eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
1
498
10.4230/LIPIcs.IPEC.2020
article
LIPIcs, Volume 180, IPEC 2020, Complete Volume
Cao, Yixin
1
https://orcid.org/0000-0002-6927-438X
Pilipczuk, Marcin
2
https://orcid.org/0000-0001-5680-7397
Hong Kong Polytechnic University, China
University of Warsaw, Poland
LIPIcs, Volume 180, IPEC 2020, Complete Volume
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020/LIPIcs.IPEC.2020.pdf
LIPIcs, Volume 180, IPEC 2020, Complete Volume
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
0:i
0:xviii
10.4230/LIPIcs.IPEC.2020.0
article
Front Matter, Table of Contents, Preface, Conference Organization
Cao, Yixin
1
https://orcid.org/0000-0002-6927-438X
Pilipczuk, Marcin
2
https://orcid.org/0000-0001-5680-7397
Hong Kong Polytechnic University, China
University of Warsaw, Poland
Front Matter, Table of Contents, Preface, Conference Organization
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.0/LIPIcs.IPEC.2020.0.pdf
Front Matter
Table of Contents
Preface
Conference Organization
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
1:1
1:13
10.4230/LIPIcs.IPEC.2020.1
article
On the Parameterized Complexity of Clique Elimination Distance
Agrawal, Akanksha
1
https://orcid.org/0000-0002-0656-7572
Ramanujan, M. S.
2
Indian Institute of Technology Madras, Chennai, India
University of Warwick, Coventry, UK
Bulian and Dawar [Algorithmica, 2016] introduced the notion of elimination distance in an effort to define new tractable parameterizations for graph problems and showed that deciding whether a given graph has elimination distance at most k to any minor-closed class of graphs is fixed-parameter tractable parameterized by k [Algorithmica, 2017].
In this paper, we consider the problem of computing the elimination distance of a given graph to the class of cluster graphs and initiate the study of the parameterized complexity of a more general version - that of obtaining a modulator to such graphs. That is, we study the (η,Clq)-Elimination Deletion problem ((η,Clq)-ED Deletion) where, for a fixed η, one is given a graph G and k ∈ ℕ and the objective is to determine whether there is a set S ⊆ V(G) such that the graph G-S has elimination distance at most η to the class of cluster graphs.
Our main result is a polynomial kernelization (parameterized by k) for this problem. As components in the proof of our main result, we develop a k^𝒪(η k + η²)n^𝒪(1)-time fixed-parameter algorithm for (η,Clq)-ED Deletion and a polynomial-time factor-min{𝒪(η⋅ opt⋅ log² n),opt^𝒪(1)} approximation algorithm for the same problem.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.1/LIPIcs.IPEC.2020.1.pdf
Elimination Distance
Cluster Graphs
Kernelization
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
2:1
2:16
10.4230/LIPIcs.IPEC.2020.2
article
Component Order Connectivity in Directed Graphs
Bang-Jensen, Jørgen
1
https://orcid.org/0000-0001-5783-7125
Eiben, Eduard
2
Gutin, Gregory
2
Wahlström, Magnus
2
Yeo, Anders
1
University of Southern Denmark, Odense, Denmark
Royal Holloway, University of London, UK
A directed graph D is semicomplete if for every pair x,y of vertices of D, there is at least one arc between x and y. Thus, a tournament is a semicomplete digraph. In the Directed Component Order Connectivity (DCOC) problem, given a digraph D = (V,A) and a pair of natural numbers k and 𝓁, we are to decide whether there is a subset X of V of size k such that the largest strong connectivity component in D-X has at most 𝓁 vertices. Note that DCOC reduces to the Directed Feedback Vertex Set problem for 𝓁 = 1. We study parameterized complexity of DCOC for general and semicomplete digraphs with the following parameters: k, 𝓁, 𝓁+k and n-𝓁. In particular, we prove that DCOC with parameter k on semicomplete digraphs can be solved in time O^*(2^(16k)) but not in time O^*(2^o(k)) unless the Exponential Time Hypothesis (ETH) fails. The upper bound O^*(2^(16k)) implies the upper bound O^*(2^(16(n-𝓁))) for the parameter n-𝓁. We complement the latter by showing that there is no algorithm of time complexity O^*(2^o(n-𝓁)) unless ETH fails. Finally, we improve (in dependency on 𝓁) the upper bound of Göke, Marx and Mnich (2019) for the time complexity of DCOC with parameter 𝓁+k on general digraphs from O^*(2^O(k𝓁 log (k𝓁))) to O^*(2^O(klog (k𝓁))). Note that Drange, Dregi and van 't Hof (2016) proved that even for the undirected version of DCOC on split graphs there is no algorithm of running time O^*(2^o(klog 𝓁)) unless ETH fails and it is a long-standing problem to decide whether Directed Feedback Vertex Set admits an algorithm of time complexity O^*(2^o(klog k)).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.2/LIPIcs.IPEC.2020.2.pdf
Parameterized Algorithms
component order connectivity
directed graphs
semicomplete digraphs
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
3:1
3:17
10.4230/LIPIcs.IPEC.2020.3
article
Close Relatives of Feedback Vertex Set Without Single-Exponential Algorithms Parameterized by Treewidth
Bergougnoux, Benjamin
1
https://orcid.org/0000-0002-6270-3663
Bonnet, Édouard
2
https://orcid.org/0000-0002-1653-5822
Brettell, Nick
3
https://orcid.org/0000-0002-1136-418X
Kwon, O-joung
4
5
https://orcid.org/0000-0003-1820-1962
Department of Informatics, University of Bergen, Norway
Université Lyon, CNRS, ENS de Lyon, Université Claude Bernard Lyon 1, LIP UMR5668, France
School of Mathematics and Statistics, Victoria University of Wellington, New Zealand
Department of Mathematics, Incheon National University, South Korea
Discrete Mathematics Group, Institute for Basic Science (IBS), Daejeon, South Korea
The Cut & Count technique and the rank-based approach have lead to single-exponential FPT algorithms parameterized by treewidth, that is, running in time 2^𝒪(tw)n^𝒪(1), for Feedback Vertex Set and connected versions of the classical graph problems (such as Vertex Cover and Dominating Set). We show that Subset Feedback Vertex Set, Subset Odd Cycle Transversal, Restricted Edge-Subset Feedback Edge Set, Node Multiway Cut, and Multiway Cut are unlikely to have such running times. More precisely, we match algorithms running in time 2^𝒪(tw log tw)n^𝒪(1) with tight lower bounds under the Exponential Time Hypothesis, ruling out 2^o(tw log tw)n^𝒪(1), where n is the number of vertices and tw is the treewidth of the input graph. Our algorithms extend to the weighted case, while our lower bounds also hold for the larger parameter pathwidth and do not require weights. We also show that, in contrast to Odd Cycle Transversal, there is no 2^o(tw log tw)n^𝒪(1)-time algorithm for Even Cycle Transversal.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.3/LIPIcs.IPEC.2020.3.pdf
Subset Feedback Vertex Set
Multiway Cut
Parameterized Algorithms
Treewidth
Graph Modification
Vertex Deletion Problems
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
4:1
4:15
10.4230/LIPIcs.IPEC.2020.4
article
Parameterized Complexity of Scheduling Chains of Jobs with Delays
Bodlaender, Hans L.
