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Exact algorithm for graph homomorphism and locally injective graph homomorphism

INFORMATION PROCESSING LETTERS 2014年第7期114卷 387-391页

作者： Rzazewski, Pawel Warsaw Univ Technol Fac Math & Informat Sci PL-00662 Warsaw Poland

For graphs G and H, a homomorphism from G to H is a function phi: V(G) -> V(H), which maps vertices adjacent in G to adjacent vertices of H. A homomorphism is locally injective if no two vertices with a common neighbor are mapped to a single vertex in H. Many cases of graph homomorphism and locally injective graph homomorphism are NP-complete, so there is little hope to design polynomial-time algorithms for them. In this paper we present an algorithm for graph homomorphism and locally injective homomorphism working in time O*((b + 2)(vertical bar V(G)vertical bar)), where b is the bandwidth of the complement of H. (C) 2014 Elsevier B.V. All rights reserved.

关键词： graph algorithms graph homomorphism Locally injective homomorphism H(2,1)-labeling Exact algorithm

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Vertex Ordering, Clustering, and Their Application to graph Partitioning

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APPLIED MATHEMATICS & INFORMATION SCIENCES 2014年第1期8卷 135-138页

作者： Yoon, Yourim Kim, Yong-Hyuk LG Elect Future IT R&D Lab Seoul 137724 South Korea Kwangwoon Univ Dept Comp Sci & Engn Seoul 139701 South Korea

We propose a new heuristic for vertex ordering and a method that splits the vertex ordering into clusters. We apply them to the graph partitioning problem. The application of these ideas incorporates reordering in genetic algorithms and the identification of clustered structures in graphs. Experimental tests on benchmark graphs showed that the new vertex-ordering scheme performed better than existing methods in terms of genetic algorithms, and that the clusters were successfully captured.

关键词： graph algorithms design of algorithms graph partitioning vertex ordering graph clustering genetic algorithm

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The cohomology ring of the GKM graph of a flag manifold of classical type

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KYOTO JOURNAL OF MATHEMATICS 2014年第3期54卷 653-677页

作者： Fukukawa, Yukiko Ishida, Hiroaki Masuda, Mikiya Osaka City Univ Dept Math Sumiyoshi Ku Osaka 5588585 Japan Osaka City Univ Adv Math Inst Sumiyoshi Ku Osaka 5588585 Japan

If a closed smooth manifold M with an action of a torus T satisfies certain conditions, then a labeled graph gm with labeling in H-2 (BT) is associated with M, which encodes a lot of geometrical information on M. For instance, the "graph cohomology" ring H*(T) (G(m)) of gm is defined to be a subring of evev(gm) H*(BT), where V(gm) is the set of vertices of gm, and is known to be often isomorphic to the equivariant cohomology H*(T) (G(m)) of M. In this paper, we determine the ring structure of H*(T) (G(m)) with Z (resp., Z[1/2]) coefficients when M is a flag manifold of type A, B, or D (resp., C) in an elementary way.

关键词： COHOMOLOGY theory RING theory FLAG manifolds (Mathematics) ISOMORPHISMS (Mathematics) graph algorithms

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Fast transformation from time series to visibility graphs

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CHAOS 2015年第8期25卷 083105-083105页

作者： Lan, Xin Mo, Hongming Chen, Shiyu Liu, Qi Deng, Yong Southwest Univ Sch Comp & Informat Sci Chongqing 400715 Peoples R China Sichuan Univ Nationalities Dept Tibetan Language Kangding 626001 Sichuan Peoples R China Vanderbilt Univ Med Ctr Dept Biomed Informat Nashville TN 37232 USA

The visibility graph method is used to transform time series into complex networks. In this letter, a fast transform algorithm is proposed for obtaining a visibility graph. Based on the strategy of "divide & conquer," the time complexity of the proposed algorithm is raised to O(n log n), which is more efficient than the previous basic algorithm whose time complexity is O(n(2)). (C) 2015 AIP Publishing LLC.

