We prove that maximum weight branchings in directed graphs can be approximated in time O(m) tip to a factor of 1 - epsilon. where epsilon > 0 is an arbitrary constant. (C) 2008 Elsevier B.V. All rights reserved.
We prove that maximum weight branchings in directed graphs can be approximated in time O(m) tip to a factor of 1 - epsilon. where epsilon > 0 is an arbitrary constant. (C) 2008 Elsevier B.V. All rights reserved.
Tarjan (1982) proposed a time algorithm for computing decomposition trees. That algorithm achieved its speed by combining 3 techniques: 1. the O(m) time algorithm for locating strong components, 2. divide-and-conqu...
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Tarjan (1982) proposed a time algorithm for computing decomposition trees. That algorithm achieved its speed by combining 3 techniques: 1. the O(m) time algorithm for locating strong components, 2. divide-and-conquer, and 3. binary search. A simpler algorithm with a faster O(m log n) running time is presented. The simplification is obtained by dropping the use of binary search; the improved running time bound is obtained from a more careful analysis. It is also shown that the problems of sorting and of computing a minimum spanning tree in an undirected graph are linear-time reducible to the decomposition tree problem.
The problem of sink-finding in a directed graph represented by an adjacency matrix, was first introduced as a counterexample to an early version of the Anderaa-Rosenberg (1973) conjecture, which stated that, for P a &...
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The problem of sink-finding in a directed graph represented by an adjacency matrix, was first introduced as a counterexample to an early version of the Anderaa-Rosenberg (1973) conjecture, which stated that, for P a ''natural'' property of graphs, the problem of ascertaining whether P holds for a graph with n vertices, represented by its adjacency matrix, necessitates the examination of 0(n2) matrix entries in the worst case. Anderaa disproved this conjecture by demonstrating that sink-finding can be accomplished using only about 3n matrix accesses. The problem of ascertaining whether a graph has a sink utilizing only 0(n) matrix accesses has since been introduced as an exercise in 2 texts on algorithms. Although it is not difficult to construct an algorithm that performs at most 3n-4 matrix accesses, this algorithm is not optimal. It is demonstrated that the optimal number of matrix accesses is actually 3n-(log n)-3.
High-performance implementations of graph algorithms are challenging to implement on new parallel hardware such as GPUs because of three challenges: (1) the difficulty of coming up with graph building blocks, (2) load...
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High-performance implementations of graph algorithms are challenging to implement on new parallel hardware such as GPUs because of three challenges: (1) the difficulty of coming up with graph building blocks, (2) load imbalance on parallel hardware, and (3) graph problems having low arithmetic intensity. To address some of these challenges, graphBLAS is an innovative, on-going effort by the graph analytics community to propose building blocks based on sparse linear algebra, which allow graph algorithms to be expressed in a performant, succinct, composable, and portable manner. In this paper, we examine the performance challenges of a linear-algebra-based approach to building graph frameworks and describe new design principles for overcoming these bottlenecks. Among the new design principles is exploiting input sparsity, which allows users to write graph algorithms without specifying push and pull direction. Exploiting output sparsity allows users to tell the backend which values of the output in a single vectorized computation they do not want computed. Load-balancing is an important feature for balancing work amongst parallel workers. We describe the important load-balancing features for handling graphs with different characteristics. The design principles described in this paper have been implemented in "graphBLAST", the first high-performance linear algebra-based graph framework on NVIDIA GPUs that is open-source. The results show that on a single GPU, graphBLAST has on average at least an order of magnitude speedup over previous graphBLAS implementations SuiteSparse and GBTL, comparable performance to the fastest GPU hardwired primitives and shared-memory graph frameworks Ligra and Gunrock, and better performance than any other GPU graph framework, while offering a simpler and more concise programming model.
Let GA be a hereditary family of graphs and Ha hereditary family of acyclically directed family of graphs. A graph G(V, E) is a GA-H reduced graph if it can be obtained from a graph GA(V, D) is an element of GA by del...
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Let GA be a hereditary family of graphs and Ha hereditary family of acyclically directed family of graphs. A graph G(V, E) is a GA-H reduced graph if it can be obtained from a graph GA(V, D) is an element of GA by deleting the edges of an edge subgraph H(V, E') is an element of H. The GA-H reduced graphs are a generalization of the complements of the H-mixed graphs. Examples of such families of GA-H reduced graphs are the interval filament graphs, the subtree filament graphs, the circular-arc filament graphs, the cactus subtree filament graphs, the 3D-interval-filament graphs and the subgraph overlap graphs. We describe polynomial time algorithms for various problems on GA-H reduced graphs, when the families GA and H have specific properties. The algorithms are to find maximum independent sets, maximum K-packings, maximum cliques, maximum induced complete bipartite subgraphs, maximum weight holes of a given parity and antiholes of a given parity. (C) 2015 Elsevier B.V. All rights reserved.
Metabolomics experiments seldom achieve their aim of comprehensively covering the entire metabolome. However, important information can be gleaned even from sparse datasets, which can be facilitated by placing the res...
