René van Bevern

Huawei Technologies · Novosibirsk Research Center

Numerous applications in scheduling, such as resource allocation or steel manufacturing, can be modeled using the NP-hard Independent Set problem (given an undirected graph and an integer \(k\), find a set of at least \(k\) pairwise non-adjacent vertices). Here, one encounters special graph classes like 2-union graphs (edge-wise unions of two inter...

Machine scheduling problems are a long-time key domain of algorithms and complexity research. A novel approach to machine scheduling problems are fixed-parameter algorithms. To stimulate this thriving research direction, we propose 15 open questions in this area whose resolution we expect to lead to the discovery of new approaches and techniques bo...

One of the most fundamental results in combinatorial optimization is the polynomial-time 3/2-approximation algorithm for the metric traveling salesman problem. It was presented by Christofides in 1976 and is well known as “the Christofides algorithm”. Recently, some authors started calling it “Christofides-Serdyukov algorithm”, pointing out that it...

Given an undirected graph with edge weights and a subset R of its edges, the Rural Postman Problem (RPP) is to find a closed walk of minimum total weight containing all edges of R. We prove that RPP is WK[1]-complete parameterized by the number and weight d of edges traversed additionally to the required ones. Thus RPP instances cannot be polynomia...

We study a dynamic vector bin packing (DVBP) problem. We show hardness for shrinking arbitrary DVBP instances to size polynomial in the number of request types or in the maximal number of requests overlapping in time. We also present a simple polynomial-time data reduction algorithm that allows to recover (1+ε)-approximate solutions for arbitrary ε...

Dealing with NP-hard problems, kernelization is a fundamental notion for polynomial-time data reduction with performance guarantees: in polynomial time, a problem instance is reduced to an equivalent instance with size upper-bounded by a function of a parameter chosen in advance. Kernelization for weighted problems particularly requires to also shr...

The NP-hard graphical traveling salesman problem (GTSP) is to find a closed walk of total minimum weight that visits (at least once) each vertex in an undirected edge-weighted and not necessarily complete graph. Recently, Bla\v{z}ej et al. [ESA 2022] showed a problem kernel with $O(\tau^3)$ vertices for GTSP, where $\tau$ is the vertex cover number...

We study a dynamic vector bin packing (DVBP) problem. We show hardness for shrinking arbitrary DVBP instances to size polynomial in the number of request types or in the maximal number of requests overlapping in time. We also present a simple polynomial-time data reduction algorithm that allows to recover $(1 + {\varepsilon})$-approximate solutions...

The NP-hard Multiple Hitting Set problem is finding a minimum-cardinality set intersecting each of the sets in a given input collection a given number of times. Generalizing a well-known data reduction algorithm due to Weihe, we show a problem kernel for Multiple Hitting Set parameterized by the Dilworth number, a graph parameter introduced by Fold...

We show algorithms for computing representative families for matroid intersections and use them in fixed-parameter algorithms for set packing, set covering, and facility location problems with multiple matroid constraints. We complement our tractability results by hardness results.

Готовящееся учебное пособие к спецкурсу Рандомизированные алгоритмы ММФ НГУ. Материал сырой, находится в разработке, может содержать матеметические и граматические ошибки. За любые замечания автор будет благодарен.

We study a problem of energy-efficiently connecting a symmetric wireless communication network: given an n-vertex graph with edge weights, find a connected spanning subgraph of minimum cost, where the cost is determined by each vertex paying the heaviest edge incident to it in the subgraph. The problem is known to be NP-hard. Strengthening this har...

Text of invited lecture at Ural Federal University, Yekaterinburg, Russian Federation, Apr 5th, 2021, with some subsequent corrections.

We show algorithms for computing representative families for matroid intersections and use them in fixed-parameter algorithms for set packing, set covering, and facility location problems with multiple matroid constraints. We complement our tractability results by hardness results.

