1,721,020 research outputs found
K-best enumeration - theory and application
Full text linkWhere an optimal solution does not contain sufficient information about a given problem instance, enumerating good solutions is a common coping strategy. In combinatorial optimization, k-best enumeration, or ranking, has been studied and applied extensively. The k shortest simple path problem in directed, weighted graphs (kSSP), introduced in 1963 by Clarke, Krikorian and Rausen, is particularly well known. Efficient existing algorithms are based on Yen's algorithm for this problem; they all feature a worst-case running time of O(kn(m + n log n)) on a graph with n vertices and m edges. Vassilevska Williams and Williams show that a polynomially faster kSSP algorithm would also result in an algorithm for the all-pairs shortest path problem with running time O(n\^{3-ε}), which seems unlikely at the moment.
We present a kSSP algorithm that is not based on Yen's algorithm, matching the state-of-the-art running time of O(kn(m + n log n)). In particular, we do not solve a single instance of the replacement path problem, a basic building block of Yen's algorithm. Instead, we make use of ideas used in Eppstein's algorithm for a similar problem where paths are allowed to be non-simple. Using our algorithm, one may find Θ(m) simple paths with a single shortest path tree computation and additional O(m + n) time per path in well-behaved cases. We also propose practical improvements for our algorithm, comprising dynamic edge pruning, lazy shortest path tree computations, and fast path simplicity checks. In a detailed computational study, we demonstrate that well-behaved cases are quite common in random graphs, grids and road networks. We showcase usefulness of the dynamic edge pruning approach on those three graph classes and on network topology graphs. Despite 40 years of heavy research on Yen-based kSSP algorithms, including involved algorithm engineering, our algorithm proves to be faster than existing algorithms by at least an order of magnitude.
However, there is not much room for improvement for the general worst case. We demonstrate that kSSP can be solved considerably faster if the input graph is restricted to have bounded treewidth. Specifically, we propose an algorithm template for enumerating the k best solutions in a bounded treewidth graph for any problem that can be expressed in counting monadic second-order logic. Our template is a generalization of Courcelle's theorem, mainly utilizing dynamic programming and a persistent heap data structure. It enumerates any constant amount of solutions in time O(n). For general k, it requires O(log n) extra time per solution, resulting in a total running time of O(n + k log n). Finding the initial solution is parallelizable, so the linear term can be dropped and we obtain a running time of O(k log n) in the PRAM model. The class of problems expressible in counting monadic second order logic contains kSSP, matching problems, or the spanning tree problem, but also a number of NP-hard problems like the traveling salesman problem, where we achieve a doubly-exponential speedup
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Upward and Orthogonal Planarity are W[1]-Hard Parameterized by Treewidth
Full text linkUpward planarity testing and Rectilinear planarity testing are central problems in graph drawing. It is known that they are both NP -complete, but XP when parameterized by treewidth. In this paper we show that these two problems are W[1]-hard parameterized by treewidth, which answers open problems posed in two earlier papers. The key step in our proof is an analysis of the All-or-Nothing Flow problem, a generalization of which was used as an intermediate step in the NP-completeness proof for both planarity testing problems. We prove that the flow problem is W[1]-hard parameterized by treewidth on planar graphs, and that the existing chain of reductions to the planarity testing problems can be adapted without blowing up the treewidth. Our reductions also show that the known nO ( tw ) -time algorithms cannot be improved to run in time no ( tw ) unless ETH fails.</p
On Families of Planar DAGs with Constant Stack Number
No full textA k-stack layout (or k-page book embedding) of a graph consists of a total order of the vertices, and a partition of the edges into k sets of non-crossing edges with respect to the vertex order. The stack number of a graph is the minimum k such that it admits a k-stack layout. In this paper we study a long-standing problem regarding the stack number of planar directed acyclic graphs (DAGs), for which the vertex order has to respect the orientation of the edges. We investigate upper and lower bounds on the stack number of several families of planar graphs: We improve the constant upper bounds on the stack number of single-source and monotone outerplanar DAGs and of outerpath DAGs, and improve the constant upper bound for upward planar 3-trees. Further, we provide computer-aided lower bounds for upward (outer-) planar DAGs
Fixed-Parameter Algorithms for Computing {RAC} Drawings of Graphs
No full textIn a right-angle crossing (RAC) drawing of a graph, each edge is represented as a polyline and edge crossings must occur at an angle of exactly
, where the number of bends on such polylines is typically restricted in some way. While structural and topological properties of RAC drawings have been the focus of extensive research, little was known about the boundaries of tractability for computing such drawings. In this paper, we initiate the study of RAC drawings from the viewpoint of parameterized complexity. In particular, we establish that computing a RAC drawing of an input graph G with at most b bends (or determining that none exists) is fixed-parameter tractable parameterized by either the feedback edge number of G, or b plus the vertex cover number of G
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
- …
