All Maximal Independent Sets and Dynamic Dominance for Sparse Graphs

We describe algorithms, based on Avis and Fukuda's reverse search paradigm, for listing all maximal independent sets in a sparse graph in polynomial time and delay per output. For bounded degree graphs, our algorithms take constant time per set generated; for minor-closed graph families, the time is O(n) per set, and for more general sparse graph families we achieve subquadratic time per set. We also describe new data structures for maintaining a dynamic vertex set S in a sparse or minor-closed graph family, and querying the number of vertices not dominated by S; for minor-closed graph families the time per update is constant, while it is sublinear for any sparse graph family. We can also maintain a dynamic vertex set in an arbitrary m-edge graph and test the independence of the maintained set in time O(sqrt m) per update. We use the domination data structures as part of our enumeration algorithms.Comment: 10 page

Efficient Path Enumeration and Structural Clustering on Massive Graphs

Graph analysis plays a crucial role in understanding the relationships and structures within complex systems. This thesis focuses on addressing fundamental problems in graph analysis, including hop-constrained s-t simple path (HC-s-t path) enumeration, batch HC-s-t path query processing, and graph structural clustering (SCAN). The objective is to develop efficient and scalable distributed algorithms to tackle these challenges, particularly in the context of billion-scale graphs. We first explore the problem of HC-s-t path enumeration. Existing solutions for this problem often suffer from inefficiency and scalability limitations, especially when dealing with billion-scale graphs. To overcome these drawbacks, we propose a novel hybrid search paradigm specifically tailored for HC-s-t path enumeration. This paradigm combines different search strategies to effectively explore the solution space. Building upon this paradigm, we devise a distributed enumeration algorithm that follows a divide-and-conquer strategy, incorporates fruitless exploration pruning, and optimizes memory consumption. Experimental evaluations on various datasets demonstrate that our algorithm achieves a significant speedup compared to existing solutions, even on datasets where they encounter out-of-memory issues. Secondly, we address the problem of batch HC-s-t path query processing. In real-world scenarios, it is common to issue multiple HC-s-t path queries simultaneously and process them as a batch. However, existing solutions often focus on optimizing the processing performance of individual queries, disregarding the benefits of processing queries concurrently. To bridge this gap, we propose the concept of HC-s path queries, which captures the common computation among different queries. We design a two-phase HC-s path query detection algorithm to identify the shared computation for a given set of HC-s-t path queries. Based on the detected HC-s path queries, we develop an efficient HC-s-t path enumeration algorithm that effectively shares the common computation. Extensive experiments on diverse datasets validate the efficiency and scalability of our algorithm for processing multiple HC-s-t path queries concurrently. Thirdly, we investigate the problem of graph structural clustering (SCAN) in billion-scale graphs. Existing distributed solutions for SCAN often lack efficiency or suffer from high memory consumption, making them impractical for large-scale graphs. To overcome these challenges, we propose a fine-grained clustering framework specifically tailored for SCAN. This framework enables effective identification of cohesive subgroups within a graph. Building upon this framework, we devise a distributed SCAN algorithm that minimizes communication overhead and reduces memory consumption throughout the execution. We also incorporate an effective workload balance mechanism that dynamically adjusts to handle skewed workloads. Experimental evaluations on real-world graphs demonstrate the efficiency and scalability of our proposed algorithm. Overall, this thesis contributes novel distributed algorithms for HC-s-t path enumeration, batch HC-s-t path query processing, and graph structural clustering. The proposed algorithms address the efficiency and scalability challenges in graph analysis, particularly on billion-scale graphs. Extensive experimental evaluations validate the superiority of our algorithms compared to existing solutions, enabling efficient and scalable graph analysis in complex systems

A Universal Machine for Biform Theory Graphs

Broadly speaking, there are two kinds of semantics-aware assistant systems for mathematics: proof assistants express the semantic in logic and emphasize deduction, and computer algebra systems express the semantics in programming languages and emphasize computation. Combining the complementary strengths of both approaches while mending their complementary weaknesses has been an important goal of the mechanized mathematics community for some time. We pick up on the idea of biform theories and interpret it in the MMTt/OMDoc framework which introduced the foundations-as-theories approach, and can thus represent both logics and programming languages as theories. This yields a formal, modular framework of biform theory graphs which mixes specifications and implementations sharing the module system and typing information. We present automated knowledge management work flows that interface to existing specification/programming tools and enable an OpenMath Machine, that operationalizes biform theories, evaluating expressions by exhaustively applying the implementations of the respective operators. We evaluate the new biform framework by adding implementations to the OpenMath standard content dictionaries.Comment: Conferences on Intelligent Computer Mathematics, CICM 2013 The final publication is available at http://link.springer.com

Data Provenance and Management in Radio Astronomy: A Stream Computing Approach

New approaches for data provenance and data management (DPDM) are required for mega science projects like the Square Kilometer Array, characterized by extremely large data volume and intense data rates, therefore demanding innovative and highly efficient computational paradigms. In this context, we explore a stream-computing approach with the emphasis on the use of accelerators. In particular, we make use of a new generation of high performance stream-based parallelization middleware known as InfoSphere Streams. Its viability for managing and ensuring interoperability and integrity of signal processing data pipelines is demonstrated in radio astronomy. IBM InfoSphere Streams embraces the stream-computing paradigm. It is a shift from conventional data mining techniques (involving analysis of existing data from databases) towards real-time analytic processing. We discuss using InfoSphere Streams for effective DPDM in radio astronomy and propose a way in which InfoSphere Streams can be utilized for large antennae arrays. We present a case-study: the InfoSphere Streams implementation of an autocorrelating spectrometer, and using this example we discuss the advantages of the stream-computing approach and the utilization of hardware accelerators

Foundations of Multi-Paradigm Modelling for Cyber-Physical Systems

This open access book coherently gathers well-founded information on the fundamentals of and formalisms for modelling cyber-physical systems (CPS). Highlighting the cross-disciplinary nature of CPS modelling, it also serves as a bridge for anyone entering CPS from related areas of computer science or engineering. Truly complex, engineered systems—known as cyber-physical systems—that integrate physical, software, and network aspects are now on the rise. However, there is no unifying theory nor systematic design methods, techniques or tools for these systems. Individual (mechanical, electrical, network or software) engineering disciplines only offer partial solutions. A technique known as Multi-Paradigm Modelling has recently emerged suggesting to model every part and aspect of a system explicitly, at the most appropriate level(s) of abstraction, using the most appropriate modelling formalism(s), and then weaving the results together to form a representation of the system. If properly applied, it enables, among other global aspects, performance analysis, exhaustive simulation, and verification. This book is the first systematic attempt to bring together these formalisms for anyone starting in the field of CPS who seeks solid modelling foundations and a comprehensive introduction to the distinct existing techniques that are multi-paradigmatic. Though chiefly intended for master and post-graduate level students in computer science and engineering, it can also be used as a reference text for practitioners