The Hierarchical Chinese Postman Problem is finding a shortest traversal of all edges of a graph respecting precedence constraints given by a partial order on classes of edges. We show that the special case with connected classes is NP-hard even on orders decomposable into a chain and an incomparable class. For the case with linearly ordered (possi...

The Hierarchical Chinese Postman Problem is finding a shortest traversal of all edges of a graph respecting precedence constraints given by a partial order on classes of edges. We show that the special case with connected classes is NP-hard even on orders decomposable into a chain and an incomparable class. For the case with linearly ordered (possi...

Kernelization is the fundamental notion for polynomial-time prepocessing with performance guarantees in parameterized algorithmics. When preprocessing weighted problems, the need of shrinking weights might arise. Marx and V\'egh [ACM Trans. Algorithms 2015] and Etscheid et al. [J. Comput. Syst. Sci. 2017] used a technique due to Frank and Tardos [C...

Presentation of article Networks 76(4):485–508, 2020

Presentation for article Historia Mathematica, 53: 118-127. 2020.

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...

Talk on preprint https://arxiv.org/abs/2011.04022

The known linear-time kernelizations for d-Hitting Set guarantee linear worst-case running times using a quadratic-size data structure (that is not fully initialized). Getting rid of this data structure, we show that problem kernels of asymptotically optimal size O(kd) for d-Hitting Set are computable in linear time and space. Additionally, we expe...

Given an undirected graph with edge weights and a subset R of its edges, the Rural Postman Problem (RPP) is to find a closed walk of minimum total weight containing all edges of R. We prove that RPP is WK[1]-complete parameterized by the number and cost d of edges traversed additionally to the required ones. Thus, in particular, RPP instances canno...

The known linear-time kernelizations for $d$-Hitting Set guarantee linear worst-case running times using a quadratic-size data structure (that is not fully initialized). Getting rid of this data structure, we show that problem kernels of asymptotically optimal size $O(k^d)$ for $d$-Hitting Set are computable in linear time and space. Additionally,...

One of the most fundamental results in combinatorial optimization is the polynomial-time 3/2-approximation algorithm for the metric traveling salesman problem. It was presented by Christofides in 1976 and is well known as "the Christofides algorithm". Recently, some authors started calling it "Christofides-Serdyukov algorithm", pointing out that th...

Given a graph G = (V, E), two vertices s, t ∈ V, and two integers k, ℓ, the Short Secluded Path problem is to find a simple s‐t‐path with at most k vertices and ℓ neighbors. We study the parameterized complexity of the problem with respect to four structural graph parameters: the vertex cover number, treewidth, feedback vertex number, and feedback...

Given a graph \(G=(V,E)\) with edge weights and a subset \(R\subseteq E\) of required edges, the NP-hard Rural Postman Problem (RPP) is to find a closed walk of minimum total weight containing all edges of R. The number b of vertices incident to an odd number of edges of R and the number c of connected components formed by the edges in R are both b...

Given a graph G=(V,E), two vertices s,t∈V, and two integers k,ℓ, the Short Secluded Path problem is to find a simple s-t-path with at most k vertices and ℓ neighbors. We study the parameterized complexity of the problem with respect to four structural graph parameters: the vertex cover number, treewidth, feedback vertex number, and feedback edge nu...

We consider an uncapacitated discrete facility location problem where the task is to decide which facilities to open and which clients to serve for maximum profit so that the facilities form an independent set in given facility-side matroids and the clients form an independent set in given client-side matroids. We show that the problem is fixed-par...

For the Routing Open Shop problem with unit execution times, the first algorithm with parameterized complexity is designed for constructing an optimal schedule. Its running time is bounded by a function (Pol(|V|) + f(m, g)) · |I|, where Pol(|V |) is a polynomial of the number of network nodes, f(m, g) is a function of the number of machines and the...

Inductive \(k\)-independent graphs generalize chordal graphs and have recently been advocated in the context of interference-avoiding wireless communication scheduling. The NP-hard problem of finding maximum-weight induced c-colorable subgraphs, which is a generalization of finding maximum independent sets, naturally occurs when selecting \(c\) set...