1
https://orcid.org/0000-0002-9297-3330
van der Wegen, Marieke
1
2
https://orcid.org/0000-0003-0899-6925
Department of Information and Computing Sciences, Utrecht University, The Netherlands
Mathematical Institute, Utrecht University, The Netherlands
In this paper, we consider the parameterized complexity of the following scheduling problem. We must schedule a number of jobs on m machines, where each job has unit length, and the graph of precedence constraints consists of a set of chains. Each precedence constraint is labelled with an integer that denotes the exact (or minimum) delay between the jobs. We study different cases; delays can be given in unary and in binary, and the case that we have a single machine is discussed separately. We consider the complexity of this problem parameterized by the number of chains, and by the thickness of the instance, which is the maximum number of chains whose intervals between release date and deadline overlap.
We show that this scheduling problem with exact delays in unary is W[t]-hard for all t, when parameterized by the thickness, even when we have a single machine (m = 1). When parameterized by the number of chains, this problem is W[1]-complete when we have a single or a constant number of machines, and W[2]-complete when the number of machines is a variable. The problem with minimum delays, given in unary, parameterized by the number of chains (and as a simple corollary, also when parameterized by the thickness) is W[1]-hard for a single or a constant number of machines, and W[2]-hard when the number of machines is variable.
With a dynamic programming algorithm, one can show membership in XP for exact and minimum delays in unary, for any number of machines, when parameterized by thickness or number of chains. For a single machine, with exact delays in binary, parameterized by the number of chains, membership in XP can be shown with branching and solving a system of difference constraints. For all other cases for delays in binary, membership in XP is open.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.4/LIPIcs.IPEC.2020.4.pdf
Scheduling
parameterized complexity
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
5:1
5:16
10.4230/LIPIcs.IPEC.2020.5
article
Vertex Deletion into Bipartite Permutation Graphs
Bożyk, Łukasz
1
https://orcid.org/0000-0002-9458-577X
Derbisz, Jan
2
Krawczyk, Tomasz
2
https://orcid.org/0000-0002-8777-269X
Novotná, Jana
1
3
https://orcid.org/0000-0002-7955-4692
Okrasa, Karolina
4
1
https://orcid.org/0000-0003-1414-3507
Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Poland
Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland
Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Faculty of Mathematics and Information Science, Warsaw University of Technology, Poland
A permutation graph can be defined as an intersection graph of segments whose endpoints lie on two parallel lines 𝓁₁ and 𝓁₂, one on each. A bipartite permutation graph is a permutation graph which is bipartite. In this paper we study the parameterized complexity of the bipartite permutation vertex deletion problem, which asks, for a given n-vertex graph, whether we can remove at most k vertices to obtain a bipartite permutation graph. This problem is NP-complete by the classical result of Lewis and Yannakakis [John M. Lewis and Mihalis Yannakakis, 1980].
We analyze the structure of the so-called almost bipartite permutation graphs which may contain holes (large induced cycles) in contrast to bipartite permutation graphs. We exploit the structural properties of the shortest hole in a such graph. We use it to obtain an algorithm for the bipartite permutation vertex deletion problem with running time f(k)n^O(1), and also give a polynomial-time 9-approximation algorithm.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.5/LIPIcs.IPEC.2020.5.pdf
permutation graphs
comparability graphs
partially ordered set
graph modification problems
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
6:1
6:18
10.4230/LIPIcs.IPEC.2020.6
article
Bounding the Mim-Width of Hereditary Graph Classes
Brettell, Nick
1
https://orcid.org/0000-0002-1136-418X
Horsfield, Jake
2
https://orcid.org/0000-0002-4388-5123
Munaro, Andrea
3
https://orcid.org/0000-0003-1509-8832
Paesani, Giacomo
4
https://orcid.org/0000-0002-2383-1339
Paulusma, Daniël
4
https://orcid.org/0000-0001-5945-9287
School of Mathematics and Statistics, Victoria University of Wellington, New Zealand
School of Computing, University of Leeds, UK
School of Mathematics and Physics, Queen’s University Belfast, UK
Department of Computer Science, Durham University, UK
A large number of NP-hard graph problems are solvable in XP time when parameterized by some width parameter. Hence, when solving problems on special graph classes, it is helpful to know if the graph class under consideration has bounded width. In this paper we consider mim-width, a particularly general width parameter that has a number of algorithmic applications whenever a decomposition is "quickly computable" for the graph class under consideration.
We start by extending the toolkit for proving (un)boundedness of mim-width of graph classes. By combining our new techniques with known ones we then initiate a systematic study into bounding mim-width from the perspective of hereditary graph classes, and make a comparison with clique-width, a more restrictive width parameter that has been well studied.
We prove that for a given graph H, the class of H-free graphs has bounded mim-width if and only if it has bounded clique-width. We show that the same is not true for (H₁,H₂)-free graphs. We identify several general classes of (H₁,H₂)-free graphs having unbounded clique-width, but bounded mim-width, illustrating the power of mim-width. Moreover, we show that a branch decomposition of constant mim-width can be found in polynomial time, for these classes. Hence, as mentioned, these results have algorithmic implications: when the input is restricted to such a class of (H₁,H₂)-free graphs, many problems become polynomial-time solvable, including classical problems such as k-Colouring and Independent Set, domination-type problems known as LC-VSVP problems, and distance versions of LC-VSVP problems, to name just a few. We also prove a number of new results showing that, for certain H₁ and H₂, the class of (H₁,H₂)-free graphs has unbounded mim-width.
Boundedness of clique-width implies boundedness of mim-width. By combining our results, which give both new bounded and unbounded cases for mim-width, with the known bounded cases for clique-width, we present summary theorems of the current state of the art for the boundedness of mim-width for (H₁,H₂)-free graphs. In particular, we classify the mim-width of (H₁,H₂)-free graphs for all pairs (H₁,H₂) with |V(H₁)| + |V(H₂)| ≤ 8. When H₁ and H₂ are connected graphs, we classify all pairs (H₁,H₂) except for one remaining infinite family and a few isolated cases.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.6/LIPIcs.IPEC.2020.6.pdf
Width parameter
mim-width
clique-width
hereditary graph class
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
7:1
7:16
10.4230/LIPIcs.IPEC.2020.7
article
Fixed-Parameter Algorithms for Longest Heapable Subsequence and Maximum Binary Tree
Chandrasekaran, Karthekeyan
1
Grigorescu, Elena
2
Istrate, Gabriel
3
4
Kulkarni, Shubhang
1
Lin, Young-San
2
Zhu, Minshen
2
University of Illinois, Urbana-Champaign, IL, USA
Purdue University, West Lafayette, IN, USA
West University of Timişoara, Romania
e-Austria Research Institute, Timişoara, Romania
A heapable sequence is a sequence of numbers that can be arranged in a min-heap data structure. Finding a longest heapable subsequence of a given sequence was proposed by Byers, Heeringa, Mitzenmacher, and Zervas (ANALCO 2011) as a generalization of the well-studied longest increasing subsequence problem and its complexity still remains open. An equivalent formulation of the longest heapable subsequence problem is that of finding a maximum-sized binary tree in a given permutation directed acyclic graph (permutation DAG). In this work, we study parameterized algorithms for both longest heapable subsequence and maximum-sized binary tree. We introduce alphabet size as a new parameter in the study of computational problems in permutation DAGs and show that this parameter with respect to a fixed topological ordering admits a complete characterization and a polynomial time algorithm. We believe that this parameter is likely to be useful in the context of optimization problems defined over permutation DAGs.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.7/LIPIcs.IPEC.2020.7.pdf
maximum binary tree
heapability
permutation directed acyclic graphs
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
8:1
8:15
10.4230/LIPIcs.IPEC.2020.8
article
Recognizing Proper Tree-Graphs
Chaplick, Steven
1
https://orcid.org/0000-0003-3501-4608
Golovach, Petr A.
