arXiv subjects

Rolf Niedermeier

Publications and source records attributed to Rolf Niedermeier.

At least 73 records · Page 4Linked to original sources

arXiv2020

As Time Goes By: Reflections on Treewidth for Temporal Graphs

Treewidth is arguably the most important structural graph parameter leading to algorithmically beneficial graph decompositions. Triggered by a strongly growing interest in temporal networks (graphs where edge sets change over time), we discuss fresh algorithmic views on temporal tree decompositions and temporal treewidth. We review and explain some of the recent work together with some encountered pitfalls, and we point out challenges for future research.

cs.DS↗

arXiv2020

Stable Roommates with Narcissistic, Single-Peaked, and Single-Crossing Preferences

The classical Stable Roommates problem is to decide whether there exists a matching of an even number of agents such that no two agents which are not matched to each other would prefer to be with each other rather than with their respectively assigned partners. We investigate Stable Roommates with complete (i.e., every agent can be matched with any other agent) or incomplete preferences, with ties (i.e., two agents are considered of equal value to some agent) or without ties. It is known that in general allowing ties makes the problem NP-complete. We provide algorithms for Stable Roommates that are, compared to those in the literature, more efficient when the input preferences are complete and have some structural property, such as being narcissistic, single-peaked, and single-crossing. However, when the preferences are incomplete and have ties, we show that being single-peaked and single-crossing does not reduce the computational complexity--Stable Roommates remains NP-complete.

cs.GT↗

arXiv2020

Efficient Computation of Optimal Temporal Walks under Waiting-Time Constraints

Node connectivity plays a central role in temporal network analysis. We provide a comprehensive study of various concepts of walks in temporal graphs, that is, graphs with fixed vertex sets but edge sets changing over time. Taking into account the temporal aspect leads to a rich set of optimization criteria for "shortest" walks. Extending and significantly broadening state-of-the-art work of Wu et al. [IEEE TKDE 2016], we provide an algorithm for computing optimal walks that is capable to deal with various optimization criteria and any linear combination of these. It runs in $O (|V| + |E| \log |E|)$ time where $|V|$ is the number of vertices and $|E|$ is the number of time edges. A central distinguishing factor to Wu et al.'s work is that our model allows to, motivated by real-world applications, respect waiting-time constraints for vertices, that is, the minimum and maximum waiting time allowed in intermediate vertices of a walk. Moreover, other than Wu et al. our algorithm also allows to search for walks that pass multiple subsequent edges in one time step, and it can optimize a richer set of optimization criteria. Our experimental studies indicate that our richer modeling can be achieved without significantly worsening the running time when compared to Wu et al.'s algorithms.

cs.DS↗

arXiv2020

Parameterized Algorithms for Matrix Completion With Radius Constraints

Considering matrices with missing entries, we study NP-hard matrix completion problems where the resulting completed matrix shall have limited (local) radius. In the pure radius version, this means that the goal is to fill in the entries such that there exists a 'center string' which has Hamming distance to all matrix rows as small as possible. In stringology, this problem is also known as Closest String with Wildcards. In the local radius version, the requested center string must be one of the rows of the completed matrix. Hermelin and Rozenberg [CPM 2014, TCS 2016] performed parameterized complexity studies for Closest String with Wildcards. We answer one of their open questions, fix a bug concerning a fixed-parameter tractability result in their work, and improve some upper running time bounds. For the local radius case, we reveal a computational complexity dichotomy. In general, our results indicate that, although being NP-hard as well, this variant often allows for faster (fixed-parameter) algorithms.

cs.DM↗

arXiv2020

Faster Binary Mean Computation Under Dynamic Time Warping

Many consensus string problems are based on Hamming distance. We replace Hamming distance by the more flexible (e.g., easily coping with different input string lengths) dynamic time warping distance, best known from applications in time series mining. Doing so, we study the problem of finding a mean string that minimizes the sum of (squared) dynamic time warping distances to a given set of input strings. While this problem is known to be NP-hard (even for strings over a three-element alphabet), we address the binary alphabet case which is known to be polynomial-time solvable. We significantly improve on a previously known algorithm in terms of worst-case running time. Moreover, we also show the practical usefulness of one of our algorithms in experiments with real-world and synthetic data. Finally, we identify special cases solvable in linear time (e.g., finding a mean of only two binary input strings) and report some empirical findings concerning combinatorial properties of optimal means.