关键词： graph algorithms TIME series analysis AFFINE transformations BIOLOGICALLY-inspired computing graph connectivity

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VERTEXICA: Your Relational Friend for graph Analytics!

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PROCEEDINGS OF THE VLDB ENDOWMENT 2014年第13期7卷 1669-1672页

作者： Jindal, Alekh Rawlani, Praynaa Wu, Eugene Madden, Samuel Deshpande, Amol Stonebraker, Mike MIT CSAIL Cambridge MA 02139 USA Univ Maryland Baltimore MD 21201 USA

In this paper, we present VERTEXICA, a graph analytics tools on top of a relational database, which is user friendly and yet highly efficient. Instead of constraining programmers to SQL, VERTEXICA offers a popular vertex-centric query interface, which is more natural for analysts to express many graph queries. The programmers simply provide their vertex-compute functions and VERTEXICA takes care of efficiently executing them in the standard SQL engine. The advantage of using VERTEXICA is its ability to leverage the relational features and enable much more sophisticated graph analysis. These include expressing graph algorithms which are difficult in vertex centric but straightforward in SQL and the ability to compose end to-end data processing pipelines, including pre- and post-processing of graphs as well as combining multiple algorithms for deeper insights. VERTEXICA has a graphical user interface and we outline several demonstration scenarios including, interactive graph analysis, complex graph analysis, and continuous and time series analysis.

关键词： graph theory Data handling graphical user interfaces Pipeline processing systems Query processing Time series analysis Data processing pipelines graph algorithms graph analytics Multiple algorithms Post processing Query interfaces Relational Database Relational features

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Fast Sequential and Parallel Vertex Relabelings

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INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE 2015年第1期26卷 33-50页

作者： Kantabutra, Sanpawat Chiang Mai Univ Fac Engn Dept Comp Engn Theory Comp Grp Chiang Mai 50200 Thailand

Given an undirected, connected, simple graph G = (V, E), two vertex labelings L-V and of the vertices of G, and a label flip operation that interchanges a pair of labels on adjacent vertices, the VERTEX RELABELING PROBLEM is to transform G from L-V into L-V' using the flip operation. Agnarsson et al. showed solving the VERTEX RELABELING PROBLEM on arbitrary graphs can be done in theta(n(2)), where n is the number of vertices in G. In this article we study the VERTEX RELABELING PROBLEM on graphs K-m,K-m and introduce the concept of parity and precise labelings. We show that when we consider the parity labeling, the problem on graphs K-m,K-m can be solved quickly in O(log m) time using or processors on an DREW PRAM. Additionally, we also show that the number of processors can be further reduced to m/log m in this case while the time complexity does not change. When the labeling is precise, the parallel time complexity increases by a factor of log in while the processor complexities remain m and m/log m. We also show that when graphs are restricted to Km, this problem can be solved optimally in O(m) time when the labeling is parity, and can be solved in O(m log m) time when the labeling is precise, thereby improving the result in Agnarsson et of for this specific case. Moreover, we generalize the result in the case of precise labeling to the cases when L-V and L-V' can be any configuration. In the end we give a conclusion and a list of some interesting open problems.

关键词： graph relabeling graph algorithms complexity

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graphCT: Multithreaded algorithms for Massive graph Analysis

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IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 2013年第11期24卷 2220-2229页

作者： Ediger, David Jiang, Karl Riedy, E. Jason Bader, David A. Georgia Inst Technol Sch Computat Sci & Engn Atlanta GA 30332 USA

The digital world has given rise to massive quantities of data that include rich semantic and complex networks. A social graph, for example, containing hundreds of millions of actors and tens of billions of relationships is not uncommon. Analyzing these large data sets, even to answer simple analytic queries, often pushes the limits of algorithms and machine architectures. We present graphCT, a scalable framework for graph analysis using parallel and multithreaded algorithms on shared memory platforms. Utilizing the unique characteristics of the Cray XMT, graphCT enables fast network analysis at unprecedented scales on a variety of input data sets. On a synthetic power law graph with 2 billion vertices and 17 billion edges, we can find the connected components in 2 minutes. We can estimate the betweenness centrality of a similar graph with 537 million vertices and over 8 billion edges in under 1 hour. graphCT is built for portability and performance.