2
https://orcid.org/0000-0002-2619-2990
Hartmann, Tim A.
3
https://orcid.org/0000-0002-1028-6351
Knop, Dušan
4
https://orcid.org/0000-0003-2588-5709
Maastricht University, The Netherlands
Department of Informatics, University of Bergen, Norway
RWTH Aachen, Germany
Department of Theoretical Computer Science, Faculty of Information Technology, Czech Technical University in Prague, Czech Republic
We investigate the parameterized complexity of the recognition problem for the proper H-graphs. The H-graphs are the intersection graphs of connected subgraphs of a subdivision of a multigraph H, and the properness means that the containment relationship between the representations of the vertices is forbidden. The class of H-graphs was introduced as a natural (parameterized) generalization of interval and circular-arc graphs by Biró, Hujter, and Tuza in 1992, and the proper H-graphs were introduced by Chaplick et al. in WADS 2019 as a generalization of proper interval and circular-arc graphs. For these graph classes, H may be seen as a structural parameter reflecting the distance of a graph to a (proper) interval graph, and as such gained attention as a structural parameter in the design of efficient algorithms. We show the following results.
- For a tree T with t nodes, it can be decided in 2^{𝒪(t² log t)} ⋅ n³ time, whether an n-vertex graph G is a proper T-graph. For yes-instances, our algorithm outputs a proper T-representation. This proves that the recognition problem for proper H-graphs, where H required to be a tree, is fixed-parameter tractable when parameterized by the size of T. Previously only NP-completeness was known.
- Contrasting to the first result, we prove that if H is not constrained to be a tree, then the recognition problem becomes much harder. Namely, we show that there is a multigraph H with 4 vertices and 5 edges such that it is NP-complete to decide whether G is a proper H-graph.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.8/LIPIcs.IPEC.2020.8.pdf
intersection graphs
H-graphs
recognition
fixed-parameter tractability
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
9:1
9:17
10.4230/LIPIcs.IPEC.2020.9
article
New Algorithms for Mixed Dominating Set
Dublois, Louis
1
Lampis, Michael
1
Paschos, Vangelis Th.
1
Université Paris-Dauphine, PSL University, CNRS, LAMSADE, Paris, France
A mixed dominating set is a set of vertices and edges that dominates all vertices and edges of a graph. We study the complexity of exact and parameterized algorithms for MDS, resolving some open questions. In particular, we settle the problem’s complexity parameterized by treewidth and pathwidth by giving an algorithm running in time O^*(5^{tw}) (improving the current best O^*(6^{tw})), and a lower bound showing that our algorithm cannot be improved under the SETH, even if parameterized by pathwidth (improving a lower bound of O^*((2-ε)^{pw})). Furthermore, by using a simple but so far overlooked observation on the structure of minimal solutions, we obtain branching algorithms which improve the best known FPT algorithm for this problem, from O^*(4.172^k) to O^*(3.510^k), and the best known exact algorithm, from O^*(2ⁿ) and exponential space, to O^*(1.912ⁿ) and polynomial space.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.9/LIPIcs.IPEC.2020.9.pdf
FPT Algorithms
Exact Algorithms
Mixed Domination
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
10:1
10:15
10.4230/LIPIcs.IPEC.2020.10
article
A Polynomial Kernel for Paw-Free Editing
Eiben, Eduard
1
https://orcid.org/0000-0003-2628-3435
Lochet, William
2
Saurabh, Saket
3
2
Department of Computer Science, Royal Holloway, University of London, Egham, UK
Department of Informatics, University of Bergen, Norway
Institute of Mathematical Sciences, Chennai, India
For a fixed graph H, the H-free Edge Editing problem asks whether we can modify a given graph G by adding or deleting at most k edges such that the resulting graph does not contain H as an induced subgraph. The problem is known to be NP-complete for all fixed H with at least 3 vertices and it admits a 2^O(k)n^O(1) algorithm. Cai and Cai [Algorithmica (2015) 71:731–757] showed that, assuming coNP ⊈ NP/poly, H-free Edge Editing does not admit a polynomial kernel whenever H or its complement is a path or a cycle with at least 4 edges or a 3-connected graph with at least one edge missing. Based on their result, very recently Marx and Sandeep [ESA 2020] conjectured that if H is a graph with at least 5 vertices, then H-free Edge Editing has a polynomial kernel if and only if H is a complete or empty graph, unless coNP ⊆ NP/poly. Furthermore they gave a list of 9 graphs, each with five vertices, such that if H-free Edge Editing for these graphs does not admit a polynomial kernel, then the conjecture is true. Therefore, resolving the kernelization of H-free Edge Editing for graphs H with 4 and 5 vertices plays a crucial role in obtaining a complete dichotomy for this problem. In this paper, we positively answer the question of compressibility for one of the last two unresolved graphs H on 4 vertices. Namely, we give the first polynomial kernel for Paw-free Edge Editing with O(k⁶) vertices.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.10/LIPIcs.IPEC.2020.10.pdf
Kernelization
Paw-free graph
H-free editing
graph modification problem
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
11:1
11:15
10.4230/LIPIcs.IPEC.2020.11
article
A General Kernelization Technique for Domination and Independence Problems in Sparse Classes
Einarson, Carl
1
Reidl, Felix
2
https://orcid.org/0000-0002-2354-3003
Royal Holloway, University of London, UK
Birkbeck, University of London, UK
We unify and extend previous kernelization techniques in sparse classes [Jochen Alber et al., 2004; Pilipczuk and Siebertz, 2018] by defining water lilies and show how they can be used in bounded expansion classes to construct linear bikernels for (r,c)-Dominating Set, (r,c)-Scattered Set, Total r-Domination, r-Roman Domination, and a problem we call (r,[λ,μ])-Domination (implying a bikernel for r-Perfect Code). At the cost of slightly changing the output graph class our bikernels can be turned into kernels. We also demonstrate how these constructions can be combined to create "multikernels", meaning graphs that represent kernels for multiple problems at once.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.11/LIPIcs.IPEC.2020.11.pdf
Dominating Set
Independence
Kernelization
Bounded Expansion
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
12:1
12:11
10.4230/LIPIcs.IPEC.2020.12
article
Parameterized Complexity of Directed Spanner Problems
Fomin, Fedor V.
1
https://orcid.org/0000-0003-1955-4612
Golovach, Petr A.
