arXiv subjects

Manuel Penschuck

Publications and source records attributed to Manuel Penschuck.

At least 19 recordsLinked to original sources

arXiv2025

Revisiting a Successful Reduction Rule for Dominating Set

Given a graph $G = (V, E)$ with $n$ vertices and $m$ edges, the DominatingSet problem asks for a set $D \subseteq V$ of minimal cardinality such that every vertex either is in $D$ or adjacent to a member of $D$. Although there is little hope for a kernelization algorithm on general graphs due to the W[2]-hardness of DominatingSet, data reduction rules are extensively used in practice. In this context, Rule1 due to Alber, Fellows, and Niedermeier [JACM 2004] has been shown to be very powerful, yet its best-known running time is $\mathcal{O}(n^3)$ ($= \mathcal{O}(nm)$) for general graphs. In this work, we propose, to the best of our knowledge, the first $\mathcal{O}(n + m)$-time algorithm for Rule1 on general graphs. We additionally propose simple, but practically significant, extensions to our algorithmic framework to further prune the input instances. We complement our theoretical claims with experiments that confirm the practicality of our approach. On average, we see significant speedups of over one order of magnitude while removing $59.8\times$ more nodes and $410.9\times$ more edges than the original formulation across a large dataset comprised of real-world and synthetic networks.

cs.DS↗

arXiv2024

Efficient Uniform Negative Edge Weights

We consider a maximum entropy edge weight model that allows for negative weights. Given a graph $G$ and possible weights $\mathcal{W}$ typically consisting of positive and negative values, the model selects edge weights $w \in \mathcal{W}^m$ uniformly at random from all weights that do not introduce a negative cycle. We propose an MCMC process and show that it converges to the required distribution. We then engineer an implementation of the process using a dynamic version of Johnson's algorithm in connection with a bidirectional Dijkstra search as well as an innovative resampling method. We empirically study the performance characteristics of these novel sampling algorithms as well as the output produced by the model.

cs.DS↗

arXiv2024

Insights into $(k,\rho)$-shortcutting algorithms

A graph is called a $(k,\rho)$-graph iff every node can reach $\rho$ of its nearest neighbors in at most k hops. This property proved useful in the analysis and design of parallel shortest-path algorithms. Any graph can be transformed into a $(k,\rho)$-graph by adding shortcuts. Formally, the $(k,\rho)$-Minimum-Shortcut problem asks to find an appropriate shortcut set of minimal cardinality. We show that the $(k,\rho)$-Minimum-Shortcut problem is NP-complete in the practical regime of $k \ge 3$ and $\rho = \Theta(n^\epsilon)$ for $\epsilon > 0$. With a related construction, we bound the approximation factor of known $(k,\rho)$-Minimum-Shortcut problem heuristics from below and propose algorithmic countermeasures improving the approximation quality. Further, we describe an integer linear problem (ILP) solving the $(k,\rho)$-Minimum-Shortcut problem optimally. Finally, we compare the practical performance and quality of all algorithms in an empirical campaign.

cs.DS↗

arXiv2023

Parallel Global Edge Switching for the Uniform Sampling of Simple Graphs with Prescribed Degrees

The uniform sampling of simple graphs matching a prescribed degree sequence is an important tool in network science, e.g. to construct graph generators or null-models. Here, the Edge Switching Markov Chain (ES-MC) is a common choice. Given an arbitrary simple graph with the required degree sequence, ES-MC carries out a large number of small changes, called edge switches, to eventually obtain a uniform sample. In practice, reasonably short runs efficiently yield approximate uniform samples. In this work, we study the problem of executing edge switches in parallel. We discuss parallelizations of ES-MC, but find that this approach suffers from complex dependencies between edge switches. For this reason, we propose the Global Edge Switching Markov Chain (G-ES-MC), an ES-MC variant with simpler dependencies. We show that G-ES-MC converges to the uniform distribution and design shared-memory parallel algorithms for ES-MC and G-ES-MC. In an empirical evaluation, we provide evidence that G-ES-MC requires not more switches than ES-MC (and often fewer), and demonstrate the efficiency and scalability of our parallel G-ES-MC implementation.

cs.DS↗

arXiv2023

Engineering Shared-Memory Parallel Shuffling to Generate Random Permutations In-Place

