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Christian Komusiewicz

Publications and source records attributed to Christian Komusiewicz.

At least 55 records · Page 3Linked to original sources
arXiv2019

h-Index Manipulation by Undoing Merges

The h-index is an important bibliographic measure used to assess the performance of researchers. Dutiful researchers merge different versions of their articles in their Google Scholar profile even though this can decrease their h-index. In this article, we study the manipulation of the h-index by undoing such merges. In contrast to manipulation by merging articles (van Bevern et al. [Artif. Intel. 240:19-35, 2016]) such manipulation is harder to detect. We present numerous results on computational complexity (from linear-time algorithms to parameterized computational hardness results) and empirically indicate that at least small improvements of the h-index by splitting merged articles are unfortunately easily achievable.

cs.DL↗
arXiv2019

Assessing the Computational Complexity of Multi-Layer Subgraph Detection

Multi-layer graphs consist of several graphs (layers) over the same vertex set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the border of computational (in)tractability for the class of subgraph detection problems on multi-layer graphs, including fundamental problems such as maximum matching, finding certain clique relaxations (motivated by community detection), or path problems. Mostly encountering hardness results, sometimes even for two or three layers, we can also spot some islands of tractability.

cs.CC↗
arXiv2019

Solving Partition Problems Almost Always Requires Pushing Many Vertices Around

A fundamental graph problem is to recognize whether the vertex set of a graph $G$ can be bipartitioned into sets $A$ and $B$ such that $G[A]$ and $G[B]$ satisfy properties $Π_A$ and $Π_B$, respectively. This so-called $(Π_A,Π_B)$-Recognition problem generalizes amongst others the recognition of $3$-colorable, bipartite, split, and monopolar graphs. In this paper, we study whether certain fixed-parameter tractable $(Π_A,Π_B)$-Recognition problems admit polynomial kernels. In our study, we focus on the first level above triviality, where $Π_A$ is the set of $P_3$-free graphs (disjoint unions of cliques, or cluster graphs), the parameter is the number of clusters in the cluster graph $G[A]$, and $Π_B$ is characterized by a set $\mathcal{H}$ of connected forbidden induced subgraphs. We prove that, under the assumption that NP is not a subset of coNP/poly, \textsc{$(Π_A,Π_B)$-Recognition} admits a polynomial kernel if and only if $\mathcal{H}$ contains a graph with at most $2$ vertices. In both the kernelization and the lower bound results, we exploit the properties of a pushing process, which is an algorithmic technique used recently by Heggerness et al. and by Kanj et al. to obtain fixed-parameter algorithms for many cases of $(Π_A,Π_B)$-Recognition, as well as several other problems.

cs.CC↗
arXiv2019

Graph Motif Problems Parameterized by Dual

Let $G=(V,E)$ be a vertex-colored graph, where $C$ is the set of colors used to color $V$. The Graph Motif (or GM) problem takes as input $G$, a multiset $M$ of colors built from $C$, and asks whether there is a subset $S\subseteq V$ such that (i) $G[S]$ is connected and (ii) the multiset of colors obtained from $S$ equals $M$. The Colorful Graph Motif (or CGM) problem is the special case of GM in which $M$ is a set, and the List-Colored Graph Motif (or LGM) problem is the extension of GM in which each vertex $v$ of $V$ may choose its color from a list $\mathcal{L}(v)\subseteq C$ of colors. We study the three problems GM, CGM, and LGM, parameterized by the dual parameter $\ell:=|V|-|M|$. For general graphs, we show that, assuming the strong exponential time hypothesis, CGM has no $(2-ε)^\ell\cdot |V|^{\mathcal{O}(1)}$-time algorithm, which implies that a previous algorithm, running in $\mathcal{O}(2^\ell\cdot |E|)$ time is optimal [Betzler et al., IEEE/ACM TCBB 2011]. We also prove that LGM is W[1]-hard with respect to $\ell$ even if we restrict ourselves to lists of at most two colors. If we constrain the input graph to be a tree, then we show that GM can be solved in $\mathcal{O}(3^\ell\cdot |V|)$ time but admits no polynomial-size problem kernel, while CGM can be solved in $\mathcal{O}(\sqrt{2}^{\ell} + |V|)$ time and admits a polynomial-size problem kernel.