1
https://orcid.org/0000-0002-2619-2990
Lochet, William
1
Misra, Pranabendu
2
Saurabh, Saket
3
1
Sharma, Roohani
2
Department of Informatics, University of Bergen, Norway
Max Planck Institute for Informatics, Saarbrücken, Germany
Institute of Mathematical Sciences, HBNI, Chennai, India
We initiate the parameterized complexity study of minimum t-spanner problems on directed graphs. For a positive integer t, a multiplicative t-spanner of a (directed) graph G is a spanning subgraph H such that the distance between any two vertices in H is at most t times the distance between these vertices in G, that is, H keeps the distances in G up to the distortion (or stretch) factor t. An additive t-spanner is defined as a spanning subgraph that keeps the distances up to the additive distortion parameter t, that is, the distances in H and G differ by at most t. The task of Directed Multiplicative Spanner is, given a directed graph G with m arcs and positive integers t and k, decide whether G has a multiplicative t-spanner with at most m-k arcs. Similarly, Directed Additive Spanner asks whether G has an additive t-spanner with at most m-k arcs. We show that
- Directed Multiplicative Spanner admits a polynomial kernel of size 𝒪(k⁴t⁵) and can be solved in randomized (4t)^k⋅ n^𝒪(1) time,
- Directed Additive Spanner is W[1]-hard when parameterized by k even if t = 1 and the input graphs are restricted to be directed acyclic graphs. The latter claim contrasts with the recent result of Kobayashi from STACS 2020 that the problem for undirected graphs is FPT when parameterized by t and k.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.12/LIPIcs.IPEC.2020.12.pdf
Graph spanners
directed graphs
parameterized complexity
kernelization
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
13:1
13:13
10.4230/LIPIcs.IPEC.2020.13
article
A Polynomial Kernel for Funnel Arc Deletion Set
Garlet Milani, Marcelo
1
https://orcid.org/0000-0001-8398-4751
Technische Universität Berlin, Chair of Logic and Semantics, Germany
In Directed Feedback Arc Set (DFAS) we search for a set of at most k arcs which intersect every cycle in the input digraph. It is a well-known open problem in parameterized complexity to decide if DFAS admits a kernel of polynomial size. We consider 𝒞-Arc Deletion Set (𝒞-ADS), a variant of DFAS where we want to remove at most k arcs from the input digraph in order to turn it into a digraph of a class 𝒞. In this work, we choose 𝒞 to be the class of funnels. Funnel-ADS is NP-hard even if the input is a DAG, but is fixed-parameter tractable with respect to k. So far no polynomial kernel for this problem was known. Our main result is a kernel for Funnel-ADS with 𝒪(k⁶) many vertices and 𝒪(k⁷) many arcs, computable in 𝒪(nm) time, where n is the number of vertices and m the number of arcs of the input digraph.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.13/LIPIcs.IPEC.2020.13.pdf
graph editing
directed feedback arc set
parameterized algorithm
kernels
funnels
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
14:1
14:19
10.4230/LIPIcs.IPEC.2020.14
article
FPT Approximation for Constrained Metric k-Median/Means
Goyal, Dishant
1
Jaiswal, Ragesh
1
Kumar, Amit
1
Indian Institute of Technology Delhi, India
The Metric k-median problem over a metric space (𝒳, d) is defined as follows: given a set L ⊆ 𝒳 of facility locations and a set C ⊆ 𝒳 of clients, open a set F ⊆ L of k facilities such that the total service cost, defined as Φ(F, C) := ∑_{x ∈ C} min_{f ∈ F} d(x, f), is minimised. The metric k-means problem is defined similarly using squared distances (i.e., d²(., .) instead of d(., .)). In many applications there are additional constraints that any solution needs to satisfy. For example, to balance the load among the facilities in resource allocation problems, a capacity u is imposed on every facility. That is, no more than u clients can be assigned to any facility. This problem is known as the capacitated k-means/k-median problem. Likewise, various other applications have different constraints, which give rise to different constrained versions of the problem such as r-gather, fault-tolerant, outlier k-means/k-median problem. Surprisingly, for many of these constrained problems, no constant-approximation algorithm is known. Moreover, the unconstrained problem itself is known [Marek Adamczyk et al., 2019] to be W[2]-hard when parameterized by k. We give FPT algorithms with constant approximation guarantee for a range of constrained k-median/means problems. For some of the constrained problems, ours is the first constant factor approximation algorithm whereas for others, we improve or match the approximation guarantee of previous works. We work within the unified framework of Ding and Xu [Ding and Xu, 2015] that allows us to simultaneously obtain algorithms for a range of constrained problems. In particular, we obtain a (3+ε)-approximation and (9+ε)-approximation for the constrained versions of the k-median and k-means problem respectively in FPT time. In many practical settings of the k-median/means problem, one is allowed to open a facility at any client location, i.e., C ⊆ L. For this special case, our algorithm gives a (2+ε)-approximation and (4+ε)-approximation for the constrained versions of k-median and k-means problem respectively in FPT time. Since our algorithm is based on simple sampling technique, it can also be converted to a constant-pass log-space streaming algorithm. In particular, here are some of the main highlights of this work:
1) For the uniform capacitated k-median/means problems our results matches previously known results of Addad et al. [Vincent Cohen-Addad and Jason Li, 2019].
2) For the r-gather k-median/means problem (clustering with lower bound on the size of clusters), our FPT approximation bounds are better than what was previously known.
3) Our approximation bounds for the fault-tolerant, outlier, and uncertain versions is better than all previously known results, albeit in FPT time.
4) For certain constrained settings such as chromatic, l-diversity, and semi-supervised k-median/means, we obtain the first constant factor approximation algorithms to the best of our knowledge.
5) Since our algorithms are based on a simple sampling based approach, we also obtain constant-pass log-space streaming algorithms for most of the above-mentioned problems.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.14/LIPIcs.IPEC.2020.14.pdf
k-means
k-median
approximation algorithms
parameterised algorithms
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
15:1
15:15
10.4230/LIPIcs.IPEC.2020.15
article
Fixed-Parameter Algorithms for Graph Constraint Logic
Hatanaka, Tatsuhiko
1
Hommelsheim, Felix
2
Ito, Takehiro
1
https://orcid.org/0000-0002-9912-6898
Kobayashi, Yusuke
3
https://orcid.org/0000-0001-9478-7307
Mühlenthaler, Moritz
4
Suzuki, Akira
1
https://orcid.org/0000-0002-5212-0202
Graduate School of Information Sciences, Tohoku University, Sendai, Japan
Fakultät für Mathematik, TU Dortmund University, Germany
Research Institute for Mathematical Sciences, Kyoto University, Japan
Laboratoire G-SCOP, Grenoble INP, Université Grenoble Alpes, France
Non-deterministic constraint logic (NCL) is a simple model of computation based on orientations of a constraint graph with edge weights and vertex demands. NCL captures PSPACE and has been a useful tool for proving algorithmic hardness of many puzzles, games, and reconfiguration problems. In particular, its usefulness stems from the fact that it remains PSPACE-complete even under severe restrictions of the weights (e.g., only edge-weights one and two are needed) and the structure of the constraint graph (e.g., planar AND/OR graphs of bounded bandwidth). While such restrictions on the structure of constraint graphs do not seem to limit the expressiveness of NCL, the building blocks of the constraint graphs cannot be limited without losing expressiveness: We consider as parameters the number of weight-one edges and the number of weight-two edges of a constraint graph, as well as the number of AND or OR vertices of an AND/OR constraint graph. We show that NCL is fixed-parameter tractable (FPT) for any of these parameters. In particular, for NCL parameterized by the number of weight-one edges or the number of AND vertices, we obtain a linear kernel. It follows that, in a sense, NCL as introduced by Hearn and Demaine is defined in the most economical way for the purpose of capturing PSPACE.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.15/LIPIcs.IPEC.2020.15.pdf
Combinatorial Reconfiguration
Nondeterministic Constraint Logic
Fixed Parameter Tractability
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
16:1
16:18
10.4230/LIPIcs.IPEC.2020.16
article
Approximation Algorithms for Steiner Tree Based on Star Contractions: A Unified View
Hušek, Radek
1
Knop, Dušan
2
https://orcid.org/0000-0003-2588-5709
Masařk, Tomáš
3
4
https://orcid.org/0000-0001-8524-4036
Computer Science Institute of Charles University, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Department of Theoretical Computer Science, Faculty of Information Technology, Czech Technical University in Prague, Czech Republic
Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Poland
Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Czech Republic
In the Steiner Tree problem, we are given an edge-weighted undirected graph G = (V,E) and a set of terminals R ⊆ V. The task is to find a connected subgraph of G containing R and minimizing the sum of weights of its edges. Steiner Tree is well known to be NP-complete and is undoubtedly one of the most studied problems in (applied) computer science.
