004 Datenverarbeitung; Informatik
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Many important graph-theoretic notions can be encoded as counting graph homomorphism problems, such as partition functions in statistical physics, in particular independent sets and colourings. In this article, we study the complexity of #(p) HOMSTOH, the problem of counting graph homomorphisms from an input graph to a graph H modulo a prime number p. Dyer and Greenhill proved a dichotomy stating that the tractability of non-modular counting graph homomorphisms depends on the structure of the target graph. Many intractable cases in non-modular counting become tractable in modular counting due to the common phenomenon of cancellation. In subsequent studies on counting modulo 2, however, the influence of the structure of H on the tractability was shown to persist, which yields similar dichotomies. <br /> Our main result states that for every tree H and every prime p the problem #pHOMSTOH is either polynomial time computable or #P-p-complete. This relates to the conjecture of Faben and Jerrum stating that this dichotomy holds for every graph H when counting modulo 2. In contrast to previous results on modular counting, the tractable cases of #pHOMSTOH are essentially the same for all values of the modulo when H is a tree. To prove this result, we study the structural properties of a homomorphism. As an important interim result, our study yields a dichotomy for the problem of counting weighted independent sets in a bipartite graph modulo some prime p. These results are the first suggesting that such dichotomies hold not only for the modulo 2 case but also for the modular counting functions of all primes p.
Spreadsheets are among the most commonly used file formats for data management, distribution, and analysis. Their widespread employment makes it easy to gather large collections of data, but their flexible canvas-based structure makes automated analysis difficult without heavy preparation. One of the common problems that practitioners face is the presence of multiple, independent regions in a single spreadsheet, possibly separated by repeated empty cells. We define such files as "multiregion" files. In collections of various spreadsheets, we can observe that some share the same layout. We present the Mondrian approach to automatically identify layout templates across multiple files and systematically extract the corresponding regions. Our approach is composed of three phases: first, each file is rendered as an image and inspected for elements that could form regions; then, using a clustering algorithm, the identified elements are grouped to form regions; finally, every file layout is represented as a graph and compared with others to find layout templates. We compare our method to state-of-the-art table recognition algorithms on two corpora of real-world enterprise spreadsheets. Our approach shows the best performances in detecting reliable region boundaries within each file and can correctly identify recurring layouts across files.
Large real-world networks typically follow a power-law degree distribution. To study such networks, numerous random graph models have been proposed. However, real-world networks are not drawn at random. Therefore, Brach et al. (27th symposium on discrete algorithms (SODA), pp 1306-1325, 2016) introduced two natural deterministic conditions: (1) a power-law upper bound on the degree distribution (PLB-U) and (2) power-law neighborhoods, that is, the degree distribution of neighbors of each vertex is also upper bounded by a power law (PLB-N). They showed that many real-world networks satisfy both properties and exploit them to design faster algorithms for a number of classical graph problems. We complement their work by showing that some well-studied random graph models exhibit both of the mentioned PLB properties. PLB-U and PLB-N hold with high probability for Chung-Lu Random Graphs and Geometric Inhomogeneous Random Graphs and almost surely for Hyperbolic Random Graphs. As a consequence, all results of Brach et al. also hold with high probability or almost surely for those random graph classes. In the second part we study three classical NP-hard optimization problems on PLB networks. It is known that on general graphs with maximum degree Delta, a greedy algorithm, which chooses nodes in the order of their degree, only achieves a Omega (ln Delta)-approximation forMinimum Vertex Cover and Minimum Dominating Set, and a Omega(Delta)-approximation forMaximum Independent Set. We prove that the PLB-U property with beta>2 suffices for the greedy approach to achieve a constant-factor approximation for all three problems. We also show that these problems are APX-hard even if PLB-U, PLB-N, and an additional power-law lower bound on the degree distribution hold. Hence, a PTAS cannot be expected unless P = NP. Furthermore, we prove that all three problems are in MAX SNP if the PLB-U property holds.
In recent years, the increased interest in application areas such as social networks has resulted in a rising popularity of graph-based approaches for storing and processing large amounts of interconnected data. To extract useful information from the growing network structures, efficient querying techniques are required.
In this paper, we propose an approach for graph pattern matching that allows a uniform handling of arbitrary constraints over the query vertices. Our technique builds on a previously introduced matching algorithm, which takes concrete host graph information into account to dynamically adapt the employed search plan during query execution. The dynamic algorithm is combined with an existing static approach for search plan generation, resulting in a hybrid technique which we further extend by a more sophisticated handling of filtering effects caused by constraint checks. We evaluate the presented concepts empirically based on an implementation for our graph pattern matching tool, the Story Diagram Interpreter, with queries and data provided by the LDBC Social Network Benchmark. Our results suggest that the hybrid technique may improve search efficiency in several cases, and rarely reduces efficiency.