cs.CC↗
arXiv2019

On the Relation of Strong Triadic Closure and Cluster Deletion

We study the parameterized and classical complexity of two related problems on undirected graphs $G=(V,E)$. In Strong Triadic Closure we aim to label the edges in $E$ as strong and weak such that at most~$k$ edges are weak and $G$ contains no induced $P_3$ with two strong edges. In Cluster Deletion, we aim to destroy all induced $P_3$s by a minimum number of edge deletions. We first show that Strong Triadic Closure admits a $4k$-vertex kernel. Then, we study parameterization by $\ell:=|E|-k$ and show that both problems are fixed-parameter tractable and unlikely to admit a polynomial kernel with respect to $\ell$. Finally, we give a dichotomy of the classical complexity of both problems on $H$-free graphs for all $H$ of order four.

cs.DS↗
arXiv2018

Exact Algorithms for Finding Well-Connected 2-Clubs in Real-World Graphs: Theory and Experiments

Finding large "cliquish" subgraphs is a central topic in graph mining and community detection. A popular clique relaxation are 2-clubs: instead of asking for subgraphs of diameter one (these are cliques), one asks for subgraphs of diameter at most two (these are 2-clubs). A drawback of the 2-club model is that it produces star-like hub-and-spoke structures as maximum-cardinality solutions. Hence, we study 2-clubs with the additional constraint to be well-connected. More specifically, we investigate the algorithmic complexity for three variants of well-connected 2-clubs, all established in the literature: robust, hereditary, and "connected" 2-clubs. Finding these more cohesive 2-clubs is NP-hard; nevertheless, we develop an exact combinatorial algorithm, extensively using efficient data reduction rules. Besides several theoretical insights we provide a number of empirical results based on an engineered implementation of our exact algorithm. In particular, the algorithm significantly outperforms existing algorithms on almost all (sparse) real-world graphs we considered.

cs.DS↗
arXiv2018

The Maximum Colorful Arborescence problem parameterized by the structure of its color hierarchy graph

Let G=(V,A) be a vertex-colored arc-weighted directed acyclic graph (DAG) rooted in some vertex r, and let H be its color hierarchy graph, defined as follows: V(H) is the color set C of G, and an arc from color c to color c' exists in H if there is an arc in G from a vertex of color c to a vertex of color c'. In this paper, we study the MAXIMUM COLORFUL ARBORESCENCE problem (or MCA), which takes as input a DAG G with the additional constraint that H is also a DAG, and aims at finding in G an arborescence rooted in r, of maximum weight, and in which no color appears more than once. The MCA problem is motivated by the inference of unknown metabolites from mass spectrometry experiments. However, whereas the problem has been studied for roughly ten years, the crucial property that H is necessarily a DAG has only been pointed out and exploited very recently. In this paper, we further investigate MCA under this new light, by providing algorithmic results for the problem, with a specific focus on fixed-parameterized tractability (FPT) issues, and relatively to different structural parameters of H. In particular, we provide an O*(3^{nhs}) time algorithm for solving MCA, where nhs is the number of vertices of indegree at least two in H, thereby improving the O*(3^{|C|}) algorithm from [Böcker et al. 2008]. We also prove that MCA is W[2]-hard relatively to the treewidth Ht of H, and further show that it is FPT relatively to Ht+lc, where lc = |V| - |C|.

cs.CC↗
arXiv2018

Parameterized Algorithms for Recognizing Monopolar and 2-Subcolorable Graphs

A graph $G$ is a $(Π_A,Π_B)$-graph if $V(G)$ can be bipartitioned into $A$ and $B$ such that $G[A]$ satisfies property $Π_A$ and $G[B]$ satisfies property $Π_B$. The $(Π_{A},Π_{B})$-Recognition problem is to recognize whether a given graph is a $(Π_A,Π_B)$-graph. There are many $(Π_{A},Π_{B})$-Recognition problems, including the recognition problems for bipartite, split, and unipolar graphs. We present efficient algorithms for many cases of $(Π_A,Π_B)$-Recognition based on a technique which we dub inductive recognition. In particular, we give fixed-parameter algorithms for two NP-hard $(Π_{A},Π_{B})$-Recognition problems, Monopolar Recognition and 2-Subcoloring. We complement our algorithmic results with several hardness results for $(Π_{A},Π_{B})$-Recognition.

cs.CC↗
arXiv2017

When can Graph Hyperbolicity be computed in Linear Time?