We observe that many approximation algorithms for Steiner Tree follow a similar scheme (meta-algorithm) and perform (exhaustively) a similar routine which we call star contraction. Here, by a star contraction, we mean finding a star-like subgraph in (the metric closure of) the input graph minimizing the ratio of its weight to the number of contained terminals minus one; and contract. It is not hard to see that the well-known MST-approximation seeks the best star to contract among those containing two terminals only. Zelikovsky’s approximation algorithm follows a similar workflow, finding the best star among those containing three terminals.
We perform an empirical study of star contractions with the relaxed condition on the number of terminals in each star contraction motivated by a recent result of Dvořák et al. [Parameterized Approximation Schemes for Steiner Trees with Small Number of Steiner Vertices, STACS 2018]. Furthermore, we propose two improvements of Zelikovsky’s 11/6-approximation algorithm and we empirically confirm that the quality of the solution returned by any of these is better than the one returned by the former algorithm. However, such an improvement is exchanged for a slower running time (up to a multiplicative factor of the number of terminals).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.16/LIPIcs.IPEC.2020.16.pdf
Steiner tree
approximation
star contractions
minimum spanning tree
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
17:1
17:16
10.4230/LIPIcs.IPEC.2020.17
article
Fixed-Parameter Tractability of the Weighted Edge Clique Partition Problem
Feldmann, Andreas Emil
1
https://orcid.org/0000-0001-6229-5332
Issac, Davis
2
https://orcid.org/0000-0001-5559-7471
Rai, Ashutosh
1
https://orcid.org/0000-0003-2429-750X
Department of Applied Mathematics, Charles University, Prague, Czech Republic
Hasso Plattner Institute, Potsdam, Germany
We develop an FPT algorithm and a compression for the Weighted Edge Clique Partition (WECP) problem, where a graph with n vertices and integer edge weights is given together with an integer k, and the aim is to find k cliques, such that every edge appears in exactly as many cliques as its weight. The problem has been previously only studied in the unweighted version called Edge Clique Partition (ECP), where the edges need to be partitioned into k cliques. It was shown that ECP admits a kernel with k² vertices [Mujuni and Rosamond, 2008], but this kernel does not extend to WECP. The previously fastest algorithm known for ECP has a runtime of 2^𝒪(k²)n^O(1) [Issac, 2019]. For WECP we develop a compression (to a slightly more general problem) with 4^k vertices, and an algorithm with runtime 2^𝒪(k^(3/2)w^(1/2)log(k/w))n^O(1), where w is the maximum edge weight. The latter in particular improves the runtime for ECP to 2^𝒪(k^(3/2)log k)n^O(1).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.17/LIPIcs.IPEC.2020.17.pdf
Edge Clique Partition
fixed-parameter tractability
kernelization
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
18:1
18:17
10.4230/LIPIcs.IPEC.2020.18
article
Parameterized Complexity of Deletion to Scattered Graph Classes
Jacob, Ashwin
1
Majumdar, Diptapriyo
2
Raman, Venkatesh
1
The Institute of Mathematical Sciences, HBNI, Chennai, India
Royal Holloway, University of London, UK
Graph-modification problems, where we add/delete a small number of vertices/edges to make the given graph to belong to a simpler graph class, is a well-studied optimization problem in all algorithmic paradigms including classical, approximation and parameterized complexity. Specifically, graph-deletion problems, where one needs to delete at most k vertices to place it in a given non-trivial hereditary (closed under induced subgraphs) graph class, captures several well-studied problems including Vertex Cover, Feedback Vertex Set, Odd Cycle Transveral, Cluster Vertex Deletion, and Perfect Deletion. Investigation into these problems in parameterized complexity has given rise to powerful tools and techniques. While a precise characterization of the graph classes for which the problem is fixed-parameter tractable (FPT) is elusive, it has long been known that if the graph class is characterized by a finite set of forbidden graphs, then the problem is FPT.
In this paper, we initiate a study of a natural variation of the problem of deletion to scattered graph classes where we need to delete at most k vertices so that in the resulting graph, each connected component belongs to one of a constant number of graph classes. A simple hitting set based approach is no longer feasible even if each of the graph classes is characterized by finite forbidden sets. As our main result, we show that this problem (in the case where each graph class has a finite forbidden set) is fixed-parameter tractable by a O^*(2^(k^O(1))) algorithm, using a combination of the well-known techniques in parameterized complexity - iterative compression and important separators. Our approach follows closely that of a related problem in the context of satisfiability [Ganian, Ramanujan, Szeider, TAlg 2017], where one wants to find a small backdoor set so that the resulting CSP (constraint satisfaction problem) instance belongs to one of several easy instances of satisfiability. While we follow the main idea from this work, there are some challenges for our problem which we needed to overcome.
When there are two graph classes with finite forbidden sets to get to, and if one of the forbidden sets has a path, then we show that the problem has a (better) singly exponential algorithm and a polynomial sized kernel. We also design an efficient FPT algorithm for a special case when one of the graph classes has an infinite forbidden set. Specifically, we give a O^*(4^k) algorithm to determine whether k vertices can be deleted from a given graph so that in the resulting graph, each connected component is a tree (the sparsest connected graph) or a clique (the densest connected graph).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.18/LIPIcs.IPEC.2020.18.pdf
Parameterized Complexity
Scattered Graph Classes
Important Separators
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
19:1
19:18
10.4230/LIPIcs.IPEC.2020.19
article
Structural Parameterizations with Modulator Oblivion
Jacob, Ashwin
1
Panolan, Fahad
2
Raman, Venkatesh
1
Sahlot, Vibha
1
The Institute of Mathematical Sciences, HBNI, Chennai, India
Department of Computer Science and Engineering, IIT Hyderabad, India
It is known that problems like Vertex Cover, Feedback Vertex Set and Odd Cycle Transversal are polynomial time solvable in the class of chordal graphs. We consider these problems in a graph that has at most k vertices whose deletion results in a chordal graph, when parameterized by k. While this investigation fits naturally into the recent trend of what are called "structural parameterizations", here we assume that the deletion set is not given.