Shuffling is the process of rearranging a sequence of elements into a random order such that any permutation occurs with equal probability. It is an important building block in a plethora of techniques used in virtually all scientific areas. Consequently considerable work has been devoted to the design and implementation of shuffling algorithms. We engineer, -- to the best of our knowledge -- for the first time, a practically fast, parallel shuffling algorithm with $\Oh{\sqrt{n}\log n}$ parallel depth that requires only poly-logarithmic auxiliary memory. Our reference implementations in Rust are freely available, easy to include in other projects, and can process large data sets approaching the size of the system's memory. In an empirical evaluation, we compare our implementations with a number of existing solutions on various computer architectures. Our algorithms consistently achieve the highest through-put on all machines. Further, we demonstrate that the runtime of our parallel algorithm is comparable to the time that other algorithms may take to acquire the memory from the operating system to copy the input.

cs.DS↗

arXiv2023

Parallel and I/O-Efficient Algorithms for Non-Linear Preferential Attachment

Preferential attachment lies at the heart of many network models aiming to replicate features of real world networks. To simulate the attachment process, conduct statistical tests, or obtain input data for benchmarks, efficient algorithms are required that are capable of generating large graphs according to these models. Existing graph generators are optimized for the most simple model, where new nodes that arrive in the network are connected to earlier nodes with a probability $P(h) \propto d$ that depends linearly on the degree $d$ of the earlier node $h$. Yet, some networks are better explained by a more general attachment probability $P(h) \propto f(d)$ for some function $f \colon \mathbb N~\to~\mathbb R$. Here, the polynomial case $f(d) = d^α$ where $α\in \mathbb R_{>0}$ is of particular interest. In this paper, we present efficient algorithms that generate graphs according to the more general models. We first design a simple yet optimal sequential algorithm for the polynomial model. We then parallelize the algorithm by identifying batches of independent samples and obtain a near-optimal speedup when adding many nodes. In addition, we present an I/O-efficient algorithm that can even be used for the fully general model. To showcase the efficiency and scalability of our algorithms, we conduct an experimental study and compare their performance to existing solutions.

cs.DS↗

arXiv2022

Algorithms for Large-scale Network Analysis and the NetworKit Toolkit

The abundance of massive network data in a plethora of applications makes scalable analysis algorithms and software tools necessary to generate knowledge from such data in reasonable time. Addressing scalability as well as other requirements such as good usability and a rich feature set, the open-source software NetworKit has established itself as a popular tool for large-scale network analysis. This chapter provides a brief overview of the contributions to NetworKit made by the DFG Priority Programme SPP 1736 Algorithms for Big Data. Algorithmic contributions in the areas of centrality computations, community detection, and sparsification are in the focus, but we also mention several other aspects -- such as current software engineering principles of the project and ways to visualize network data within a NetworKit-based workflow.

cs.SI↗

arXiv2021

Near optimal sparsity-constrained group testing: improved bounds and algorithms

Recent advances in noiseless non-adaptive group testing have led to a precise asymptotic characterization of the number of tests required for high-probability recovery in the sublinear regime $k = n^θ$ (with $θ\in (0,1)$), with $n$ individuals among which $k$ are infected. However, the required number of tests may increase substantially under real-world practical constraints, notably including bounds on the maximum number $Δ$ of tests an individual can be placed in, or the maximum number $Γ$ of individuals in a given test. While previous works have given recovery guarantees for these settings, significant gaps remain between the achievability and converse bounds. In this paper, we substantially or completely close several of the most prominent gaps. In the case of $Δ$-divisible items, we show that the definite defectives (DD) algorithm coupled with a random regular design is asymptotically optimal in dense scaling regimes, and optimal to within a factor of $\eul$ more generally; we establish this by strengthening both the best known achievability and converse bounds. In the case of $Γ$-sized tests, we provide a comprehensive analysis of the regime $Γ= Θ(1)$, and again establish a precise threshold proving the asymptotic optimality of SCOMP (a slight refinement of DD) equipped with a tailored pooling scheme. Finally, for each of these two settings, we provide near-optimal adaptive algorithms based on sequential splitting, and provably demonstrate gaps between the performance of optimal adaptive and non-adaptive algorithms.

cs.DS↗

arXiv2021

Engineering Uniform Sampling of Graphs with a Prescribed Power-law Degree Sequence