Об одном подходе Бодлендера, Цыгана, Кратча и Недерлова

This work studies the parameterized complexity of finding secluded solutions to classical combinatorial optimization problems on graphs such as finding minimum s-t separators, feedback vertex sets, dominating sets, maximum independent sets, and vertex deletion problems for hereditary graph properties: Herein, one searches not only to minimize or ma...

We study a problem that models safely routing a convoy through a transportation network, where any vertex adjacent to the travel path of the convoy requires additional precaution: Given a graph G = (V, E), two vertices s, t ∈ V , and two integers k, , we search for a simple s-t-path with at most k vertices and at most neighbors. We study the proble...

Inductive k-independent graphs generalize chordal graphs and have recently been advocated in the context of interference-avoiding wireless communication scheduling. The NP-hard problem of finding maximum-weight induced c-colorable subgraphs, which is a generalization of finding maximum independent sets, naturally occurs when selecting c sets of pai...

The NP-hard problem of finding maximum-weight induced c-colorable subgraphs, which is a generalization of finding maximum independent sets, naturally occurs when selecting c sets of pairwise non-conflicting jobs (modeled as graph vertices). We investigate the parameterized complexity of this problem with respect to the solution size on inductive k-...

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 subgra...

We study an NP-hard problem motivated by energy-efficiently maintaining the connectivity of a symmetric wireless sensor communication network. Given an edge-weighted \(n\)-vertex graph, find a connected spanning subgraph of minimum cost, where the cost is determined by letting each vertex pay the most expensive edge incident to it in the subgraph....

Machine scheduling problems are a long-time key domain of algorithms and complexity research. A novel approach to machine scheduling problems are fixed-parameter algorithms. To stimulate this thriving research direction, we propose 15 interesting open questions in this area.

We study the problem of non-preemptively scheduling n jobs, each job j with a release time t_j, a deadline d_j, and a processing time p_j, on m parallel identical machines. Cieliebak et al. considered the two constraints |d_j-t_j| ≤ λp_j and |d_j-t_j| ≤ p_j+σ and showed the problem to be NP-hard for any λ>1 and for any σ≥2. We complement their resu...

The partition of graphs into ``nice'' subgraphs is a central algorithmic problem with strong ties to matching theory. We study the partitioning of undirected graphs into same-size stars, a problem known to be NP-complete even for the case of stars on three vertices. We perform a thorough computational complexity study of the problem on subclasses o...

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 s...

Finding the origin of short phrases propagating through the web has been formalized by Leskovec et al. [ACM SIGKDD 2009] as DAG PARTITIONING: given an arc-weighted directed acyclic graph on n vertices and m arcs, delete arcs with total weight at most k such that each resulting weakly-connected component contains exactly one sink—a vertex without ou...

Finding a vertex subset in a graph that satisfies a certain property is one of the most-studied topics in algorithmic graph theory. The focus herein is often on minimizing or maximizing the size of the solution, that is, the size of the desired vertex set. In several applications, however, we also want to limit the "exposure" of the solution to the...

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...

Negatively answering a question posed by Mnich and Wiese (Math. Program. 154(1–2):533–562), we show that P2|prec,pj∈{1, 2}|Cmax, 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...

Visualizing hypergraphs, systems of subsets of some universe, has continuously attracted research interest in the last decades. We study a natural kind of hypergraph visualization called subdivision drawings. Dinkla et al. [Comput. Graph. Forum ’12] claimed that only few hypergraphs have a subdivision drawing. However, this statement seems to be ba...

The h-index is an important bibliographic measure used to assess the performance of researchers. Van Bevern et al. [Artif. Intel., to appear] showed that, despite computational worst-case hardness results, substantial manipulation of the h-index of Google Scholar author profiles is possible by merging articles. Complementing this work, we study the...

For a fixed graph F, 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 H of induced...