Hyperbolicity measures, in terms of (distance) metrics, how close a given graph is to being a tree. Due to its relevance in modeling real-world networks, hyperbolicity has seen intensive research over the last years. Unfortunately, the best known algorithms for computing the hyperbolicity number of a graph (the smaller, the more tree-like) have running time $O(n^4)$, where $n$ is the number of graph vertices. Exploiting the framework of parameterized complexity analysis, we explore possibilities for "linear-time FPT" algorithms to compute hyperbolicity. For instance, we show that hyperbolicity can be computed in time $O(2^{O(k)} + n +m)$ ($m$ being the number of graph edges) while at the same time, unless the SETH fails, there is no $2^{o(k)}n^2$-time algorithm.

cs.CC↗
arXiv2016

Parameterizing edge modification problems above lower bounds

We study the parameterized complexity of a variant of the $F$-free Editing problem: Given a graph $G$ and a natural number $k$, is it possible to modify at most $k$ edges in $G$ so that the resulting graph contains no induced subgraph isomorphic to $F$? In our variant, the input additionally contains a vertex-disjoint packing $\mathcal{H}$ of induced subgraphs of $G$, which provides a lower bound $h(\mathcal{H})$ on the number of edge modifications required to transform $G$ into an $F$-free graph. While earlier works used the number $k$ as parameter or structural parameters of the input graph $G$, we consider instead the parameter $\ell:=k-h(\mathcal{H})$, that is, the number of edge modifications above the lower bound $h(\mathcal{H})$. We develop a framework of generic data reduction rules to show fixed-parameter tractability with respect to $\ell$ for $K_3$-Free Editing, Feedback Arc Set in Tournaments, and Cluster Editing when the packing $\mathcal{H}$ contains subgraphs with bounded solution size. For $K_3$-Free Editing, we also prove NP-hardness in case of edge-disjoint packings of $K_3$s and $\ell=0$, while for $K_q$-Free Editing and $q\ge 6$, NP-hardness for $\ell=0$ even holds for vertex-disjoint packings of $K_q$s. In addition, we provide NP-hardness results for $F$-free Vertex Deletion, were the aim is to delete a minimum number of vertices to make the input graph $F$-free.

cs.DM↗
arXiv2016

A parameterized approximation algorithm for the mixed and windy Capacitated Arc Routing Problem: theory and experiments

We prove that any polynomial-time $α(n)$-approximation algorithm for the $n$-vertex metric asymmetric Traveling Salesperson Problem yields a polynomial-time $O(α(C))$-approximation algorithm for the mixed and windy Capacitated Arc Routing Problem, where $C$ is the number of weakly connected components in the subgraph induced by the positive-demand arcs---a small number in many applications. In conjunction with known results, we obtain constant-factor approximations for $C\in O(\log n)$ and $O(\log C/\log\log C)$-approximations in general. Experiments show that our algorithm, together with several heuristic enhancements, outperforms many previous polynomial-time heuristics. Finally, since the solution quality achievable in polynomial time appears to mainly depend on $C$ and since $C=1$ in almost all benchmark instances, we propose the Ob benchmark set, simulating cities that are divided into several components by a river.

cs.DS↗
arXiv2016

H-Index Manipulation by Merging Articles: Models, Theory, and Experiments

An author's profile on Google Scholar consists of indexed articles and associated data, such as the number of citations and the H-index. The author is allowed to merge articles; this may affect the H-index. We analyze the (parameterized) computational complexity of maximizing the H-index using article merges. Herein, to model realistic manipulation scenarios, we define a compatibility graph whose edges correspond to plausible merges. Moreover, we consider several different measures for computing the citation count of a merged article. For the measure used by Google Scholar, we give an algorithm that maximizes the H-index in linear time if the compatibility graph has constant-size connected components. In contrast, if we allow to merge arbitrary articles (that is, for compatibility graphs that are cliques), then already increasing the H-index by one is NP-hard. Experiments on Google Scholar profiles of AI researchers show that the H-index can be manipulated substantially only if one merges articles with highly dissimilar titles.

cs.DL↗
arXiv2016

Parameterized Algorithmics for Graph Modification Problems: On Interactions with Heuristics

In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain property. For example, the Cluster Deletion problem asks to delete as few edges as possible such that the resulting graph is a disjoint union of cliques. Graph modification problems appear in numerous applications, including the analysis of biological and social networks. Typically, graph modification problems are NP-hard, making them natural candidates for parameterized complexity studies. We discuss several fruitful interactions between the development of fixed-parameter algorithms and the design of heuristics for graph modification problems, featuring quite different aspects of mutual benefits.