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Metabolomics experiments seldom achieve their aim of comprehensively covering the entire metabolome. However, important information can be gleaned even from sparse datasets, which can be facilitated by placing the results within the context of known metabolic networks. Here we present a method that allows the automatic assignment of identified metabolites to positions within known metabolic networks, and, furthermore, allows automated extraction of sub-networks of biological significance. This latter feature is possible by use of a gap-filling algorithm. The utility of the algorithm in reconstructing and mining of metabolomics data is shown on two independent datasets generated with LC-MS LTQ-Orbitrap mass spectrometry. Biologically relevant metabolic sub-networks were extracted from both datasets. Moreover, a number of metabolites, whose presence eluded automatic selection within mass spectra, could be identified retrospectively by virtue of their inferred presence through gap filling.
Let G = (V, E) be a simple undirected graph with a set V of vertices and a set E of edges. Each vertex v is an element of V has a demand d(v) is an element of Z(+), and a cost c(v) is an element of R+, where Z(+) and ...
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Let G = (V, E) be a simple undirected graph with a set V of vertices and a set E of edges. Each vertex v is an element of V has a demand d(v) is an element of Z(+), and a cost c(v) is an element of R+, where Z(+) and R+ denote the set of nonnegative integers and the set of nonnegative reals, respectively. The source location problem with vertex-connectivity requirements in a given graph G asks to find a set S of vertices minimizing Sigma(v is an element of S) c(v) such that there are at least d(v) pairwise vertex-disjoint paths from S to v for each vertex v is an element of V-S. It is known that the problem is not approximable within a ratio of O(ln Sigma(v is an element of V) d(v)), unless NP has an O(N-loglogN)-time deterministic algorithm. Also, it is known that even if every vertex has a uniform cost and d* = 4 holds, then the problem is NP-hard, where d* = max{d(v) vertical bar v is an element of V}. In this paper, we consider the problem in the case where every vertex has uniform cost. We propose a simple greedy algorithm for providing a max{d*, 2d* - 6}-approximate solution to the problem in O(min{d*, root vertical bar V vertical bar d*vertical bar V vertical bar(2)) time, while we also show that there exists an instance for which it provides no better than a (d* - 1)-approximate solution. Especially, in the case of d* <= 4, we give a tight analysis to show that it achieves an approximation ratio of 3. We also show the APX-hardness of the problem even restricted to d* <= 4. (C) 2009 Elsevier B.V. All rights reserved.
We develop a research community extraction algorithm from large bibliographic data, which was preliminarily reported in Horiike et al. [10] and Nakamura et al. [18]. A research community in bibliographic data is consi...
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We develop a research community extraction algorithm from large bibliographic data, which was preliminarily reported in Horiike et al. [10] and Nakamura et al. [18]. A research community in bibliographic data is considered to be a set of the linked texts holding a common topic, in other words, it is a dense subgraph embedded in the directed graph. Our method is based on the maximum flow algorithm for finding web communities by Flake et al. [5]. We propose improvements of the algorithm to select community nodes and initial seeds taking account of the restriction that any directed graph is acyclic. We examine the improved algorithm for the list of keywords frequently appearing in the bibliographic data. In addition we propose a simple method to extract characteristic keywords for deciding initial seed nodes. This method is also evaluated by experiments.
A tree t-spanner T of a graph G is a spanning tree in which the distance between every pair of vertices is at most t times their distance in G. This notion is motivated by applications in communication networks, distr...
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A tree t-spanner T of a graph G is a spanning tree in which the distance between every pair of vertices is at most t times their distance in G. This notion is motivated by applications in communication networks, distributed systems, and network design. This paper studies graph-theoretic, algorithmic, and complexity issues about tree spanners. It is shown that a tree 1-spanner, if it exists, in a weighted graph with m edges and n vertices is a minimum spanning tree and can be found in O(m log beta(m, n)) time, where beta(m, n) = min{iota\log((iota)) n less than or equal to m/n}. On the other hand, for any fixed t > 1, the problem of determining the existence of a tree t-spanner in a weighted graph is proven to be NP-complete. For unweighted graphs, it is shown that constructing a tree t-spanner takes linear time, whereas determining the existence of a tree t-spanner is NP-complete for any fixed t greater than or equal to 4. A theorem that captures the structure of tree 2-spanners is presented for unweighted graphs. For digraphs, an O((m + n)alpha(m, n)) algorithm is provided for finding a tree t-spanner with t as small as possible, where alpha(m, n) is a functional inverse of Ackerman's function. The results for tree spanners on undirected graphs are extended to ''quasi-tree spanners'' on digraphs. Furthermore, linear-time algorithms are derived for verifying tree spanners and quasi-tree spanners.
Cloud computing services have found widespread use recently. Offloading computations to public clouds has many benefits albeit harming the privacy of users and data. Homomorphic encryption facilitates cloud computing ...
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ISBN:
(纸本)9798350343557
Cloud computing services have found widespread use recently. Offloading computations to public clouds has many benefits albeit harming the privacy of users and data. Homomorphic encryption facilitates cloud computing services that can do computations over encrypted data without requiring decryption and this enables privacy-preserving applications. In this paper, we propose an approach for confidentially finding islands (connected components) in a graph. We present various performance evaluation results and show that privacy-preservation can be achieved with a cost of computation overhead.
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