cs.DM↗

arXiv2019

Adapting Stable Matchings to Evolving Preferences

Adaptivity to changing environments and constraints is key to success in modern society. We address this by proposing "incrementalized versions" of Stable Marriage and Stable Roommates. That is, we try to answer the following question: for both problems, what is the computational cost of adapting an existing stable matching after some of the preferences of the agents have changed. While doing so, we also model the constraint that the new stable matching shall be not too different from the old one. After formalizing these incremental versions, we provide a fairly comprehensive picture of the computational complexity landscape of Incremental Stable Marriage and Incremental Stable Roommates. To this end, we exploit the parameters "degree of change" both in the input (difference between old and new preference profile) and in the output (difference between old and new stable matching). We obtain both hardness and tractability results, in particular showing a fixed-parameter tractability result with respect to the parameter "distance between old and new stable matching".

cs.GT↗

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

Enumerating Isolated Cliques in Temporal Networks

Isolation is a concept from the world of clique enumeration that is mostly used to model communities that do not have much contact to the outside world. Herein, a clique is considered isolated if it has few edges connecting it to the rest of the graph. Motivated by recent work on enumerating cliques in temporal networks, we lift the isolation concept to this setting. We discover that the addition of the time dimension leads to six distinct natural isolation concepts. Our main contribution is the development of fixed-parameter enumeration algorithms for five of these six clique types employing the parameter "degree of isolation". On the empirical side, we implement and test these algorithms on (temporal) social network data, obtaining encouraging preliminary results.

cs.DS↗

arXiv2019

On Coalitional Manipulation for Multiwinner Elections: Shortlisting

Shortlisting of candidates--selecting a group of "best" candidates--is a special case of multiwinner elections. We provide the first in-depth study of the computational complexity of strategic voting for shortlisting based on the perhaps most basic voting rule in this scenario, l-Bloc (every voter approves l candidates). In particular, we investigate the influence of several tie-breaking mechanisms (e.g., pessimistic versus optimistic) and group evaluation functions (e.g., egalitarian versus utilitarian). Among other things, conclude that in an egalitarian setting strategic voting may indeed be computationally intractable regardless of the tie-breaking rule. Altogether, we provide a fairly comprehensive picture of the computational complexity landscape so far in the literature of this neglected scenario.

cs.MA↗

arXiv2019

Listing All Maximal $k$-Plexes in Temporal Graphs

Many real-world networks evolve over time, that is, new contacts appear and old contacts may disappear. They can be modeled as temporal graphs where interactions between vertices (which represent people in the case of social networks) are represented by time-stamped edges. One of the most fundamental problems in (social) network analysis is community detection, and one of the most basic primitives to model a community is a clique. Addressing the problem of finding communities in temporal networks, Viard et al. [TCS 2016] introduced $Δ$-cliques as a natural temporal version of cliques. Himmel et al. [SNAM 2017] showed how to adapt the well-known Bron-Kerbosch algorithm to enumerate $Δ$-cliques. We continue this work and improve and extend the algorithm of Himmel et al. to enumerate temporal $k$-plexes (notably, cliques are the special case $k=1$). We define a $Δ$-$k$-plex as a set of vertices and a time interval, where during this time interval each vertex has in each consecutive $Δ+ 1$ time steps at least one edge to all but at most $k-1$ vertices in the chosen set of vertices. We develop a recursive algorithm for enumerating all maximal $Δ$-$k$-plexs and perform experiments on real-world social networks that demonstrate the practical feasibility of our approach. In particular, for the special case of $Δ$-1-plexes (that is, $Δ$-cliques), we observe that our algorithm is on average significantly faster than the previous algorithms by Himmel et al. [SNAM 2017] and Viard et al. [IPL 2018] for enumerating $Δ$-cliques.

cs.DS↗

arXiv2019

Robustness Among Multiwinner Voting Rules

We investigate how robust the results of committee elections are to small changes in the input preference orders, depending on the voting rules used. We find that for typical rules the effect of making a single swap of adjacent candidates in a single preference order is either that (1) at most one committee member might be replaced, or (2) it is possible that the whole committee will be replaced. We also show that the problem of computing the smallest number of swaps that lead to changing the election outcome is typically NP-hard, but there are natural FPT algorithms. Finally, for a number of rules we assess experimentally the average number of random swaps necessary to change the election result.

