbn:de:0030-drops-153869},
doi = {10.4230/LIPIcs.IPEC.2021.3},
annote = {Keywords: Fine-grained complexity, First-order logic, Orthogonal vectors}
}
Document
A New Framework for Kernelization Lower Bounds: The Case of Maximum Minimal Vertex Cover
Abstract
In the Maximum Minimal Vertex Cover (MMVC) problem, we are given a graph G and a positive integer k, and the objective is to decide whether G contains a minimal vertex cover of size at least k. Motivated by the kernelization of MMVC with parameter k, our main contribution is to introduce a simple general framework to obtain lower bounds on the degrees of a certain type of polynomial kernels for vertex-optimization problems, which we call {lop-kernels}. Informally, this type of kernels is required to preserve large optimal solutions in the reduced instance, and captures the vast majority of existing kernels in the literature. As a consequence of this framework, we show that the trivial quadratic kernel for MMVC is essentially optimal, answering a question of Boria et al. [Discret. Appl. Math. 2015], and that the known cubic kernel for Maximum Minimal Feedback Vertex Set is also essentially optimal. On the positive side, given the (plausible) non-existence of subquadratic kernels for MMVC on general graphs, we provide subquadratic kernels on H-free graphs for several graphs H, such as the bull, the paw, or the complete graphs, by making use of the Erdős-Hajnal property in order to find an appropriate decomposition. Finally, we prove that MMVC does not admit polynomial kernels parameterized by the size of a minimum vertex cover of the input graph, even on bipartite graphs, unless NP ⊆ coNP / poly. This indicates that parameters smaller than the solution size are unlike to yield polynomial kernels for MMVC.
Cite as
Júlio Araújo, Marin Bougeret, Victor Campos, and Ignasi Sau. A New Framework for Kernelization Lower Bounds: The Case of Maximum Minimal Vertex Cover. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 4:1-4:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{araujo_et_al:LIPIcs.IPEC.2021.4,
author = {Ara\'{u}jo, J\'{u}lio and Bougeret, Marin and Campos, Victor and Sau, Ignasi},
title = {{A New Framework for Kernelization Lower Bounds: The Case of Maximum Minimal Vertex Cover}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {4:1--4:19},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.4},
URN = {urn:nbn:de:0030-drops-153879},
doi = {10.4230/LIPIcs.IPEC.2021.4},
annote = {Keywords: Maximum minimal vertex cover, parameterized complexity, polynomial kernel, kernelization lower bound, Erd\H{o}s-Hajnal property, induced subgraphs}
}
Document
CNF Satisfiability in a Subspace and Related Problems
Abstract
We introduce the problem of finding a satisfying assignment to a CNF formula that must further belong to a prescribed input subspace. Equivalent formulations of the problem include finding a point outside a union of subspaces (the Union-of-Subspace Avoidance (USA) problem), and finding a common zero of a system of polynomials over 𝔽₂ each of which is a product of affine forms.
We focus on the case of k-CNF formulas (the k-Sub-Sat problem). Clearly, k-Sub-Sat is no easier than k-SAT, and might be harder. Indeed, via simple reductions we show that 2-Sub-Sat is NP-hard, and W[1]-hard when parameterized by the co-dimension of the subspace. We also prove that the optimization version Max-2-Sub-Sat is NP-hard to approximate better than the trivial 3/4 ratio even on satisfiable instances.
On the algorithmic front, we investigate fast exponential algorithms which give non-trivial savings over brute-force algorithms. We give a simple branching algorithm with running time (1.5)^r for 2-Sub-Sat, where r is the subspace dimension, as well as an O^*(1.4312)ⁿ time algorithm where n is the number of variables.
Turning to k-Sub-Sat for k ⩾ 3, while known algorithms for solving a system of degree k polynomial equations already imply a solution with running time ≈ 2^{r(1-1/2k)}, we explore a more combinatorial approach. Based on an analysis of critical variables (a key notion underlying the randomized k-SAT algorithm of Paturi, Pudlak, and Zane), we give an algorithm with running time ≈ {n choose {⩽t}} 2^{n-n/k} where n is the number of variables and t is the co-dimension of the subspace. This improves upon the running time of the polynomial equations approach for small co-dimension. Our combinatorial approach also achieves polynomial space in contrast to the algebraic approach that uses exponential space. We also give a PPZ-style algorithm for k-Sub-Sat with running time ≈ 2^{n-n/2k}. This algorithm is in fact oblivious to the structure of the subspace, and extends when the subspace-membership constraint is replaced by any constraint for which partial satisfying assignments can be efficiently completed to a full satisfying assignment. Finally, for systems of O(n) polynomial equations in n variables over 𝔽₂, we give a fast exponential algorithm when each polynomial has bounded degree irreducible factors (but can otherwise have large degree) using a degree reduction trick.
Cite as
Vikraman Arvind and Venkatesan Guruswami. CNF Satisfiability in a Subspace and Related Problems. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 5:1-5:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{arvind_et_al:LIPIcs.IPEC.2021.5,
author = {Arvind, Vikraman and Guruswami, Venkatesan},
title = {{CNF Satisfiability in a Subspace and Related Problems}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {5:1--5:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.5},
URN = {urn:nbn:de:0030-drops-153886},
doi = {10.4230/LIPIcs.IPEC.2021.5},
annote = {Keywords: CNF Satisfiability, Exact exponential algorithms, Hardness results}
}
Document
Twin-Width Is Linear in the Poset Width
Abstract
Twin-width is a new parameter informally measuring how diverse are the neighbourhoods of the graph vertices, and it extends also to other binary relational structures, e.g. to digraphs and posets. It was introduced just very recently, in 2020 by Bonnet, Kim, Thomassé and Watrigant. One of the core results of these authors is that FO model checking on graph classes of bounded twin-width is in FPT. With that result, they also claimed that posets of bounded width have bounded twin-width, thus capturing prior result on FO model checking of posets of bounded width in FPT. However, their translation from poset width to twin-width was indirect and giving only a very loose double-exponential bound. We prove that posets of width d have twin-width at most 8d with a direct and elementary argument, and show that this bound is tight up to a constant factor. Specifically, for posets of width 2 we prove that in the worst case their twin-width is also equal 2. These two theoretical results are complemented with straightforward algorithms to construct the respective contraction sequence for a given poset.
Cite as
Jakub Balabán and Petr Hliněný. Twin-Width Is Linear in the Poset Width. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 6:1-6:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{balaban_et_al:LIPIcs.IPEC.2021.6,
author = {Balab\'{a}n, Jakub and Hlin\v{e}n\'{y}, Petr},
title = {{Twin-Width Is Linear in the Poset Width}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {6:1--6:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.6},
URN = {urn:nbn:de:0030-drops-153895},
doi = {10.4230/LIPIcs.IPEC.2021.6},
annote = {Keywords: twin-width, digraph, poset, FO model checking, contraction sequence}
}
Document
Dynamic Kernels for Hitting Sets and Set Packing
Abstract
Computing small kernels for the hitting set problem is a well-studied computational problem where we are given a hypergraph with n vertices and m hyperedges, each of size d for some small constant d, and a parameter k. The task is to compute a new hypergraph, called a kernel, whose size is polynomial with respect to the parameter k and which has a size-k hitting set if, and only if, the original hypergraph has one. State-of-the-art algorithms compute kernels of size k^d (which is a polynomial kernel size as d is a constant), and they do so in time m⋅ 2^d poly(d) for a small polynomial poly(d) (which is a linear runtime as d is again a constant).