We consider the following common network analysis problem: given a degree sequence $\mathbf{d} = (d_1, \dots, d_n) \in \mathbb N^n$ return a uniform sample from the ensemble of all simple graphs with matching degrees. In practice, the problem is typically solved using Markov Chain Monte Carlo approaches, such as Edge-Switching or Curveball, even if no practical useful rigorous bounds are known on their mixing times. In contrast, Arman et al. sketch Inc-Powerlaw, a novel and much more involved algorithm capable of generating graphs for power-law bounded degree sequences with $γ\gtrapprox 2.88$ in expected linear time. For the first time, we give a complete description of the algorithm and add novel switchings. To the best of our knowledge, our open-source implementation of Inc-Powerlaw is the first practical generator with rigorous uniformity guarantees for the aforementioned degree sequences. In an empirical investigation, we find that for small average-degrees Inc-Powerlaw is very efficient and generates graphs with one million nodes in less than a second. For larger average-degrees, parallelism can partially mitigate the increased running-time.

cs.DS↗

arXiv2021

Efficient and accurate group testing via Belief Propagation: an empirical study

The group testing problem asks for efficient pooling schemes and algorithms that allow to screen moderately large numbers of samples for rare infections. The goal is to accurately identify the infected samples while conducting the least possible number of tests. Exploring the use of techniques centred around the Belief Propagation message passing algorithm, we suggest a new test design that significantly increases the accuracy of the results. The new design comes with Belief Propagation as an efficient inference algorithm. Aiming for results on practical rather than asymptotic problem sizes, we conduct an experimental study.

cs.AI↗

arXiv2020

Simulating Population Protocols in Sub-Constant Time per Interaction

We consider the problem of efficiently simulating population protocols. In the population model, we are given a distributed system of $n$ agents modeled as identical finite-state machines. In each time step, a pair of agents is selected uniformly at random to interact. In an interaction, agents update their states according to a common transition function. We empirically and analytically analyze two classes of simulators for this model. First, we consider sequential simulators executing one interaction after the other. Key to the performance of these simulators is the data structure storing the agents' states. For our analysis, we consider plain arrays, binary search trees, and a novel Dynamic Alias Table data structure. Secondly, we consider batch processing to efficiently update the states of multiple independent agents in one step. For many protocols considered in literature, our simulator requires amortized sub-constant time per interaction and is fast in practice: given a fixed time budget, the implementation of our batched simulator is able to simulate population protocols several orders of magnitude larger compared to the sequential competitors, and can carry out $2^{50}$ interactions among the same number of agents in less than 400s.

cs.DS↗

arXiv2020

Recent Advances in Scalable Network Generation

Random graph models are frequently used as a controllable and versatile data source for experimental campaigns in various research fields. Generating such data-sets at scale is a non-trivial task as it requires design decisions typically spanning multiple areas of expertise. Challenges begin with the identification of relevant domain-specific network features, continue with the question of how to compile such features into a tractable model, and culminate in algorithmic details arising while implementing the pertaining model. In the present survey, we explore crucial aspects of random graph models with known scalable generators. We begin by briefly introducing network features considered by such models, and then discuss random graphs alongside with generation algorithms. Our focus lies on modelling techniques and algorithmic primitives that have proven successful in obtaining massive graphs. We consider concepts and graph models for various domains (such as social network, infrastructure, ecology, and numerical simulations), and discuss generators for different models of computation (including shared-memory parallelism, massive-parallel GPUs, and distributed systems).

cs.DS↗

arXiv2020

The random 2-SAT partition function

We show that throughout the satisfiable phase the normalised number of satisfying assignments of a random $2$-SAT formula converges in probability to an expression predicted by the cavity method from statistical physics. The proof is based on showing that the Belief Propagation algorithm renders the correct marginal probability that a variable is set to `true' under a uniformly random satisfying assignment.

math.PR↗

arXiv2019

Bidirectional Text Compression in External Memory

Bidirectional compression algorithms work by substituting repeated substrings by references that, unlike in the famous LZ77-scheme, can point to either direction. We present such an algorithm that is particularly suited for an external memory implementation. We evaluate it experimentally on large data sets of size up to 128 GiB (using only 16 GiB of RAM) and show that it is significantly faster than all known LZ77 compressors, while producing a roughly similar number of factors. We also introduce an external memory decompressor for texts compressed with any uni- or bidirectional compression scheme.