Duplicate detection describes the process of finding multiple representations of the same real-world entity in the absence of a unique identifier, and has many application areas, such as customer relationship management, genealogy and social sciences, or online shopping. Due to the increasing amount of data in recent years, the problem has become even more challenging on the one hand, but has led to a renaissance in duplicate detection research on the other hand.
This thesis examines the effects and opportunities of transitive relationships on the duplicate detection process. Transitivity implies that if record pairs ⟨ri,rj⟩ and ⟨rj,rk⟩ are classified as duplicates, then also record pair ⟨ri,rk⟩ has to be a duplicate. However, this reasoning might contradict with the pairwise classification, which is usually based on the similarity of objects. An essential property of similarity, in contrast to equivalence, is that similarity is not necessarily transitive.
First, we experimentally evaluate the effect of an increasing data volume on the threshold selection to classify whether a record pair is a duplicate or non-duplicate. Our experiments show that independently of the pair selection algorithm and the used similarity measure, selecting a suitable threshold becomes more difficult with an increasing number of records due to an increased probability of adding a false duplicate to an existing cluster. Thus, the best threshold changes with the dataset size, and a good threshold for a small (possibly sampled) dataset is not necessarily a good threshold for a larger (possibly complete) dataset. As data grows over time, earlier selected thresholds are no longer a suitable choice, and the problem becomes worse for datasets with larger clusters.
Second, we present with the Duplicate Count Strategy (DCS) and its enhancement DCS++ two alternatives to the standard Sorted Neighborhood Method (SNM) for the selection of candidate record pairs. DCS adapts SNMs window size based on the number of detected duplicates and DCS++ uses transitive dependencies to save complex comparisons for finding duplicates in larger clusters. We prove that with a proper (domain- and data-independent!) threshold, DCS++ is more efficient than SNM without loss of effectiveness.
Third, we tackle the problem of contradicting pairwise classifications. Usually, the transitive closure is used for pairwise classifications to obtain a transitively closed result set. However, the transitive closure disregards negative classifications. We present three new and several existing clustering algorithms and experimentally evaluate them on various datasets and under various algorithm configurations. The results show that the commonly used transitive closure is inferior to most other clustering algorithms, especially for the precision of results. In scenarios with larger clusters, our proposed EMCC algorithm is, together with Markov Clustering, the best performing clustering approach for duplicate detection, although its runtime is longer than Markov Clustering due to the subexponential time complexity. EMCC especially outperforms Markov Clustering regarding the precision of the results and additionally has the advantage that it can also be used in scenarios where edge weights are not available.
Polyglot programming allows developers to use multiple programming languages within the same software project. While it is common to use more than one language in certain programming domains, developers also apply polyglot programming for other purposes such as to re-use software written in other languages. Although established approaches to polyglot programming come with significant limitations, for example, in terms of performance and tool support, developers still use them to be able to combine languages.
Polyglot virtual machines (VMs) such as GraalVM provide a new level of polyglot programming, allowing languages to directly interact with each other. This reduces the amount of glue code needed to combine languages, results in better performance, and enables tools such as debuggers to work across languages. However, only a little research has focused on novel tools that are designed to support developers in building software with polyglot VMs. One reason is that tool-building is often an expensive activity, another one is that polyglot VMs are still a moving target as their use cases and requirements are not yet well understood.
In this thesis, we present an approach that builds on existing self-sustaining programming systems such as Squeak/Smalltalk to enable exploratory programming, a practice for exploring and gathering software requirements, and re-use their extensive tool-building capabilities in the context of polyglot VMs. Based on TruffleSqueak, our implementation for the GraalVM, we further present five case studies that demonstrate how our approach helps tool developers to design and build tools for polyglot programming. We further show that TruffleSqueak can also be used by application developers to build and evolve polyglot applications at run-time and by language and runtime developers to understand the dynamic behavior of GraalVM languages and internals. Since our platform allows all these developers to apply polyglot programming, it can further help to better understand the advantages, use cases, requirements, and challenges of polyglot VMs. Moreover, we demonstrate that our approach can also be applied to other polyglot VMs and that insights gained through it are transferable to other programming systems.
We conclude that our research on tools for polyglot programming is an important step toward making polyglot VMs more approachable for developers in practice. With good tool support, we believe polyglot VMs can make it much more common for developers to take advantage of multiple languages and their ecosystems when building software.