We generalize this task to the dynamic setting where hyperedges may continuously be added or deleted and one constantly has to keep track of a size-k^d hitting set kernel in memory (including moments when no size-k hitting set exists). This paper presents a deterministic solution with worst-case time 3^d poly(d) for updating the kernel upon hyperedge inserts and time 5^d poly(d) for updates upon deletions. These bounds nearly match the time 2^d poly(d) needed by the best static algorithm per hyperedge. Let us stress that for constant d our algorithm maintains a dynamic hitting set kernel with constant, deterministic, worst-case update time that is independent of n, m, and the parameter k. As a consequence, we also get a deterministic dynamic algorithm for keeping track of size-k hitting sets in d-hypergraphs with update times O(1) and query times O(c^k) where c = d - 1 + O(1/d) equals the best base known for the static setting.
Cite as
Max Bannach, Zacharias Heinrich, Rüdiger Reischuk, and Till Tantau. Dynamic Kernels for Hitting Sets and Set Packing. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{bannach_et_al:LIPIcs.IPEC.2021.7,
author = {Bannach, Max and Heinrich, Zacharias and Reischuk, R\"{u}diger and Tantau, Till},
title = {{Dynamic Kernels for Hitting Sets and Set Packing}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {7:1--7:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.7},
URN = {urn:nbn:de:0030-drops-153900},
doi = {10.4230/LIPIcs.IPEC.2021.7},
annote = {Keywords: Kernelization, Dynamic Algorithms, Hitting Set, Set Packings}
}
Document
(Sub)linear Kernels for Edge Modification Problems Towards Structured Graph Classes
Abstract
In a (parameterized) graph edge modification problem, we are given a graph G, an integer k and a (usually well-structured) class of graphs 𝒢, and ask whether it is possible to transform G into a graph G' ∈ 𝒢 by adding and/or removing at most k edges. Parameterized graph edge modification problems received considerable attention in the last decades.
In this paper, we focus on finding small kernels for edge modification problems. One of the most studied problems is the Cluster Editing problem, in which the goal is to partition the vertex set into a disjoint union of cliques. Even if this problem admits a 2k kernel [Cao and Chen, 2012], this kernel does not reduce the size of most instances. Therefore, we explore the question of whether linear kernels are a theoretical limit in edge modification problems, in particular when the target graphs are very structured (such as a partition into cliques for instance). We prove, as far as we know, the first sublinear kernel for an edge modification problem. Namely, we show that Clique + Independent Set Deletion, which is a restriction of Cluster Deletion, admits a kernel of size O(k/log k).
We also obtain small kernels for several other edge modification problems. We prove that Split Addition (and the equivalent Split Deletion) admits a linear kernel, improving the existing quadratic kernel of Ghosh et al. [Ghosh et al., 2015]. We complement this result by proving that Trivially Perfect Addition admits a quadratic kernel (improving the cubic kernel of Guo [Guo, 2007]), and finally prove that its triangle-free version (Starforest Deletion) admits a linear kernel, which is optimal under ETH.
Cite as
Gabriel Bathie, Nicolas Bousquet, and Théo Pierron. (Sub)linear Kernels for Edge Modification Problems Towards Structured Graph Classes. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{bathie_et_al:LIPIcs.IPEC.2021.8,
author = {Bathie, Gabriel and Bousquet, Nicolas and Pierron, Th\'{e}o},
title = {{(Sub)linear Kernels for Edge Modification Problems Towards Structured Graph Classes}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {8:1--8:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.8},
URN = {urn:nbn:de:0030-drops-153918},
doi = {10.4230/LIPIcs.IPEC.2021.8},
annote = {Keywords: kernelization, graph editing, split graphs, (sub)linear kernels}
}
Document
Parameterized Complexities of Dominating and Independent Set Reconfiguration
Abstract
We settle the parameterized complexities of several variants of independent set reconfiguration and dominating set reconfiguration, parameterized by the number of tokens. We show that both problems are XL-complete when there is no limit on the number of moves and XNL-complete when a maximum length 𝓁 for the sequence is given in binary in the input. The problems are known to be XNLP-complete when 𝓁 is given in unary instead, and W[1]- and W[2]-hard respectively when 𝓁 is also a parameter. We complete the picture by showing membership in those classes.
Moreover, we show that for all the variants that we consider, token sliding and token jumping are equivalent under pl-reductions. We introduce partitioned variants of token jumping and token sliding, and give pl-reductions between the four variants that have precise control over the number of tokens and the length of the reconfiguration sequence.
Cite as
Hans L. Bodlaender, Carla Groenland, and Céline M. F. Swennenhuis. Parameterized Complexities of Dominating and Independent Set Reconfiguration. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{bodlaender_et_al:LIPIcs.IPEC.2021.9,
author = {Bodlaender, Hans L. and Groenland, Carla and Swennenhuis, C\'{e}line M. F.},
title = {{Parameterized Complexities of Dominating and Independent Set Reconfiguration}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {9:1--9:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.9},
URN = {urn:nbn:de:0030-drops-153920},
doi = {10.4230/LIPIcs.IPEC.2021.9},
annote = {Keywords: Parameterized complexity, independent set reconfiguration, dominating set reconfiguration, W-hierarchy, XL, XNL, XNLP}
}
Document
Twin-Width and Polynomial Kernels
Abstract
We study the existence of polynomial kernels for parameterized problems without a polynomial kernel on general graphs, when restricted to graphs of bounded twin-width. It was previously observed in [Bonnet et al., ICALP'21] that the problem k-Independent Set allows no polynomial kernel on graph of bounded twin-width by a very simple argument, which extends to several other problems such as k-Independent Dominating Set, k-Path, k-Induced Path, k-Induced Matching. In this work, we examine the k-Dominating Set and variants of k-Vertex Cover for the existence of polynomial kernels.
As a main result, we show that k-Dominating Set does not admit a polynomial kernel on graphs of twin-width at most 4 under a standard complexity-theoretic assumption. The reduction is intricate, especially due to the effort to bring the twin-width down to 4, and it can be tweaked to work for Connected k-Dominating Set and Total k-Dominating Set with a slightly worse bound on the twin-width.
On the positive side, we obtain a simple quadratic vertex kernel for Connected k-Vertex Cover and Capacitated k-Vertex Cover on graphs of bounded twin-width. These kernels rely on that graphs of bounded twin-width have Vapnik-Chervonenkis (VC) density 1, that is, for any vertex set X, the number of distinct neighborhoods in X is at most c⋅|X|, where c is a constant depending only on the twin-width. Interestingly the kernel applies to any graph class of VC density 1, and does not require a witness sequence. We also present a more intricate O(k^{1.5}) vertex kernel for Connected k-Vertex Cover.