One method to solve them is to compute a k-sized or an approximate (f(k) sized, for a function f) chordal vertex deletion set and then use the structural properties of the graph to design an algorithm. This method leads to at least k^O(k)n^O(1) running time when we use the known parameterized or approximation algorithms for finding a k-sized chordal deletion set on an n vertex graph.
In this work, we design 2^O(k)n^O(1) time algorithms for these problems. Our algorithms do not compute a chordal vertex deletion set (or even an approximate solution). Instead, we construct a tree decomposition of the given graph in time 2^O(k)n^O(1) where each bag is a union of four cliques and O(k) vertices. We then apply standard dynamic programming algorithms over this special tree decomposition. This special tree decomposition can be of independent interest.
Our algorithms are, what are sometimes called permissive in the sense that given an integer k, they detect whether the graph has no chordal vertex deletion set of size at most k or output the special tree decomposition and solve the problem.
We also show lower bounds for the problems we deal with under the Strong Exponential Time Hypothesis (SETH).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.19/LIPIcs.IPEC.2020.19.pdf
Parameterized Complexity
Chordal Graph
Tree Decomposition
Strong Exponential Time Hypothesis
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
20:1
20:14
10.4230/LIPIcs.IPEC.2020.20
article
Parameterized Complexity of Geodetic Set
Kellerhals, Leon
1
https://orcid.org/0000-0001-6565-3983
Koana, Tomohiro
1
https://orcid.org/0000-0002-8684-0611
Technische Universität Berlin, Faculty IV, Algorithmics and Computational Complexity, Germany
A vertex set S of a graph G is geodetic if every vertex of G lies on a shortest path between two vertices in S. Given a graph G and k ∈ ℕ, the NP-hard Geodetic Set problem asks whether there is a geodetic set of size at most k. Complementing various works on Geodetic Set restricted to special graph classes, we initiate a parameterized complexity study of Geodetic Set and show, on the negative side, that Geodetic Set is W[1]-hard when parameterized by feedback vertex number, path-width, and solution size, combined. On the positive side, we develop fixed-parameter algorithms with respect to the feedback edge number, the tree-depth, and the modular-width of the input graph.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.20/LIPIcs.IPEC.2020.20.pdf
NP-hard graph problems
Shortest paths
Tree-likeness
Parameter hierarchy
Data reduction
Integer linear programming
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
21:1
21:10
10.4230/LIPIcs.IPEC.2020.21
article
Parameterized Complexity of Graph Burning
Kobayashi, Yasuaki
1
https://orcid.org/0000-0003-3244-6915
Otachi, Yota
2
https://orcid.org/0000-0002-0087-853X
Kyoto University, Japan
Nagoya University, Japan
Graph Burning asks, given a graph G = (V,E) and an integer k, whether there exists (b₀,… ,b_{k-1}) ∈ V^{k} such that every vertex in G has distance at most i from some b_i. This problem is known to be NP-complete even on connected caterpillars of maximum degree 3. We study the parameterized complexity of this problem and answer all questions arose by Kare and Reddy [IWOCA 2019] about parameterized complexity of the problem. We show that the problem is W[2]-complete parameterized by k and that it does not admit a polynomial kernel parameterized by vertex cover number unless NP ⊆ coNP/poly. We also show that the problem is fixed-parameter tractable parameterized by clique-width plus the maximum diameter among all connected components. This implies the fixed-parameter tractability parameterized by modular-width, by treedepth, and by distance to cographs. Although the parameterization by distance to split graphs cannot be handled with the clique-width argument, we show that this is also tractable by a reduction to a generalized problem with a smaller solution size.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.21/LIPIcs.IPEC.2020.21.pdf
Graph burning
parameterized complexity
fixed-parameter tractability
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
22:1
22:18
10.4230/LIPIcs.IPEC.2020.22
article
Finding Optimal Triangulations Parameterized by Edge Clique Cover
Korhonen, Tuukka
1
Department of Computer Science, University of Helsinki, Finland
Many graph problems can be formulated as a task of finding an optimal triangulation of a given graph with respect to some notion of optimality. In this paper we give algorithms to such problems parameterized by the size of a minimum edge clique cover (cc) of the graph. The parameter cc is both natural and well-motivated in many problems on this setting. For example, in the perfect phylogeny problem cc is at most the number of taxa, in fractional hypertreewidth cc is at most the number of hyperedges, and in treewidth of Bayesian networks cc is at most the number of non-root nodes of the Bayesian network.
Our results are based on the framework of potential maximal cliques. We show that the number of minimal separators of graphs is at most 2^cc and the number of potential maximal cliques is at most 3^cc. Furthermore, these objects can be listed in times O^*(2^cc) and O^*(3^cc), respectively, even when no edge clique cover is given as input; the O^*(⋅) notation omits factors polynomial in the input size. Using these enumeration algorithms we obtain O^*(3^cc) time algorithms for problems in the potential maximal clique framework, including for example treewidth, minimum fill-in, and feedback vertex set. We also obtain an O^*(3^m) time algorithm for fractional hypertreewidth, where m is the number of hyperedges. In the case when an edge clique cover of size cc' is given as an input we further improve the time complexity to O^*(2^cc') for treewidth, minimum fill-in, and chordal sandwich. This implies an O^*(2^n) time algorithm for perfect phylogeny, where n is the number of taxa. We also give polynomial space algorithms with time complexities O^*(9^cc') and O^*(9^(cc + O(log^2 cc))) for problems in this framework.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.22/LIPIcs.IPEC.2020.22.pdf
Treewidth
Minimum fill-in
Perfect phylogeny
Fractional hypertreewidth
Potential maximal cliques
Edge clique cover
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
23:1
23:18
10.4230/LIPIcs.IPEC.2020.23
article
The Asymmetric Travelling Salesman Problem In Sparse Digraphs
Kowalik, Łukasz
1
https://orcid.org/0000-0002-7546-2969
Majewski, Konrad
2
https://orcid.org/0000-0002-3922-7953
Institute of Informatics, University of Warsaw, Poland
Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, Poland
Asymmetric Travelling Salesman Problem (ATSP) and its special case Directed Hamiltonicity are among the most fundamental problems in computer science. The dynamic programming algorithm running in time 𝒪^*(2ⁿ) developed almost 60 years ago by Bellman, Held and Karp, is still the state of the art for both of these problems.
In this work we focus on sparse digraphs.
First, we recall known approaches for Undirected Hamiltonicity and TSP in sparse graphs and we analyse their consequences for Directed Hamiltonicity and ATSP in sparse digraphs, either by adapting the algorithm, or by using reductions. In this way, we get a number of running time upper bounds for a few classes of sparse digraphs, including 𝒪^*(2^(n/3)) for digraphs with both out- and indegree bounded by 2, and 𝒪^*(3^(n/2)) for digraphs with outdegree bounded by 3.