cs.GT↗

arXiv2019

Co-Clustering Under the Maximum Norm

Co-clustering, that is, partitioning a numerical matrix into homogeneous submatrices, has many applications ranging from bioinformatics to election analysis. Many interesting variants of co-clustering are NP-hard. We focus on the basic variant of co-clustering where the homogeneity of a submatrix is defined in terms of minimizing the maximum distance between two entries. In this context, we spot several NP-hard as well as a number of relevant polynomial-time solvable special cases, thus charting the border of tractability for this challenging data clustering problem. For instance, we provide polynomial-time solvability when having to partition the rows and columns into two subsets each (meaning that one obtains four submatrices). When partitioning rows and columns into three subsets each, however, we encounter NP-hardness even for input matrices containing only values from {0, 1, 2}.

cs.DM↗

arXiv2019

Tight Hardness Results for Consensus Problems on Circular Strings and Time Series

Consensus problems for strings and sequences appear in numerous application contexts, ranging from bioinformatics over data mining to machine learning. Closing some gaps in the literature, we show that several fundamental problems in this context are NP- and W[1]-hard, and that the known (partially brute-force) algorithms are close to optimality assuming the Exponential Time Hypothesis. Among our main contributions is to settle the complexity status of computing a mean in dynamic time warping spaces which, as pointed out by Brill et al. [DMKD 2019], suffered from many unproven or false assumptions in the literature. We prove this problem to be NP-hard and additionally show that a recent dynamic programming algorithm is essentially optimal. In this context, we study a broad family of circular string alignment problems. This family also serves as a key for our hardness reductions, and it is of independent (practical) interest in molecular biology. In particular, we show tight hardness and running time lower bounds for Circular Consensus String; notably, the corresponding non-circular version is easily linear-time solvable.

cs.DM↗

arXiv2018

Parameterized Aspects of Triangle Enumeration

The task of listing all triangles in an undirected graph is a fundamental graph primitive with numerous applications. It is trivially solvable in time cubic in the number of vertices. It has seen a significant body of work contributing to both theoretical aspects (e.g., lower and upper bounds on running time, adaption to new computational models) as well as practical aspects (e.g. algorithms tuned for large graphs). Motivated by the fact that the worst-case running time is cubic, we perform a systematic parameterized complexity study of triangle enumeration. We provide both positive results (new enumerative kernelizations, "subcubic" parameterized solving algorithms) as well as negative results (presumable uselessness in terms of "faster" parameterized algorithms of certain parameters such as graph diameter). To this end, we introduce new and extend previous concepts.

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

Parameterized Dynamic Cluster Editing

We introduce a dynamic version of the NP-hard graph problem Cluster Editing. The essential point here is to take into account dynamically evolving input graphs: Having a cluster graph (that is, a disjoint union of cliques) that represents a solution for the first input graph, can we cost-efficiently transform it into a "similar" cluster graph that is a solution for the second ("subsequent") input graph? This model is motivated by several application scenarios, including incremental clustering, the search for compromise clusterings, or also local search in graph-based data clustering. We thoroughly study six problem variants (edge editing, edge deletion, edge insertion; each combined with two distance measures between cluster graphs). We obtain both fixed-parameter tractability as well as (parameterized) hardness results, thus (except for three open questions) providing a fairly complete picture of the parameterized computational complexity landscape under the two perhaps most natural parameterizations: the distance of the new "similar" cluster graph to (i) the second input graph and to (ii) the input cluster graph.

cs.DM↗

arXiv2018

A Linear-Time Algorithm for Maximum-Cardinality Matching on Cocomparability Graphs

Finding maximum-cardinality matchings in undirected graphs is arguably one of the most central graph problems. For general m-edge and n-vertex graphs, it is well-known to be solvable in $O(m \sqrt{n})$ time. We develop a linear-time algorithm to find maximum-cardinality matchings on cocomparability graphs, a prominent subclass of perfect graphs that contains interval graphs as well as permutation graphs. Our algorithm is based on the recently discovered Lexicographic Depth First Search (LDFS).

cs.DS↗