Open Shop is a classical scheduling problem: given a set \(\mathcal J\) of jobs and a set \(\mathcal M\) of machines, find a minimum-makespan schedule to process each job \(J_i\in \mathcal J\) on each machine \(M_q\in \mathcal M\) for a given amount \(p_{iq}\) of time such that each machine processes only one job at a time and each job is processed...

The NP-hard Distinct Vectors problem asks to delete as many columns as possible from a matrix such that all rows in the resulting matrix are still pairwise distinct. Our main result is that, for binary matrices, there is a complexity dichotomy for Distinct Vectors based on the maximum (H) and the minimum (h) pairwise Hamming distance between matrix...

We give an analog of the Myhill–Nerode theorem from formal language theory for hypergraphs and use it to derive the following results for two NP-hard hypergraph problems. (1) We provide an algorithm for testing whether a hypergraph has cutwidth at most k that runs in linear time for constant k. In terms of parameterized complexity theory, the probl...

A c-interval is the disjoint union of c intervals over the natural numbers. The c-Interval Multicover problem is the special case of Set Multicover where all sets available for covering are c-intervals. We strengthen known APX-hardness results for c-Interval Multicover, show W[1]-hardness when parameterized by the solution size, and present fixed-p...

We show that any α(n)-approximation algorithm for the n-vertex metric asymmetric Traveling Salesperson problem yields O(α(C))-approximation algorithms for various mixed, windy, and capacitated arc routing problems. Herein, C is the number of weakly-connected components in the subgraph induced by the positive-demand arcs, a number that can be expect...

We study the problem of non-preemptively scheduling $n$ jobs, each job $j$ with a release time $t_j$, a deadline $d_j$, and a processing time $p_j$, on a minimum number $m$ of parallel identical machines. Cieliebak et al. (2004) considered the two constraints $|d_j-t_j|\leq \lambda p_j$ and $|d_j-t_j|\leq p_j +\sigma$ and showed the problem to be N...

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, which may affect the H-index. We analyze the parameterized complexity of maximizing the H-index using article merges. Herein, to model realistic manipulation scenarios, we...

A balanced partition is a clustering of a graph into a given number of equal-sized parts. For instance, the Bisection problem asks to remove at most k edges in order to partition the vertices into two equal-sized parts. We prove that Bisection is FPT for the distance to constant cliquewidth if we are given the deletion set. This implies FPT algorit...

We introduce a graph-theoretic vertex dissolution model that applies to a number of redistribution scenarios such as gerrymandering in political districting or work balancing in an online situation. The central aspect of our model is the deletion of certain vertices and the redistribution of their load to neighboring vertices in a completely balanc...

Google Scholar allows merging multiple article versions into one. This merging affects the H-index computed by Google Scholar. We analyze the parameterized complexity of maximizing the H-index using article merges. Herein, multiple possible measures for computing the citation count of a merged article are considered. Among others, for the measure u...

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This thesis aims for the development of efficient algorithms to exactly solve four selected NP-hard graph and hypergraph problems arising in the fields of scheduling, steel manufactoring, software engineering, radio frequency allocation, computer-aided circuit design, and social network analysis. NP-hard problems presumably cannot be solved exactly...

We introduce a novel graph-theoretic dissolution model which applies to a number of redistribution scenarios such as gerrymandering or work economization. The central aspect of our model is to delete some vertices and redistribute their "load" to neighboring vertices in a completely balanced way. We investigate how the underlying graph structure, t...

The partition of graphs into nice subgraphs is a central algorithmic problem with strong ties to matching theory. We study the partitioning of undirected graphs into stars, a problem known to be NP-complete even for the case of stars on three vertices. We perform a thorough computational complexity study of the problem on subclasses of perfect grap...

Given an undirected graph with edge costs and edge demands, the Capacitated Arc Routing problem (CARP) asks for minimum-cost routes for equal-capacity vehicles so as to satisfy all demands. Constant-factor polynomial-time approximation algorithms were proposed for CARP with triangle inequality, while CARP was claimed to be NP-hard to approximate wi...