Finally we show that deciding if a graph has twin-width at most 1 can be done in polynomial time, and observe that most graph optimization/decision problems can be solved in polynomial time on graphs of twin-width at most 1.
Cite as
Édouard Bonnet, Eun Jung Kim, Amadeus Reinald, Stéphan Thomassé, and Rémi Watrigant. Twin-Width and Polynomial Kernels. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{bonnet_et_al:LIPIcs.IPEC.2021.10,
author = {Bonnet, \'{E}douard and Kim, Eun Jung and Reinald, Amadeus and Thomass\'{e}, St\'{e}phan and Watrigant, R\'{e}mi},
title = {{Twin-Width and Polynomial Kernels}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {10:1--10:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.10},
URN = {urn:nbn:de:0030-drops-153932},
doi = {10.4230/LIPIcs.IPEC.2021.10},
annote = {Keywords: Twin-width, kernelization, lower bounds, Dominating Set}
}
Document
A New Parametrization for Independent Set Reconfiguration and Applications to RNA Kinetics
Abstract
In this paper, we study the Independent Set (IS) reconfiguration problem in graphs. An IS reconfiguration is a scenario transforming an IS L into another IS R, inserting/removing vertices one step at a time while keeping the cardinalities of intermediate sets greater than a specified threshold. We focus on the bipartite variant where only start and end vertices are allowed in intermediate ISs. Our motivation is an application to the RNA energy barrier problem from bioinformatics, for which a natural parameter would be the difference between the initial IS size and the threshold.
We first show the para-NP hardness of the problem with respect to this parameter. We then investigate a new parameter, the cardinality range, denoted by ρ which captures the maximum deviation of the reconfiguration scenario from optimal sets (formally, ρ is the maximum difference between the cardinalities of an intermediate IS and an optimal IS). We give two different routes to show that this problem is in XP for ρ: The first is a direct O(n²)-space, O(n^{2ρ+2.5})-time algorithm based on a separation lemma; The second builds on a parameterized equivalence with the directed pathwidth problem, leading to a O(n^{ρ+1})-space, O(n^{ρ+2})-time algorithm for the reconfiguration problem through an adaptation of a prior result by Tamaki [Tamaki, 2011]. This equivalence is an interesting result in its own right, connecting a reconfiguration problem (which is essentially a connectivity problem within a reconfiguration network) with a structural parameter for an auxiliary graph.
We demonstrate the practicality of these algorithms, and the relevance of our introduced parameter, by considering the application of our algorithms on random small-degree instances for our problem. Moreover, we reformulate the computation of the energy barrier between two RNA secondary structures, a classic hard problem in computational biology, as an instance of bipartite reconfiguration. Our results on IS reconfiguration thus yield an XP algorithm in O(n^{ρ+2}) for the energy barrier problem, improving upon a partial O(n^{2ρ+2.5}) algorithm for the problem.
Cite as
Laurent Bulteau, Bertrand Marchand, and Yann Ponty. A New Parametrization for Independent Set Reconfiguration and Applications to RNA Kinetics. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{bulteau_et_al:LIPIcs.IPEC.2021.11,
author = {Bulteau, Laurent and Marchand, Bertrand and Ponty, Yann},
title = {{A New Parametrization for Independent Set Reconfiguration and Applications to RNA Kinetics}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {11:1--11:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.11},
URN = {urn:nbn:de:0030-drops-153946},
doi = {10.4230/LIPIcs.IPEC.2021.11},
annote = {Keywords: reconfiguration problems - parameterized algorithms - RNA bioinformatics - directed pathwidth}
}
Document
Lower Bounds for Conjunctive and Disjunctive Turing Kernels
Abstract
The non-existence of polynomial kernels for OR- and AND-compositional problems is now a well-established result. Some of these problems have adaptive or non-adaptive polynomial Turing kernels. Up to now, most known polynomial Turing kernels are non-adaptive and most of them are of the conjunctive or disjunctive kind. For some problems it has been conjectured that the existence of polynomial Turing kernels is unlikely. For instance, either all or none of the WK[1]-complete problems have polynomial Turing kernels. While it has been conjectured that they do not, a proof tying their non-existence to some complexity theoretic assumption is still missing and seems to be beyond the reach of today’s standard techniques.
In this paper, we prove that OR-compositional problems and all WK[1]-hard problems do not have conjunctive polynomial kernels, a special type of non-adaptive Turing kernels, under the assumption that coNP ⊈ NP/poly. Similarly, it is unlikely that AND-compositional problems have disjunctive polynomial kernels. Moreover, we present a way to prove that the parameterized versions of some ⊕ P-hard problems, for instance, Odd Path on planar graphs, do not have conjunctive or disjunctive polynomial kernels, unless coNP ⊆ NP/poly. Finally, we identify a problem that is unlikely to have either a conjunctive or disjunctive polynomial kernel, unless coNP ⊆ NP/poly, due to a reduction from an NP-hard problem instead: Weighted Odd Path on planar graphs.
Cite as
Elisabet Burjons and Peter Rossmanith. Lower Bounds for Conjunctive and Disjunctive Turing Kernels. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{burjons_et_al:LIPIcs.IPEC.2021.12,
author = {Burjons, Elisabet and Rossmanith, Peter},
title = {{Lower Bounds for Conjunctive and Disjunctive Turing Kernels}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {12:1--12:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.12},
URN = {urn:nbn:de:0030-drops-153953},
doi = {10.4230/LIPIcs.IPEC.2021.12},
annote = {Keywords: Parameterized Complexity, Turing kernels}
}
Document
Improved Kernels for Edge Modification Problems
Abstract
In an edge modification problem, we are asked to modify at most k edges of a given graph to make the graph satisfy a certain property. Depending on the operations allowed, we have the completion problems and the edge deletion problems. A great amount of efforts have been devoted to understanding the kernelization complexity of these problems. We revisit several well-studied edge modification problems, and develop improved kernels for them:
- a 2 k-vertex kernel for the cluster edge deletion problem,
- a 3 k²-vertex kernel for the trivially perfect completion problem,
- a 5 k^{1.5}-vertex kernel for the split completion problem and the split edge deletion problem, and
- a 5 k^{1.5}-vertex kernel for the pseudo-split completion problem and the pseudo-split edge deletion problem. Moreover, our kernels for split completion and pseudo-split completion have only O(k^{2.5}) edges. Our results also include a 2 k-vertex kernel for the strong triadic closure problem, which is related to cluster edge deletion.