Our main results are focused on digraphs of bounded average outdegree d. The baseline for ATSP here is a simple enumeration of cycle covers which can be done in time bounded by 𝒪^*(μ(d)ⁿ) for a function μ(d) ≤ (⌈d⌉!)^(1/⌈d⌉). One can also observe that Directed Hamiltonicity can be solved in randomized time 𝒪^*((2-2^(-d))ⁿ) and polynomial space, by adapting a recent result of Björklund [ISAAC 2018] stated originally for Undirected Hamiltonicity in sparse bipartite graphs. We present two new deterministic algorithms for ATSP: the first running in time 𝒪(2^(0.441(d-1)n)) and polynomial space, and the second in exponential space with running time of 𝒪^*(τ(d)^(n/2)) for a function τ(d) ≤ d.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.23/LIPIcs.IPEC.2020.23.pdf
asymmetric traveling salesman problem
Hamiltonian cycle
sparse graphs
exponential algorithm
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
24:1
24:15
10.4230/LIPIcs.IPEC.2020.24
article
On the Parameterized Complexity of Reconfiguration of Connected Dominating Sets
Lokshtanov, Daniel
1
Mouawad, Amer E.
2
Panolan, Fahad
3
Siebertz, Sebastian
4
University of California Santa Barbara, CA, USA
Department of Computer Science, American University of Beirut, Lebanon
Department of Computer Science and Engineering, IIT Hyderabad, India
University of Bremen, Germany
In a reconfiguration version of a decision problem 𝒬 the input is an instance of 𝒬 and two feasible solutions S and T. The objective is to determine whether there exists a step-by-step transformation between S and T such that all intermediate steps also constitute feasible solutions. In this work, we study the parameterized complexity of the Connected Dominating Set Reconfiguration problem (CDS-R). It was shown in previous work that the Dominating Set Reconfiguration problem (DS-R) parameterized by k, the maximum allowed size of a dominating set in a reconfiguration sequence, is fixed-parameter tractable on all graphs that exclude a biclique K_{d,d} as a subgraph, for some constant d ≥ 1. We show that the additional connectivity constraint makes the problem much harder, namely, that CDS-R is W[1]-hard parameterized by k+𝓁, the maximum allowed size of a dominating set plus the length of the reconfiguration sequence, already on 5-degenerate graphs. On the positive side, we show that CDS-R parameterized by k is fixed-parameter tractable, and in fact admits a polynomial kernel on planar graphs.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.24/LIPIcs.IPEC.2020.24.pdf
reconfiguration
parameterized complexity
connected dominating set
graph structure theory
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
25:1
25:17
10.4230/LIPIcs.IPEC.2020.25
article
On the Fine-Grained Parameterized Complexity of Partial Scheduling to Minimize the Makespan
Nederlof, Jesper
1
Swennenhuis, Céline M. F.
2
Utrecht University, Algorithms and Complexity Group, The Netherlands
Eindhoven University of Technology, Combinatorial Optimization Group, The Netherlands
We study a natural variant of scheduling that we call partial scheduling: In this variant an instance of a scheduling problem along with an integer k is given and one seeks an optimal schedule where not all, but only k jobs, have to be processed.
Specifically, we aim to determine the fine-grained parameterized complexity of partial scheduling problems parameterized by k for all variants of scheduling problems that minimize the makespan and involve unit/arbitrary processing times, identical/unrelated parallel machines, release/due dates, and precedence constraints. That is, we investigate whether algorithms with runtimes of the type f(k)n^𝒪(1) or n^𝒪(f(k)) exist for a function f that is as small as possible.
Our contribution is two-fold: First, we categorize each variant to be either in 𝖯, NP-complete and fixed-parameter tractable by k, or 𝖶[1]-hard parameterized by k. Second, for many interesting cases we further investigate the run time on a finer scale and obtain run times that are (almost) optimal assuming the Exponential Time Hypothesis. As one of our main technical contributions, we give an 𝒪(8^k k(|V|+|E|)) time algorithm to solve instances of partial scheduling problems minimizing the makespan with unit length jobs, precedence constraints and release dates, where G = (V,E) is the graph with precedence constraints.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.25/LIPIcs.IPEC.2020.25.pdf
Fixed-Parameter Tractability
Scheduling
Precedence Constraints
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
26:1
26:16
10.4230/LIPIcs.IPEC.2020.26
article
On the Parameterized Complexity of Maximum Degree Contraction Problem
Saurabh, Saket
1
2
Tale, Prafullkumar
3
The Institute Of Mathematical Sciences, HBNI, Chennai, India
University of Bergen, Norway
CISPA - Helmholtz Center for Information Security, Saarbrücken, Germany
In the Maximum Degree Contraction problem, input is a graph G on n vertices, and integers k, d, and the objective is to check whether G can be transformed into a graph of maximum degree at most d, using at most k edge contractions. A simple brute-force algorithm that checks all possible sets of edges for a solution runs in time n^𝒪(k). As our first result, we prove that this algorithm is asymptotically optimal, upto constants in the exponents, under Exponential Time Hypothesis (ETH).
Belmonte, Golovach, van't Hof, and Paulusma studied the problem in the realm of Parameterized Complexity and proved, among other things, that it admits an FPT algorithm running in time (d + k)^(2k) ⋅ n^𝒪(1) = 2^𝒪(k log (k+d)) ⋅ n^𝒪(1), and remains NP-hard for every constant d ≥ 2 (Acta Informatica (2014)). We present a different FPT algorithm that runs in time 2^𝒪(dk) ⋅ n^𝒪(1). In particular, our algorithm runs in time 2^𝒪(k) ⋅ n^𝒪(1), for every fixed d. In the same article, the authors asked whether the problem admits a polynomial kernel, when parameterized by k + d. We answer this question in the negative and prove that it does not admit a polynomial compression unless NP ⊆ coNP/poly.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.26/LIPIcs.IPEC.2020.26.pdf
Graph Contraction Problems
FPT Algorithm
Lower Bound
ETH
No Polynomial Kernel
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
27:1
27:3
10.4230/LIPIcs.IPEC.2020.27
article
PACE Solver Description: Fluid
Bannach, Max
1
https://orcid.org/0000-0002-6475-5512
Berndt, Sebastian
2
https://orcid.org/0000-0003-4177-8081
Schuster, Martin
3
Wienöbst, Marcel
1
Institute for Theoretical Computer Science, Universität zu Lübeck, Germany
Institute for IT Security, Universität zu Lübeck, Germany
Institute for Epidemiology, Kiel University, Germany
This document describes the heuristic for computing treedepth decompositions of undirected graphs used by our solve fluid. The heuristic runs four different strategies to find a solution and finally outputs the best solution obtained by any of them. Two strategies are score-based and iteratively remove the vertex with the best score. The other two strategies iteratively search for vertex separators and remove them. We also present implementation strategies and data structures that significantly improve the run time complexity and might be interesting on their own.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.27/LIPIcs.IPEC.2020.27.pdf
treedepth
heuristics
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
28:1
28:4
10.4230/LIPIcs.IPEC.2020.28
article
PACE Solver Description: PID^⋆
Bannach, Max
1
https://orcid.org/0000-0002-6475-5512
Berndt, Sebastian
2
https://orcid.org/0000-0003-4177-8081
Schuster, Martin
3
Wienöbst, Marcel
1
Institute for Theoretical Computer Science, Universität zu Lübeck, Germany
Institute for IT Security, Universität zu Lübeck, Germany
Institute for Epidemiology, Kiel University, Germany