cs.DS↗
arXiv2016

Tight Running Time Lower Bounds for Vertex Deletion Problems

For a graph class $Π$, the $Π$-Vertex Deletion problem has as input an undirected graph $G=(V,E)$ and an integer $k$ and asks whether there is a set of at most $k$ vertices that can be deleted from $G$ such that the resulting graph is a member of $Π$. By a classic result of Lewis and Yannakakis [J. Comput. Syst. Sci. '80], $Π$-Vertex Deletion is NP-hard for all hereditary properties $Π$. We adapt the original NP-hardness construction to show that under the Exponential Time Hypothesis (ETH) tight complexity results can be obtained. We show that $Π$-Vertex Deletion does not admit a $2^{o(n)}$-time algorithm where $n$ is the number of vertices in $G$. We also obtain a dichotomy for running time bounds that include the number $m$ of edges in the input graph: On the one hand, if $Π$ contains all independent sets, then there is no $2^{o(n+m)}$-time algorithm for $Π$-Vertex Deletion. On the other hand, if there is a fixed independent set that is not contained in $Π$ and containment in $Π$ can determined in $2^{O(n)}$ time or $2^{o(m)}$ time, then $Π$-Vertex Deletion can be solved in $2^{O(\sqrt{m})}+O(n)$ or $2^{o({m})}+O(n)$ time, respectively. We also consider restrictions on the domain of the input graph $G$. For example, we obtain that $Π$-Vertex Deletion cannot be solved in $2^{o(\sqrt{n})}$ time if $G$ is planar and $Π$ is hereditary and contains and excludes infinitely many planar graphs. Finally, we provide similar results for the problem variant where the deleted vertex set has to induce a connected graph.

cs.DS↗
arXiv2016

Precedence-constrained scheduling problems parameterized by partial order width

Negatively answering a question posed by Mnich and Wiese (Math. Program. 154(1-2):533-562), we show that P2|prec,$p_j{\in}\{1,2\}$|$C_{\max}$, the problem of finding a non-preemptive minimum-makespan schedule for precedence-constrained jobs of lengths 1 and 2 on two parallel identical machines, is W[2]-hard parameterized by the width of the partial order giving the precedence constraints. To this end, we show that Shuffle Product, the problem of deciding whether a given word can be obtained by interleaving the letters of $k$ other given words, is W[2]-hard parameterized by $k$, thus additionally answering a question posed by Rizzi and Vialette (CSR 2013). Finally, refining a geometric algorithm due to Servakh (Diskretn. Anal. Issled. Oper. 7(1):75-82), we show that the more general Resource-Constrained Project Scheduling problem is fixed-parameter tractable parameterized by the partial order width combined with the maximum allowed difference between the earliest possible and factual starting time of a job.

math.OC↗
arXiv2015

Well-Formed Separator Sequences, with an Application to Hypergraph Drawing

Given a hypergraph $H$, the Planar Support problem asks whether there is a planar graph $G$ on the same vertex set as $H$ such that each hyperedge induces a connected subgraph of $G$. Planar Support is motivated by applications in graph drawing and data visualization. We show that Planar Support is fixed-parameter tractable when parameterized by the number of hyperedges in the input hypergraph and the outerplanarity number of the sought planar graph. To this end, we develop novel structural results for $r$-outerplanar triangulated disks, showing that they admit sequences of separators with structural properties enabling data reduction. This allows us to obtain a problem kernel for Planar Support, thus showing its fixed-parameter tractability.

cs.DM↗
arXiv2015

Parameterized Complexity of Critical Node Cuts

We consider the following natural graph cut problem called Critical Node Cut (CNC): Given a graph $G$ on $n$ vertices, and two positive integers $k$ and $x$, determine whether $G$ has a set of $k$ vertices whose removal leaves $G$ with at most $x$ connected pairs of vertices. We analyze this problem in the framework of parameterized complexity. That is, we are interested in whether or not this problem is solvable in $f(κ) \cdot n^{O(1)}$ time (i.e., whether or not it is fixed-parameter tractable), for various natural parameters $κ$. We consider four such parameters: - The size $k$ of the required cut. - The upper bound $x$ on the number of remaining connected pairs. - The lower bound $y$ on the number of connected pairs to be removed. - The treewidth $w$ of $G$. We determine whether or not CNC is fixed-parameter tractable for each of these parameters. We determine this also for all possible aggregations of these four parameters, apart from $w+k$. Moreover, we also determine whether or not CNC admits a polynomial kernel for all these parameterizations. That is, whether or not there is an algorithm that reduces each instance of CNC in polynomial time to an equivalent instance of size $κ^{O(1)}$, where $κ$ is the given parameter.

cs.DS↗