Cite as
Yixin Cao and Yuping Ke. Improved Kernels for Edge Modification Problems. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 13:1-13:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{cao_et_al:LIPIcs.IPEC.2021.13,
author = {Cao, Yixin and Ke, Yuping},
title = {{Improved Kernels for Edge Modification Problems}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {13:1--13:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.13},
URN = {urn:nbn:de:0030-drops-153965},
doi = {10.4230/LIPIcs.IPEC.2021.13},
annote = {Keywords: Kernelization, edge modification, cluster, trivially perfect graphs, split graphs}
}
Document
Preprocessing for Outerplanar Vertex Deletion: An Elementary Kernel of Quartic Size
Abstract
In the ℱ-Minor-Free Deletion problem one is given an undirected graph G, an integer k, and the task is to determine whether there exists a vertex set S of size at most k, so that G-S contains no graph from the finite family ℱ as a minor. It is known that whenever ℱ contains at least one planar graph, then ℱ-Minor-Free Deletion admits a polynomial kernel, that is, there is a polynomial-time algorithm that outputs an equivalent instance of size k^{𝒪(1)} [Fomin, Lokshtanov, Misra, Saurabh; FOCS 2012]. However, this result relies on non-constructive arguments based on well-quasi-ordering and does not provide a concrete bound on the kernel size.
We study the Outerplanar Deletion problem, in which we want to remove at most k vertices from a graph to make it outerplanar. This is a special case of ℱ-Minor-Free Deletion for the family ℱ = {K₄, K_{2,3}}. The class of outerplanar graphs is arguably the simplest class of graphs for which no explicit kernelization size bounds are known. By exploiting the combinatorial properties of outerplanar graphs we present elementary reduction rules decreasing the size of a graph. This yields a constructive kernel with 𝒪(k⁴) vertices and edges. As a corollary, we derive that any minor-minimal obstruction to having an outerplanar deletion set of size k has 𝒪(k⁴) vertices and edges.
Cite as
Huib Donkers, Bart M. P. Jansen, and Michał Włodarczyk. Preprocessing for Outerplanar Vertex Deletion: An Elementary Kernel of Quartic Size. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 14:1-14:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{donkers_et_al:LIPIcs.IPEC.2021.14,
author = {Donkers, Huib and Jansen, Bart M. P. and W{\l}odarczyk, Micha{\l}},
title = {{Preprocessing for Outerplanar Vertex Deletion: An Elementary Kernel of Quartic Size}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {14:1--14:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.14},
URN = {urn:nbn:de:0030-drops-153979},
doi = {10.4230/LIPIcs.IPEC.2021.14},
annote = {Keywords: fixed-parameter tractability, kernelization, outerplanar graphs}
}
Document
Maximum Matching in Almost Linear Time on Graphs of Bounded Clique-Width
Abstract
Recently, independent groups of researchers have presented algorithms to compute a maximum matching in Õ(f(k) ⋅ (n+m)) time, for some computable function f, within the graphs where some clique-width upper bound is at most k (e.g., tree-width, modular-width and P₄-sparseness). However, to the best of our knowledge, the existence of such algorithm within the graphs of bounded clique-width has remained open until this paper. Indeed, we cannot even apply Courcelle’s theorem to this problem directly, because a matching cannot be expressed in MSO₁ logic.
Our first contribution is an almost linear-time algorithm to compute a maximum matching in any bounded clique-width graph, being given a corresponding clique-width expression. It can be used to also compute the Edmonds-Gallai decomposition. For that, we do apply Courcelle’s theorem, but in order to compute the cardinality of a maximum matching rather than the matching itself, via the classic Tutte-Berge formula. To obtain with this approach a maximum matching, we need to combine it with a recursive dissection scheme for bounded clique-width graphs based on the existence of balanced edge-cuts with bounded neighbourhood diversity, and with a distributed version of Courcelle’s theorem (Courcelle and Vanicat, DAM 2016) - of which we present here a slightly stronger version than the standard one in the literature - in order to evaluate the Tutte-Berge formula on various subgraphs of the input.
Finally, for the bipartite graphs of clique-width at most k, we present an alternative Õ(k²⋅(n+m))-time algorithm for the problem. The algorithm is randomized and it is based on a completely different approach than above: combining various reductions to matching and flow problems on bounded tree-width graphs with a very recent result on the parameterized complexity of linear programming (Dong et. al., STOC'21). Our results for bounded clique-width graphs extend many prior works on the complexity of Maximum Matching within cographs, distance-hereditary graphs, series-parallel graphs and other subclasses.
Cite as
Guillaume Ducoffe. Maximum Matching in Almost Linear Time on Graphs of Bounded Clique-Width. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 15:1-15:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{ducoffe:LIPIcs.IPEC.2021.15,
author = {Ducoffe, Guillaume},
title = {{Maximum Matching in Almost Linear Time on Graphs of Bounded Clique-Width}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {15:1--15:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.15},
URN = {urn:nbn:de:0030-drops-153987},
doi = {10.4230/LIPIcs.IPEC.2021.15},
annote = {Keywords: Maximum Matching, Maximum b-matching, Clique-width, Tree-width, Courcelle’s theorem, FPT in P}
}
Document
Optimal Centrality Computations Within Bounded Clique-Width Graphs
Abstract
Given an n-vertex m-edge graph G of clique-width at most k, and a corresponding k-expression, we present algorithms for computing some well-known centrality indices (eccentricity and closeness) that run in O(2^{O(k)}(n+m)^{1+ε}) time for any ε > 0. Doing so, we can solve various distance problems within the same amount of time, including: the diameter, the center, the Wiener index and the median set. Our run-times match conditional lower bounds of Coudert et al. (SODA'18) under the Strong Exponential-Time Hypothesis. On our way, we get a distance-labeling scheme for n-vertex m-edge graphs of clique-width at most k, using O(klog²{n}) bits per vertex and constructible in Õ(k(n+m)) time from a given k-expression. Doing so, we match the label size obtained by Courcelle and Vanicat (DAM 2016), while we considerably improve the dependency on k in their scheme. As a corollary, we get an Õ(kn²)-time algorithm for computing All-Pairs Shortest-Paths on n-vertex graphs of clique-width at most k, being given a k-expression. This partially answers an open question of Kratsch and Nelles (STACS'20). Our algorithms work for graphs with non-negative vertex-weights, under two different types of distances studied in the literature. For that, we introduce a new type of orthogonal range query as a side contribution of this work, that might be of independent interest.
Cite as
Guillaume Ducoffe. Optimal Centrality Computations Within Bounded Clique-Width Graphs. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 16:1-16:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{ducoffe:LIPIcs.IPEC.2021.16,
author = {Ducoffe, Guillaume},
title = {{Optimal Centrality Computations Within Bounded Clique-Width Graphs}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {16:1--16:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.16},
URN = {urn:nbn:de:0030-drops-153995},
doi = {10.4230/LIPIcs.IPEC.2021.16},
annote = {Keywords: Clique-width, Centralities computation, Facility Location problems, Distance-labeling scheme, Fine-grained complexity in P, Graph theory}
}
Document
Polynomial Kernels for Strictly Chordal Edge Modification Problems
Abstract
We consider the Strictly Chordal Editing problem, where one is given an undirected graph G = (V,E) and a parameter k ∈ ℕ and seeks to edit (add or delete) at most k edges from G to obtain a strictly chordal graph. Problems Strictly Chordal Completion and Strictly Chordal Deletion are defined similarly, by only allowing edge additions for the former, and only edge deletions for the latter. Strictly chordal graphs are a generalization of 3-leaf power graphs and a subclass of 4-leaf power graphs. They can be defined, e.g., as dart and gem-free chordal graphs. We prove the NP-completeness for all three variants of the problem and provide an O(k³) vertex-kernel for the completion version and O(k⁴) vertex-kernels for the two others.