cs.DS↗

arXiv2019

Fragile Complexity of Comparison-Based Algorithms

We initiate a study of algorithms with a focus on the computational complexity of individual elements, and introduce the fragile complexity of comparison-based algorithms as the maximal number of comparisons any individual element takes part in. We give a number of upper and lower bounds on the fragile complexity for fundamental problems, including Minimum, Selection, Sorting and Heap Construction. The results include both deterministic and randomized upper and lower bounds, and demonstrate a separation between the two settings for a number of problems. The depth of a comparator network is a straight-forward upper bound on the worst case fragile complexity of the corresponding fragile algorithm. We prove that fragile complexity is a different and strictly easier property than the depth of comparator networks, in the sense that for some problems a fragile complexity equal to the best network depth can be achieved with less total work and that with randomization, even a lower fragile complexity is possible.

cs.DS↗

arXiv2019

Efficiently Generating Geometric Inhomogeneous and Hyperbolic Random Graphs

Hyperbolic random graphs (HRG) and geometric inhomogeneous random graphs (GIRG) are two similar generative network models that were designed to resemble complex real world networks. In particular, they have a power-law degree distribution with controllable exponent $β$, and high clustering that can be controlled via the temperature $T$. We present the first implementation of an efficient GIRG generator running in expected linear time. Besides varying temperatures, it also supports underlying geometries of higher dimensions. It is capable of generating graphs with ten million edges in under a second on commodity hardware. The algorithm can be adapted to HRGs. Our resulting implementation is the fastest sequential HRG generator, despite the fact that we support non-zero temperatures. Though non-zero temperatures are crucial for many applications, most existing generators are restricted to $T = 0$. Our generators support parallelization, although this is not the focus of this paper. We note that our generators draw from the correct probability distribution, i.e., they involve no approximation. Besides the generators themselves, we also provide an efficient algorithm to determine the non-trivial dependency between the average degree of the resulting graph and the input parameters of the GIRG model. This makes it possible to specify the expected average degree as input. Moreover, we investigate the differences between HRGs and GIRGs, shedding new light on the nature of the relation between the two models. Although HRGs represent, in a certain sense, a special case of the GIRG model, we find that a straight-forward inclusion does not hold in practice. However, the difference is negligible for most use cases.

cs.DS↗

arXiv2019

Communication-free Massively Distributed Graph Generation

Analyzing massive complex networks yields promising insights about our everyday lives. Building scalable algorithms to do so is a challenging task that requires a careful analysis and an extensive evaluation. However, engineering such algorithms is often hindered by the scarcity of publicly~available~datasets. Network generators serve as a tool to alleviate this problem by providing synthetic instances with controllable parameters. However, many network generators fail to provide instances on a massive scale due to their sequential nature or resource constraints. Additionally, truly scalable network generators are few and often limited in their realism. In this work, we present novel generators for a variety of network models that are frequently used as benchmarks. By making use of pseudorandomization and divide-and-conquer schemes, our generators follow a communication-free paradigm. The resulting generators are thus embarrassingly parallel and have a near optimal scaling behavior. This allows us to generate instances of up to $2^{43}$ vertices and $2^{47}$ edges in less than 22 minutes on 32768 cores. Therefore, our generators allow new graph families to be used on an unprecedented scale.

cs.DC↗

arXiv2018

Parallel and I/O-efficient Randomisation of Massive Networks using Global Curveball Trades

Graph randomisation is a crucial task in the analysis and synthesis of networks. It is typically implemented as an edge switching process (ESMC) repeatedly swapping the nodes of random edge pairs while maintaining the degrees involved. Curveball is a novel approach that instead considers the whole neighbourhoods of randomly drawn node pairs. Its Markov chain converges to a uniform distribution, and experiments suggest that it requires less steps than the established ESMC. Since trades however are more expensive, we study Curveball's practical runtime by introducing the first efficient Curveball algorithms: the I/O-efficient EM-CB for simple undirected graphs and its internal memory pendant IM-CB. Further, we investigate global trades processing every node in a graph during a single super step, and show that undirected global trades converge to a uniform distribution and perform superior in practice. We then discuss EM-GCB and EM-PGCB for global trades and give experimental evidence that EM-PGCB achieves the quality of the state-of-the-art ESMC algorithm EM-ES nearly one order of magnitude faster.

cs.DS↗