538 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

    Get PDF
    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    A survey of Bayesian Network structure learning

    Get PDF

    Traversing combinatorial 0/1-polytopes via optimization

    Get PDF
    In this paper, we present a new framework that exploits combinatorial optimization for efficiently generating a large variety of combinatorial objects based on graphs, matroids, posets and polytopes. Our method relies on a simple and versatile algorithm for computing a Hamilton path on the skeleton of any 0/1-polytope \conv(X), where X\seq \{0,1\}^n. The algorithm uses as a black box any algorithm that solves a variant of the classical linear optimization problem~min⁥{w⋅x∣x∈X}\min\{w\cdot x\mid x\in X\}, and the resulting delay, i.e., the running time per visited vertex on the Hamilton path, is only by a factor of log⁥n\log n larger than the running time of the optimization algorithm. When XX encodes a particular class of combinatorial objects, then traversing the skeleton of the polytope~\conv(X) along a Hamilton path corresponds to listing the combinatorial objects by local change operations, i.e., we obtain Gray code listings. As concrete results of our general framework, we obtain efficient algorithms for generating all (cc-optimal) bases and independent sets in a matroid; (cc-optimal) spanning trees, forests, matchings, maximum matchings, and cc-optimal matchings in a general graph; vertex covers, minimum vertex covers, cc-optimal vertex covers, stable sets, maximum stable sets and cc-optimal stable sets in a bipartite graph; as well as antichains, maximum antichains, cc-optimal antichains, and cc-optimal ideals of a poset. Specifically, the delay and space required by these algorithms are polynomial in the size of the matroid ground set, graph, or poset, respectively. Furthermore, all of these listings correspond to Hamilton paths on the corresponding combinatorial polytopes, namely the base polytope, matching polytope, vertex cover polytope, stable set polytope, chain polytope and order polytope, respectively. As another corollary from our framework, we obtain an \cO(t_{\upright{LP}} \log n) delay algorithm for the vertex enumeration problem on 0/1-polytopes {x∈Rn∣Ax≀b}\{x\in\mathbb{R}^n\mid Ax\leq b\}, where A∈Rm×nA\in \mathbb{R}^{m\times n} and~b∈Rmb\in\mathbb{R}^m, and t_{\upright{LP}} is the time needed to solve the linear program min⁥{w⋅x∣Ax≀b}\min\{w\cdot x\mid Ax\leq b\}. This improves upon the 25-year old \cO(t_{\upright{LP}}\,n) delay algorithm due to Bussieck and L\"ubbecke

    Parameterized Graph Modification Beyond the Natural Parameter

    Get PDF

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

    Get PDF
    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Parameterized Graph Modification Beyond the Natural Parameter

    Get PDF

    Deep Learning Techniques for Multi-Dimensional Medical Image Analysis

    Get PDF

    GraphflowDB: Scalable Query Processing on Graph-Structured Relations

    Get PDF
    Finding patterns over graph-structured datasets is ubiquitous and integral to a wide range of analytical applications, e.g., recommendation and fraud detection. When expressed in the high-level query languages of database management systems (DBMSs), these patterns correspond to many-to-many join computations, which generate very large intermediate relations during query processing and degrade the performance of existing systems. This thesis argues that modern query processors need to adopt two novel techniques to be efficient on growing many-to-many joins: (i) worst-case optimal join algorithms; and (ii) factorized representations. Traditional query processors generate join plans that use binary joins, which in iteration take two relations, base or intermediate, to join and produce a new relation. The theory of worst-case optimal joins have shown that this style of join processing can be provably suboptimal and hence generate unnecessarily large intermediate results. This can be avoided on cyclic join queries if the join is performed in a multi-way fashion a join-attribute-at-a-time. As its first contribution, this thesis proposes the design and implementation of a query processor and optimizer that can generate plans that mix worst-case optimal joins, i.e., attribute-at-a-time joins and binary joins, i.e., table-at-a-time joins. In contrast to prior approaches with novel join optimizers that require solving hard computational problems, such as computing low-width hypertree decompositions of queries, our join optimizer is cost-based and uses a traditional dynamic programming approach with a new cost metric. On acyclic queries, or acyclic parts of queries, sometimes the generation of large intermediate results cannot be avoided. Yet, the theory of factorization has shown that often such intermediate results can be highly compressible if they contain multi-valued dependencies between join attributes. Factorization proposes two relation representation schemes, called f- and d-representations, to represent the large intermediate results generated under many-to-many joins in a compressed format. Existing proposals to adopt factorized representations require designing processing on fully materialized general tries and novel operators that operate on entire tries, which are not easy to adopt in existing systems. As a second contribution, we describe the implementation of a novel query processing approach we call factorized vector execution that adopts f-representations. Factorized vector execution extends the traditional vectorized query processors to use multiple blocks of vectors instead of a single block allowing us to factorize intermediate results and delay or even avoid Cartesian products. Importantly, our design ensures that every core operator in the system still performs computations on vectors. As a third contribution, we further describe how to extend our factorized vector execution model with novel operators to adopt d-representations, which extend f-representations with cached and reused sub-relations. Our design here is based on using nested hash tables that can point to sub-relations instead of copying them and on directed acyclic graph-based query plans. All of our techniques are implemented in the GraphflowDB system, which was developed throughout the years to facilitate the research in this thesis. We demonstrate that GraphflowDB’s query processor can outperform existing approaches and systems by orders of magnitude on both micro-benchmarks and end-to-end benchmarks. The designs proposed in this thesis adopt common-wisdom query processing techniques of pipelining, vector-based execution, and morsel-driven parallelism to ensure easy adoption in existing systems. We believe the design can serve as a blueprint for how to adopt these techniques in existing DBMSs to make them more efficient on workloads with many-to-many joins

    Operational Research: methods and applications

    Get PDF
    This is the final version. Available on open access from Taylor & Francis via the DOI in this recordThroughout its history, Operational Research has evolved to include methods, models and algorithms that have been applied to a wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first summarises the up-to-date knowledge and provides an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion and used as a point of reference by a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes

    Ophelia

    Get PDF
    Ophelia (1851-2) is the title of a Pre-Raphaelite painting by John Everett Millais narrating the final moments of Shakespeare’s heroine in Hamlet (1599-1601): the former is considered the best-known picture in all Victorian art and the latter, the greatest work in English literature. Nonetheless, Ophelia owes its significance and enduring popularity to these monumental artworks, as well as the fantasies of “Woman” she embodies in successive discourses, and the material, semantic, and social networks she progressively integrates. The eight-hundred years span of such networks, their size and complexity across media and cultures, seem proof enough to consider Ophelia a “hyperobject.” Although Timothy Morton introduced it as a philosophical and ecological concept to deal with “things that are massively distributed in time and space relative to humans,” Ophelia shows the same characteristic properties (viscosity, nonlocality, temporal undularity, phasing, interobjectivity) and ontological structure, a mesh constituted by a dynamic mixture of strands in which component objects interact, and gaps in which they withdraw remaining unknowable. The reconceptualization constructs Ophelia as a new object of transdisciplinary research, overcoming limitations of previous studies that focused on character analysis, historical period, or discipline. Further, the hyperobject provides an ideal medium in which Ophelia arises, develops, and is resolved or abandoned as problem, and of which the answers to that problem are also part. The chapters that follow will address three questions about Millais’ Ophelia: What is Millais’ answer to Ophelia? Where does Ophelia fit in art history and modernity? What did Millais want from Ophelia and what does Ophelia want from the public
    • 

    corecore