Cite as
Maël Dumas, Anthony Perez, and Ioan Todinca. Polynomial Kernels for Strictly Chordal Edge Modification Problems. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 17:1-17:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{dumas_et_al:LIPIcs.IPEC.2021.17,
author = {Dumas, Ma\"{e}l and Perez, Anthony and Todinca, Ioan},
title = {{Polynomial Kernels for Strictly Chordal Edge Modification Problems}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {17:1--17:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.17},
URN = {urn:nbn:de:0030-drops-154005},
doi = {10.4230/LIPIcs.IPEC.2021.17},
annote = {Keywords: Parameterized complexity, kernelization algorithms, graph modification, strictly chordal graphs}
}
Document
On Extended Formulations For Parameterized Steiner Trees
Abstract
We present a novel linear program (LP) for the Steiner Tree problem, where a set of terminal vertices needs to be connected by a minimum weight tree in a graph G = (V,E) with non-negative edge weights. This well-studied problem is NP-hard and therefore does not have a compact extended formulation (describing the convex hull of all Steiner trees) of polynomial size, unless P=NP. On the other hand, Steiner Tree is fixed-parameter tractable (FPT) when parameterized by the number k of terminals, and can be solved in O(3^k|V|+2^k|V|²) time via the Dreyfus-Wagner algorithm. A natural question thus is whether the Steiner Tree problem admits an extended formulation of comparable size. We first answer this in the negative by proving a lower bound on the extension complexity of the Steiner Tree polytope, which, for some constant c > 0, implies that no extended formulation of size f(k)2^{cn} exists for any function f. However, we are able to circumvent this lower bound due to the fact that the edge weights are non-negative: we prove that Steiner Tree admits an integral LP with O(3^k|E|) variables and constraints. The size of our LP matches the runtime of the Dreyfus-Wagner algorithm, and our poof gives a polyhedral perspective on this classic algorithm. Our proof is simple, and additionally improves on a previous result by Siebert et al. [2018], who gave an integral LP of size O((2k/e)^k)|V|^{O(1)}.
Cite as
Andreas Emil Feldmann and Ashutosh Rai. On Extended Formulations For Parameterized Steiner Trees. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 18:1-18:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{feldmann_et_al:LIPIcs.IPEC.2021.18,
author = {Feldmann, Andreas Emil and Rai, Ashutosh},
title = {{On Extended Formulations For Parameterized Steiner Trees}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {18:1--18:16},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.18},
URN = {urn:nbn:de:0030-drops-154010},
doi = {10.4230/LIPIcs.IPEC.2021.18},
annote = {Keywords: Steiner trees, integral linear program, extension complexity, fixed-parameter tractability}
}
Document
An Investigation of the Recoverable Robust Assignment Problem
Abstract
We investigate the so-called recoverable robust assignment problem on complete bipartite graphs, a mainstream problem in robust optimization: For two given linear cost functions c₁ and c₂ on the edges and a given integer k, the goal is to find two perfect matchings M₁ and M₂ that minimize the objective value c₁(M₁)+c₂(M₂), subject to the constraint that M₁ and M₂ have at least k edges in common.
We derive a variety of results on this problem. First, we show that the problem is W[1]-hard with respect to parameter k, and also with respect to the complementary parameter k' = n/2-k. This hardness result holds even in the highly restricted special case where both cost functions c₁ and c₂ only take the values 0 and 1. (On the other hand, containment of the problem in XP is straightforward to see.) Next, as a positive result we construct a polynomial time algorithm for the special case where one cost function is Monge, whereas the other one is Anti-Monge. Finally, we study the variant where matching M₁ is frozen, and where the optimization goal is to compute the best corresponding matching M₂. This problem variant is known to be contained in the randomized parallel complexity class RNC², and we show that it is at least as hard as the infamous problem Exact Red-Blue Matching in Bipartite Graphs whose computational complexity is a long-standing open problem.
Cite as
Dennis Fischer, Tim A. Hartmann, Stefan Lendl, and Gerhard J. Woeginger. An Investigation of the Recoverable Robust Assignment Problem. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 19:1-19:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{fischer_et_al:LIPIcs.IPEC.2021.19,
author = {Fischer, Dennis and Hartmann, Tim A. and Lendl, Stefan and Woeginger, Gerhard J.},
title = {{An Investigation of the Recoverable Robust Assignment Problem}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {19:1--19:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.19},
URN = {urn:nbn:de:0030-drops-154025},
doi = {10.4230/LIPIcs.IPEC.2021.19},
annote = {Keywords: assignment problem, matchings, exact matching, robust optimization, fixed paramter tractablity, RNC}
}
Document
Dynamic Data Structures for Timed Automata Acceptance
Abstract
We study a variant of the classical membership problem in automata theory, which consists of deciding whether a given input word is accepted by a given automaton. We do so through the lenses of parameterized dynamic data structures: we assume that the automaton is fixed and its size is the parameter, while the input word is revealed as in a stream, one symbol at a time following the natural order on positions. The goal is to design a dynamic data structure that can be efficiently updated upon revealing the next symbol, while maintaining the answer to the query on whether the word consisting of symbols revealed so far is accepted by the automaton. We provide complexity bounds for this dynamic acceptance problem for timed automata that process symbols interleaved with time spans. The main contribution is a dynamic data structure that maintains acceptance of a fixed one-clock timed automaton 𝒜 with amortized update time 2^{𝒪(|𝒜|)} per input symbol.
Cite as
Alejandro Grez, Filip Mazowiecki, Michał Pilipczuk, Gabriele Puppis, and Cristian Riveros. Dynamic Data Structures for Timed Automata Acceptance. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 20:1-20:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{grez_et_al:LIPIcs.IPEC.2021.20,
author = {Grez, Alejandro and Mazowiecki, Filip and Pilipczuk, Micha{\l} and Puppis, Gabriele and Riveros, Cristian},
title = {{Dynamic Data Structures for Timed Automata Acceptance}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {20:1--20:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.20},
URN = {urn:nbn:de:0030-drops-154037},
doi = {10.4230/LIPIcs.IPEC.2021.20},
annote = {Keywords: timed automata, data stream, dynamic data structure}
}
Document
Close Relatives (Of Feedback Vertex Set), Revisited
Abstract
At IPEC 2020, Bergougnoux, Bonnet, Brettell, and Kwon (Close Relatives of Feedback Vertex Set Without Single-Exponential Algorithms Parameterized by Treewidth, IPEC 2020, LIPIcs vol. 180, pp. 3:1-3:17) showed that a number of problems related to the classic Feedback Vertex Set (FVS) problem do not admit a 2^{o(k log k)} ⋅ n^{𝒪(1)}-time algorithm on graphs of treewidth at most k, assuming the Exponential Time Hypothesis. This contrasts with the 3^{k} ⋅ k^{𝒪(1)} ⋅ n-time algorithm for FVS using the Cut&Count technique.