This document provides a short overview of our treedepth solver PID^{⋆} in the version that we submitted to the exact track of the PACE challenge 2020. The solver relies on the positive-instance driven dynamic programming (PID) paradigm that was discovered in the light of earlier iterations of the PACE in the context of treewidth. It was recently shown that PID can be used to solve a general class of vertex pursuit-evasion games - which include the game theoretic characterization of treedepth. Our solver PID^{⋆} is build on top of this characterization.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.28/LIPIcs.IPEC.2020.28.pdf
treedepth
positive-instance driven
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
29:1
29:4
10.4230/LIPIcs.IPEC.2020.29
article
PACE Solver Description: tdULL
Brokkelkamp, Ruben
1
https://orcid.org/0000-0003-1223-4616
van Venetië, Raymond
2
https://orcid.org/0000-0002-5118-911X
de Vries, Mees
3
Westerdiep, Jan
2
https://orcid.org/0000-0002-7028-5676
Centrum Wiskunde & Informatica (CWI), The Netherlands
Korteweg-de Vries Institute, University of Amsterdam, The Netherlands
University of Amsterdam, The Netherlands
We describe tdULL, an algorithm for computing treedepth decompositions of minimal depth. An implementation was submitted to the exact track of PACE 2020. tdULL is a branch and bound algorithm branching on inclusion-minimal separators.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.29/LIPIcs.IPEC.2020.29.pdf
PACE 2020
treedepth
treedepth decomposition
vertex ranking
minimal separators
branch and bound
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
30:1
30:4
10.4230/LIPIcs.IPEC.2020.30
article
PACE Solver Description: SMS
Korhonen, Tuukka
1
Department of Computer Science, University of Helsinki, Finland
We describe SMS, our submission to the exact treedepth track of PACE 2020. SMS computes the treedepth of a graph by branching on the Small Minimal Separators of the graph.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.30/LIPIcs.IPEC.2020.30.pdf
Treedepth
PACE 2020
SMS
Minimal separators
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
31:1
31:4
10.4230/LIPIcs.IPEC.2020.31
article
PACE Solver Description: Computing Exact Treedepth via Minimal Separators
Xu, Zijian
1
Mao, Dejun
1
Suppakitpaisarn, Vorapong
1
The University of Tokyo, Japan
This is a description of team xuzijian629’s treedepth solver submitted to PACE 2020. As we use a top-down approach, we enumerate all possible minimal separators at each step. The enumeration is sped up by several novel pruning techniques and is based on our conjecture that we can always have an optimal decomposition without using separators with size larger than treewidth. Although we cannot theoretically guarantee that our algorithm based on the unproved conjecture can always give an optimal solution, it can give optimal solutions for all instances in our experiments. The algorithm solved 68 private instances and placed 5th in the competition.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.31/LIPIcs.IPEC.2020.31.pdf
Treedepth
Minimal Separators
Experimental Algorithm
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
32:1
32:4
10.4230/LIPIcs.IPEC.2020.32
article
PACE Solver Description: Tree Depth with FlowCutter
Strasser, Ben
1
https://orcid.org/0000-0002-3391-6221
Independent Researcher, Germany
We describe the FlowCutter submission to the PACE 2020 heuristic tree-depth challenge. The task of the challenge consists of computing an elimination tree of small height for a given graph. At its core our submission uses a nested dissection approach, with FlowCutter as graph bisection algorithm.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.32/LIPIcs.IPEC.2020.32.pdf
tree depth
graph algorithm
partitioning
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
33:1
33:4
10.4230/LIPIcs.IPEC.2020.33
article
PACE Solver Description: Finding Elimination Trees Using ExTREEm - a Heuristic Solver for the Treedepth Decomposition Problem
Swat, Sylwester
1
https://orcid.org/0000-0001-8763-0045
Institute of Computing Science, Poznan University of Technology, Poland
This article briefly describes the most important algorithms and techniques used in the treedepth decomposition heuristic solver called "ExTREEm", submitted to the 5th Parameterized Algorithms and Computational Experiments Challenge (PACE 2020) co-organized with the 15th International Symposium on Parameterized and Exact Computation (IPEC 2020).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.33/LIPIcs.IPEC.2020.33.pdf
Treedepth decomposition
elimination tree
separator
PACE 2020
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
34:1
34:4
10.4230/LIPIcs.IPEC.2020.34
article
PACE Solver Description: Bute-Plus: A Bottom-Up Exact Solver for Treedepth
Trimble, James
1
https://orcid.org/0000-0001-7282-8745
School of Computing Science, University of Glasgow, Scotland, UK
This note introduces Bute-Plus, an exact solver for the treedepth problem. The core of the solver is a positive-instance driven dynamic program that constructs an elimination tree of minimum depth in a bottom-up fashion. Three features greatly improve the algorithm’s run time. The first of these is a specialised trie data structure. The second is a domination rule. The third is a heuristic presolve step can quickly find a treedepth decomposition of optimal depth for many instances.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.34/LIPIcs.IPEC.2020.34.pdf
Treedepth
Elimination Tree
Graph Algorithms
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
35:1
35:4
10.4230/LIPIcs.IPEC.2020.35
article
PACE Solver Description: Tweed-Plus: A Subtree-Improving Heuristic Solver for Treedepth
Trimble, James
1
https://orcid.org/0000-0001-7282-8745
School of Computing Science, University of Glasgow, Scotland, UK
This paper introduces Tweed-Plus, a heuristic solver for the treedepth problem. The solver uses two well-known algorithms to create an initial elimination tree: nested dissection (making use of the Metis library) and the minimum-degree heuristic. After creating an elimination tree of the entire input graph, the solver continues to apply nested dissection and the minimum-degree heuristic to parts of the graph with the aim of replacing subtrees of the elimination tree with alternatives of lower depth.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.35/LIPIcs.IPEC.2020.35.pdf
Treedepth
Elimination Tree
Heuristics
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
36:1
36:4
10.4230/LIPIcs.IPEC.2020.36
article
PACE Solver Description: Sallow: A Heuristic Algorithm for Treedepth Decompositions
Wrochna, Marcin
1
https://orcid.org/0000-0001-9346-2172
University of Oxford, UK
We describe a heuristic algorithm for computing treedepth decompositions, submitted for the https://pacechallenge.org/2020 challenge. It relies on a variety of greedy algorithms computing elimination orderings, as well as a Divide & Conquer approach on balanced cuts obtained using a from-scratch reimplementation of the 2016 FlowCutter algorithm by Hamann & Strasser [Michael Hamann and Ben Strasser, 2018].
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.36/LIPIcs.IPEC.2020.36.pdf
treedepth
decomposition
heuristic
weak colouring numbers
eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
180
37:1
37:18
10.4230/LIPIcs.IPEC.2020.37
article
The PACE 2020 Parameterized Algorithms and Computational Experiments Challenge: Treedepth
Kowalik, Łukasz
1
https://orcid.org/0000-0002-7546-2969
Mucha, Marcin
1
Nadara, Wojciech
1
Pilipczuk, Marcin
1
Sorge, Manuel
1
Wygocki, Piotr
1
Institute of Informatics, University of Warsaw, Poland
This year’s Parameterized Algorithms and Computational Experiments challenge (PACE 2020) was devoted to the problem of computing the treedepth of a given graph. Altogether 51 participants from 20 teams, 12 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 and the differences in their performance on our benchmark dataset.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol180-ipec2020/LIPIcs.IPEC.2020.37/LIPIcs.IPEC.2020.37.pdf
computing treedepth
contest
implementation challenge
FPT