Identity management is at the forefront of applications’ security posture. It separates the unauthorised user from the legitimate individual. Identity management models have evolved from the isolated to the centralised paradigm and identity federations. Within this advancement, the identity provider emerged as a trusted third party that holds a powerful position. Allen postulated the novel self-sovereign identity paradigm to establish a new balance. Thus, extensive research is required to comprehend its virtues and limitations. Analysing the new paradigm, initially, we investigate the blockchain-based self-sovereign identity concept structurally. Moreover, we examine trust requirements in this context by reference to patterns. These shapes comprise major entities linked by a decentralised identity provider. By comparison to the traditional models, we conclude that trust in credential management and authentication is removed. Trust-enhancing attribute aggregation based on multiple attribute providers provokes a further trust shift. Subsequently, we formalise attribute assurance trust modelling by a metaframework. It encompasses the attestation and trust network as well as the trust decision process, including the trust function, as central components. A secure attribute assurance trust model depends on the security of the trust function. The trust function should consider high trust values and several attribute authorities. Furthermore, we evaluate classification, conceptual study, practical analysis and simulation as assessment strategies of trust models. For realising trust-enhancing attribute aggregation, we propose a probabilistic approach. The method exerts the principle characteristics of correctness and validity. These values are combined for one provider and subsequently for multiple issuers. We embed this trust function in a model within the self-sovereign identity ecosystem. To practically apply the trust function and solve several challenges for the service provider that arise from adopting self-sovereign identity solutions, we conceptualise and implement an identity broker. The mediator applies a component-based architecture to abstract from a single solution. Standard identity and access management protocols build the interface for applications. We can conclude that the broker’s usage at the side of the service provider does not undermine self-sovereign principles, but fosters the advancement of the ecosystem. The identity broker is applied to sample web applications with distinct attribute requirements to showcase usefulness for authentication and attribute-based access control within a case study.
Modeling and Formal Analysis of Meta-Ecosystems with Dynamic Structure using Graph Transformation
(2022)
The dynamics of ecosystems is of crucial importance. Various model-based approaches exist to understand and analyze their internal effects. In this paper, we model the space structure dynamics and ecological dynamics of meta-ecosystems using the formal technique of Graph Transformation (short GT). We build GT models to describe how a meta-ecosystem (modeled as a graph) can evolve over time (modeled by GT rules) and to analyze these GT models with respect to qualitative properties such as the existence of structural stabilities. As a case study, we build three GT models describing the space structure dynamics and ecological dynamics of three different savanna meta-ecosystems. The first GT model considers a savanna meta-ecosystem that is limited in space to two ecosystem patches, whereas the other two GT models consider two savanna meta-ecosystems that are unlimited in the number of ecosystem patches and only differ in one GT rule describing how the space structure of the meta-ecosystem grows. In the first two GT models, the space structure dynamics and ecological dynamics of the meta-ecosystem shows two main structural stabilities: the first one based on grassland-savanna-woodland transitions and the second one based on grassland-desert transitions. The transition between these two structural stabilities is driven by high-intensity fires affecting the tree components. In the third GT model, the GT rule for savanna regeneration induces desertification and therefore a collapse of the meta-ecosystem. We believe that GT models provide a complementary avenue to that of existing approaches to rigorously study ecological phenomena.
Cyber-physical systems often encompass complex concurrent behavior with timing constraints and probabilistic failures on demand. The analysis whether such systems with probabilistic timed behavior adhere to a given specification is essential. When the states of the system can be represented by graphs, the rule-based formalism of Probabilistic Timed Graph Transformation Systems (PTGTSs) can be used to suitably capture structure dynamics as well as probabilistic and timed behavior of the system. The model checking support for PTGTSs w.r.t. properties specified using Probabilistic Timed Computation Tree Logic (PTCTL) has been already presented. Moreover, for timed graph-based runtime monitoring, Metric Temporal Graph Logic (MTGL) has been developed for stating metric temporal properties on identified subgraphs and their structural changes over time.
In this paper, we (a) extend MTGL to the Probabilistic Metric Temporal Graph Logic (PMTGL) by allowing for the specification of probabilistic properties, (b) adapt our MTGL satisfaction checking approach to PTGTSs, and (c) combine the approaches for PTCTL model checking and MTGL satisfaction checking to obtain a Bounded Model Checking (BMC) approach for PMTGL. In our evaluation, we apply an implementation of our BMC approach in AutoGraph to a running example.
The analysis of behavioral models such as Graph Transformation Systems (GTSs) is of central importance in model-driven engineering. However, GTSs often result in intractably large or even infinite state spaces and may be equipped with multiple or even infinitely many start graphs. To mitigate these problems, static analysis techniques based on finite symbolic representations of sets of states or paths thereof have been devised. We focus on the technique of k-induction for establishing invariants specified using graph conditions. To this end, k-induction generates symbolic paths backwards from a symbolic state representing a violation of a candidate invariant to gather information on how that violation could have been reached possibly obtaining contradictions to assumed invariants. However, GTSs where multiple agents regularly perform actions independently from each other cannot be analyzed using this technique as of now as the independence among backward steps may prevent the gathering of relevant knowledge altogether.
In this paper, we extend k-induction to GTSs with multiple agents thereby supporting a wide range of additional GTSs. As a running example, we consider an unbounded number of shuttles driving on a large-scale track topology, which adjust their velocity to speed limits to avoid derailing. As central contribution, we develop pruning techniques based on causality and independence among backward steps and verify that k-induction remains sound under this adaptation as well as terminates in cases where it did not terminate before.