During their live talk at IPEC 2020, Bergougnoux et al. posed a number of open questions, which we answer in this work.
- Subset Even Cycle Transversal, Subset Odd Cycle Transversal, Subset Feedback Vertex Set can be solved in time 2^{𝒪(k log k)} ⋅ n in graphs of treewidth at most k. This matches a lower bound for Even Cycle Transversal of Bergougnoux et al. and improves the polynomial factor in some of their upper bounds.
- Subset Feedback Vertex Set and Node Multiway Cut can be solved in time 2^{𝒪(k log k)} ⋅ n, if the input graph is given as a cliquewidth expression of size n and width k.
- Odd Cycle Transversal can be solved in time 4^k ⋅ k^{𝒪(1)} ⋅ n if the input graph is given as a cliquewidth expression of size n and width k. Furthermore, the existence of a constant ε > 0 and an algorithm performing this task in time (4-ε)^k ⋅ n^{𝒪(1)} would contradict the Strong Exponential Time Hypothesis. A common theme of the first two algorithmic results is to represent connectivity properties of the current graph in a state of a dynamic programming algorithm as an auxiliary forest with 𝒪(k) nodes. This results in a 2^{𝒪(k log k)} bound on the number of states for one node of the tree decomposition or cliquewidth expression and allows to compare two states in k^{𝒪(1)} time, resulting in linear time dependency on the size of the graph or the input cliquewidth expression.
Cite as
Hugo Jacob, Thomas Bellitto, Oscar Defrain, and Marcin Pilipczuk. Close Relatives (Of Feedback Vertex Set), Revisited. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 21:1-21:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{jacob_et_al:LIPIcs.IPEC.2021.21,
author = {Jacob, Hugo and Bellitto, Thomas and Defrain, Oscar and Pilipczuk, Marcin},
title = {{Close Relatives (Of Feedback Vertex Set), Revisited}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {21:1--21:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.21},
URN = {urn:nbn:de:0030-drops-154049},
doi = {10.4230/LIPIcs.IPEC.2021.21},
annote = {Keywords: feedback vertex set, treewidth, cliquewidth}
}
Document
Long Paths Make Pattern-Counting Hard, and Deep Trees Make It Harder
Abstract
We study the counting problem known as #PPM, whose input is a pair of permutations π and τ (called pattern and text, respectively), and the task is to find the number of subsequences of τ that have the same relative order as π. A simple brute-force approach solves #PPM for a pattern of length k and a text of length n in time O(n^{k+1}), while Berendsohn, Kozma and Marx have recently shown that under the exponential time hypothesis (ETH), it cannot be solved in time f(k) n^{o(k/log k)} for any function f. In this paper, we consider the restriction of #PPM, known as 𝒞-Pattern #PPM, where the pattern π must belong to a hereditary permutation class 𝒞. Our goal is to identify the structural properties of 𝒞 that determine the complexity of 𝒞-Pattern #PPM.
We focus on two such structural properties, known as the long path property (LPP) and the deep tree property (DTP). Assuming ETH, we obtain these results:
1) If 𝒞 has the LPP, then 𝒞-Pattern #PPM cannot be solved in time f(k)n^{o(√k)} for any function f, and
2) if 𝒞 has the DTP, then 𝒞-Pattern #PPM cannot be solved in time f(k)n^{o(k/log² k)} for any function f.
Furthermore, when 𝒞 is one of the so-called monotone grid classes, we show that if 𝒞 has the LPP but not the DTP, then 𝒞-Pattern #PPM can be solved in time f(k)n^{O(√ k)}. In particular, the lower bounds above are tight up to the polylog terms in the exponents.
Cite as
Vít Jelínek, Michal Opler, and Jakub Pekárek. Long Paths Make Pattern-Counting Hard, and Deep Trees Make It Harder. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 22:1-22:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{jelinek_et_al:LIPIcs.IPEC.2021.22,
author = {Jel{\'\i}nek, V{\'\i}t and Opler, Michal and Pek\'{a}rek, Jakub},
title = {{Long Paths Make Pattern-Counting Hard, and Deep Trees Make It Harder}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {22:1--22:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.22},
URN = {urn:nbn:de:0030-drops-154050},
doi = {10.4230/LIPIcs.IPEC.2021.22},
annote = {Keywords: Permutation pattern matching, subexponential algorithm, conditional lower bounds, tree-width}
}
Document
A Polynomial Kernel for Bipartite Permutation Vertex Deletion
Abstract
In a permutation graph, vertices represent the elements of a permutation, and edges represent pairs of elements that are reversed by the permutation. In the Permutation Vertex Deletion problem, given an undirected graph G and an integer k, the objective is to test whether there exists a vertex subset S ⊆ V(G) such that |S| ≤ k and G-S is a permutation graph. The parameterized complexity of Permutation Vertex Deletion is a well-known open problem. Bożyk et al. [IPEC 2020] initiated a study towards this problem by requiring that G-S be a bipartite permutation graph (a permutation graph that is bipartite). They called this the Bipartite Permutation Vertex Deletion (BPVD) problem. They showed that the problem admits a factor 9-approximation algorithm as well as a fixed parameter tractable (FPT) algorithm running in time 𝒪(9^k |V(G)|⁹). And they posed the question {whether BPVD admits a polynomial kernel.}
We resolve this question in the affirmative by designing a polynomial kernel for BPVD. In particular, we obtain the following: Given an instance (G,k) of BPVD, in polynomial time we obtain an equivalent instance (G',k') of BPVD such that k' ≤ k, and |V(G')|+|E(G')| ≤ k^{𝒪(1)}.
Cite as
Lawqueen Kanesh, Jayakrishnan Madathil, Abhishek Sahu, Saket Saurabh, and Shaily Verma. A Polynomial Kernel for Bipartite Permutation Vertex Deletion. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{kanesh_et_al:LIPIcs.IPEC.2021.23,
author = {Kanesh, Lawqueen and Madathil, Jayakrishnan and Sahu, Abhishek and Saurabh, Saket and Verma, Shaily},
title = {{A Polynomial Kernel for Bipartite Permutation Vertex Deletion}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {23:1--23:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.23},
URN = {urn:nbn:de:0030-drops-154065},
doi = {10.4230/LIPIcs.IPEC.2021.23},
annote = {Keywords: kernelization, bipartite permutation graph, bicliques}
}
Document
Hardness of Metric Dimension in Graphs of Constant Treewidth
Abstract
The Metric Dimension problem asks for a minimum-sized resolving set in a given (unweighted, undirected) graph G. Here, a set S ⊆ V(G) is resolving if no two distinct vertices of G have the same distance vector to S. The complexity of Metric Dimension in graphs of bounded treewidth remained elusive in the past years. Recently, Bonnet and Purohit [IPEC 2019] showed that the problem is W[1]-hard under treewidth parameterization. In this work, we strengthen their lower bound to show that Metric Dimension is NP-hard in graphs of treewidth 24.
Cite as
Shaohua Li and Marcin Pilipczuk. Hardness of Metric Dimension in Graphs of Constant Treewidth. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 24:1-24:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{li_et_al:LIPIcs.IPEC.2021.24,
author = {Li, Shaohua and Pilipczuk, Marcin},
title = {{Hardness of Metric Dimension in Graphs of Constant Treewidth}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {24:1--24:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.24},
URN = {urn:nbn:de:0030-drops-154071},
doi = {10.4230/LIPIcs.IPEC.2021.24},
annote = {Keywords: Graph algorithms, parameterized complexity, width parameters, NP-hard}
}
Document
Classification of OBDD Size for Monotone 2-CNFs
Abstract
We introduce a new graph parameter called linear upper maximum induced matching width lu-mim width, denoted for a graph G by lu(G). We prove that the smallest size of the obdd for φ, the monotone 2-cnf corresponding to G, is sandwiched between 2^{lu(G)} and n^{O(lu(G))}. The upper bound is based on a combinatorial statement that might be of an independent interest. We show that the bounds in terms of this parameter are best possible.
The new parameter is closely related to two existing parameters: linear maximum induced matching width (lmim width) and linear special induced matching width (lsim width). We prove that lu-mim width lies strictly in between these two parameters, being dominated by lsim width and dominating lmim width. We conclude that neither of the two existing parameters can be used instead of lu-mim width to characterize the size of obdds for monotone 2-cnfs and this justifies introduction of the new parameter.
Cite as
Igor Razgon. Classification of OBDD Size for Monotone 2-CNFs. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 25:1-25:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{razgon:LIPIcs.IPEC.2021.25,
author = {Razgon, Igor},
title = {{Classification of OBDD Size for Monotone 2-CNFs}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {25:1--25:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.25},
URN = {urn:nbn:de:0030-drops-154081},
doi = {10.4230/LIPIcs.IPEC.2021.25},
annote = {Keywords: Ordered Binary Decision Diagrams, Monotone 2-CNFs, Width parameters of graphs, upper and lower bounds}
}
Document
The PACE 2021 Parameterized Algorithms and Computational Experiments Challenge: Cluster Editing
Abstract
The Parameterized Algorithms and Computational Experiments challenge (PACE) 2021 was devoted to engineer algorithms solving the NP-hard Cluster Editing problem, also known as Correlation Clustering: Given an undirected graph the task is to compute a minimum number of edges to insert or remove in a way that the resulting graph is a cluster graph, that is, a graph in which each connected component is a clique.
Altogether 67 participants from 21 teams, 11 countries, and 3 continents submitted their implementations to the competition. In this report, we describe the setup of the challenge, the selection of benchmark instances, and the ranking of the participating teams. We also briefly discuss the approaches used in the submitted solvers.
Cite as
Leon Kellerhals, Tomohiro Koana, André Nichterlein, and Philipp Zschoche. The PACE 2021 Parameterized Algorithms and Computational Experiments Challenge: Cluster Editing. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 26:1-26:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{kellerhals_et_al:LIPIcs.IPEC.2021.26,
author = {Kellerhals, Leon and Koana, Tomohiro and Nichterlein, Andr\'{e} and Zschoche, Philipp},
title = {{The PACE 2021 Parameterized Algorithms and Computational Experiments Challenge: Cluster Editing}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {26:1--26:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.26},
URN = {urn:nbn:de:0030-drops-154096},
doi = {10.4230/LIPIcs.IPEC.2021.26},
annote = {Keywords: Correlation Clustering, Cluster Editing, Algorithm Engineering, FPT, Kernelization, Heuristics}
}
Document
PACE Solver Description
PACE Solver Description: The KaPoCE Exact Cluster Editing Algorithm
Abstract
The cluster editing problem is to transform an input graph into a cluster graph by performing a minimum number of edge editing operations. A cluster graph is a graph where each connected component is a clique. An edit operation can be either adding a new edge or removing an existing edge. In this write-up we outline the core techniques used in the exact cluster editing algorithm of the KaPoCE framework (contains also a heuristic solver), submitted to the exact track of the 2021 PACE challenge.
Cite as
Thomas Bläsius, Philipp Fischbeck, Lars Gottesbüren, Michael Hamann, Tobias Heuer, Jonas Spinner, Christopher Weyand, and Marcus Wilhelm. PACE Solver Description: The KaPoCE Exact Cluster Editing Algorithm. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 27:1-27:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{blasius_et_al:LIPIcs.IPEC.2021.27,
author = {Bl\"{a}sius, Thomas and Fischbeck, Philipp and Gottesb\"{u}ren, Lars and Hamann, Michael and Heuer, Tobias and Spinner, Jonas and Weyand, Christopher and Wilhelm, Marcus},
title = {{PACE Solver Description: The KaPoCE Exact Cluster Editing Algorithm}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {27:1--27:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.27},
URN = {urn:nbn:de:0030-drops-154109},
doi = {10.4230/LIPIcs.IPEC.2021.27},
annote = {Keywords: cluster editing}
}
Document
PACE Solver Description
PACE Solver Description: ADE-Solver
Abstract
This document describes our exact solver "ADE" for the unweighted cluster editing problem submitted to the PACE 2021 competition. The solver’s core consists of an FPT-algorithm using a branch and bound strategy in conjunction with several data reduction rules.
Cite as
Alexander Bille, Dominik Brandenstein, and Emanuel Herrendorf. PACE Solver Description: ADE-Solver. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 28:1-28:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{bille_et_al:LIPIcs.IPEC.2021.28,
author = {Bille, Alexander and Brandenstein, Dominik and Herrendorf, Emanuel},
title = {{PACE Solver Description: ADE-Solver}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {28:1--28:4},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.28},
URN = {urn:nbn:de:0030-drops-154112},
doi = {10.4230/LIPIcs.IPEC.2021.28},
annote = {Keywords: Unweighted Cluster Editing}
}
Document
PACE Solver Description
PACE Solver Description: PaSTEC - PAths, Stars and Twins to Edit Towards Clusters
Abstract
This document describes our exact Cluster Editing solver, PaSTEC, which got the third place in the 2021 PACE Challenge.
Cite as
Valentin Bartier, Gabriel Bathie, Nicolas Bousquet, Marc Heinrich, Théo Pierron, and Ulysse Prieto. PACE Solver Description: PaSTEC - PAths, Stars and Twins to Edit Towards Clusters. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 29:1-29:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{bartier_et_al:LIPIcs.IPEC.2021.29,
author = {Bartier, Valentin and Bathie, Gabriel and Bousquet, Nicolas and Heinrich, Marc and Pierron, Th\'{e}o and Prieto, Ulysse},
title = {{PACE Solver Description: PaSTEC - PAths, Stars and Twins to Edit Towards Clusters}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {29:1--29:4},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.29},
URN = {urn:nbn:de:0030-drops-154129},
doi = {10.4230/LIPIcs.IPEC.2021.29},
annote = {Keywords: cluster editing, exact algorithm, star packing, twins}
}
Document
PACE Solver Description
PACE Solver Description: PACA-JAVA
Abstract
We describe PACA-JAVA, an algorithm for solving the cluster editing problem submitted for the exact track of the Parameterized Algorithms and Computational Experiments challenge (PACE) in 2021. The algorithm solves the cluster editing problem by applying data-reduction rules, performing a layout heuristic, local search, iterative ILP verification, and branch-and-bound. We implemented the algorithm in the scope of a student project at the University of Bremen.
Cite as
Jona Dirks, Mario Grobler, Roman Rabinovich, Yannik Schnaubelt, Sebastian Siebertz, and Maximilian Sonneborn. PACE Solver Description: PACA-JAVA. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 30:1-30:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{dirks_et_al:LIPIcs.IPEC.2021.30,
author = {Dirks, Jona and Grobler, Mario and Rabinovich, Roman and Schnaubelt, Yannik and Siebertz, Sebastian and Sonneborn, Maximilian},
title = {{PACE Solver Description: PACA-JAVA}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {30:1--30:4},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.30},
URN = {urn:nbn:de:0030-drops-154138},
doi = {10.4230/LIPIcs.IPEC.2021.30},
annote = {Keywords: Cluster editing, parameterized complexity, PACE 2021}
}
Document
PACE Solver Description
PACE Solver Description: KaPoCE: A Heuristic Cluster Editing Algorithm
Abstract
The cluster editing problem is to transform an input graph into a cluster graph by performing a minimum number of edge editing operations. A cluster graph is a graph where each connected component is a clique. An edit operation can be either adding a new edge or removing an existing edge. In this write-up we outline the core techniques used in the heuristic cluster editing algorithm of the Karlsruhe and Potsdam Cluster Editing (KaPoCE) framework, submitted to the heuristic track of the 2021 PACE challenge.
Cite as
Thomas Bläsius, Philipp Fischbeck, Lars Gottesbüren, Michael Hamann, Tobias Heuer, Jonas Spinner, Christopher Weyand, and Marcus Wilhelm. PACE Solver Description: KaPoCE: A Heuristic Cluster Editing Algorithm. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 31:1-31:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{blasius_et_al:LIPIcs.IPEC.2021.31,
author = {Bl\"{a}sius, Thomas and Fischbeck, Philipp and Gottesb\"{u}ren, Lars and Hamann, Michael and Heuer, Tobias and Spinner, Jonas and Weyand, Christopher and Wilhelm, Marcus},
title = {{PACE Solver Description: KaPoCE: A Heuristic Cluster Editing Algorithm}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {31:1--31:4},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.31},
URN = {urn:nbn:de:0030-drops-154147},
doi = {10.4230/LIPIcs.IPEC.2021.31},
annote = {Keywords: cluster editing, local search, variable neighborhood search}
}
Document
PACE Solver Description
PACE Solver Description: CluES - a Heuristic Solver for the Cluster Editing Problem
Abstract
This article briefly describes the most important algorithms and techniques used in the cluster editing heuristic solver called "CluES", submitted to the 6th Parameterized Algorithms and Computational Experiments Challenge (PACE 2021).
Cite as
Sylwester Swat. PACE Solver Description: CluES - a Heuristic Solver for the Cluster Editing Problem. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 32:1-32:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{swat:LIPIcs.IPEC.2021.32,
author = {Swat, Sylwester},
title = {{PACE Solver Description: CluES - a Heuristic Solver for the Cluster Editing Problem}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {32:1--32:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.32},
URN = {urn:nbn:de:0030-drops-154157},
doi = {10.4230/LIPIcs.IPEC.2021.32},
annote = {Keywords: Cluster editing, heuristic solver, graph algorithms, PACE 2021}
}
Document
PACE Solver Description
PACE Solver Description: μSolver - Heuristic Track
Abstract
This document describes our heuristic Cluster Editing solver, μSolver, which got the third place in the 2021 PACE Challenge. We present the local search and kernelization techniques for Cluster Editing that are implemented in the solver.
Cite as
Valentin Bartier, Gabriel Bathie, Nicolas Bousquet, Marc Heinrich, Théo Pierron, and Ulysse Prieto. PACE Solver Description: μSolver - Heuristic Track. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 33:1-33:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{bartier_et_al:LIPIcs.IPEC.2021.33,
author = {Bartier, Valentin and Bathie, Gabriel and Bousquet, Nicolas and Heinrich, Marc and Pierron, Th\'{e}o and Prieto, Ulysse},
title = {{PACE Solver Description: \muSolver - Heuristic Track}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {33:1--33:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.33},
URN = {urn:nbn:de:0030-drops-154161},
doi = {10.4230/LIPIcs.IPEC.2021.33},
annote = {Keywords: kernelization, graph editing, clustering, local search}
}
Document
PACE Solver Description
PACE Solver Description: A Simplified Threshold Accepting Approach for the Cluster Editing Problem
Abstract
We present a simple heuristic for the Cluster Editing Problem as presented in the Parameterized Algorithms and Computational Experiments (PACE) 2021. Our method makes use of a simple Threshold Accepting strategy and employs single neighborhood moves only.
Despite its simplicity, the results of the method are encouraging. However, and this has to be expected, the approach cannot ultimately win in a competitive setting such as PACE 2021. Nevertheless, some interesting insights can be derived from such a simple method, as this gives an idea of how good results can be by a comparable basic approach with a reasonable implementation effort.
Cite as
Martin Josef Geiger. PACE Solver Description: A Simplified Threshold Accepting Approach for the Cluster Editing Problem. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 34:1-34:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{geiger:LIPIcs.IPEC.2021.34,
author = {Geiger, Martin Josef},
title = {{PACE Solver Description: A Simplified Threshold Accepting Approach for the Cluster Editing Problem}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {34:1--34:2},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.34},
URN = {urn:nbn:de:0030-drops-154176},
doi = {10.4230/LIPIcs.IPEC.2021.34},
annote = {Keywords: Cluster Editing Problem, Threshold Accepting, Local Search}
}
Document
PACE Solver Description
PACE Solver Description: Cluster Editing Kernelization Using CluES
Abstract
This article briefly describes the most important algorithms and techniques used in the cluster editing kernelization solver called "CluES", submitted to the 6th Parameterized Algorithms and Computational Experiments Challenge (PACE 2021).
Cite as
Sylwester Swat. PACE Solver Description: Cluster Editing Kernelization Using CluES. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 35:1-35:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
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@InProceedings{swat:LIPIcs.IPEC.2021.35,
author = {Swat, Sylwester},
title = {{PACE Solver Description: Cluster Editing Kernelization Using CluES}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {35:1--35:3},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.35},
URN = {urn:nbn:de:0030-drops-154186},
doi = {10.4230/LIPIcs.IPEC.2021.35},
annote = {Keywords: Cluster editing, kernelization, graph algorithms, PACE 2021}
}