关键词： graph algorithms network analysis Cray XMT multithreaded architectures high-performance computing

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Fast Parallel Conversion of Edge List to Adjacency List for Large-Scale graphs 15

Fast Parallel Conversion of Edge List to Adjacency List for ...

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Simulation Multiconference

作者： Shaikh Arifuzzaman Maleq Khan Department of Computer Science Virginia Tech Network Dynamics & Simulation Science Lab Virginia Bioinformatics Institute Virginia Tech

ISBN: (纸本)9781510801011

In the era of Bigdata, we are deluged with massive graph data emerged from numerous social and scientific applications. In most cases, graph data are generated as lists of edges (edge list), where an edge denotes a link between a pair of entities. However, most of the graph algorithms work efficiently when information of the adjacent nodes (adjacency list) for each node is readily available. Although the conversion from edge list to adjacency list can be trivially done on the fly for small graphs, such conversion becomes challenging for the emerging large-scale graphs consisting billions of nodes and edges. These graphs do not fit into the main memory of a single computing machine and thus require distributed-memory parallel or external-memory algorithms. In this paper, we present efficient MPI-based distributed memory parallel algorithms for converting edge lists to adjacency lists. To the best of our knowledge, this is the first work on this problem. To address the critical load balancing issue, we present a parallel load balancing scheme which improves both time and space efficiency significantly. Our fast parallel algorithm works on massive graphs, achieves very good speedups, and scales to large number of processors. The algorithm can convert an edge list of a graph with 20 billion edges to the adjacency list in less than 2 minutes using 1024 processors. Denoting the number of nodes, edges and processors by n, m, and P, respectively, the time complexity of our algorithm is O(m/P + n + P) which provides a speedup factor of at least Ω(min{P, d_(avg)}), where d_(avg) is the average degree of the nodes. The algorithm has a space complexity of O(m/P), which is optimal.

关键词： Parallel algorithms Massive graphs Bigdata Edge List Adjacency List Load Balancing Parallel algorithms Load balancing edges Edge of a figure or solid graph data speedup factor space complexities graph algorithms PROCESSOR Ganglia LIST concurrent conversion distributed memory

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Extending SPARQL with graph functions 2

Extending SPARQL with graph functions

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IEEE International Conference on Big Data

作者： Mizell, David Maschhoff, Kristyn J. Reinhardt, Steven P. Cray Inc YarcData Seattle WA 98164 USA

ISBN: (纸本)9781479956661

Much of the early domain-specific success with graph analytics has been with algorithms whose results are based on global graph structure. An example of such an algorithm is betweenness centrality, whose value for any vertex potentially depends on the number of shortest paths between all pairs of vertices in the entire graph. YarcData's Urika (TM) customers use SPARQL's graph-oriented pattern-matching capabilities, but many of them also require a capability to call graph functions such as betweenness centrality. This customer feedback led us to combine SPARQL 1.1's query capabilities with classical and emerging graph-analytic algorithms (e.g., community detection, shortest path, betweenness, BadRank). With this capability, a SPARQL query can select a specific subgraph of interest, pass that subgraph to a graph algorithms for deep analysis, and then pass those results back to an enclosing SPARQL query that post-processes those results as needed. With the Summer 2014 Urika release, we have extended the SPARQL implementation with a graph-function capability and a small set of built-in graph functions. We describe our design approach and our experiences with this first release, including anecdotal evidence of dramatically higher performance. Built-in graph functions represent an important step in the maturation of graph analysis and SPARQL. As common motifs emerge from use cases, those motifs may be mapped to specific graph functions that can be highly tuned for much higher performance than will be possible for SPARQL. Identifying those motifs and developing the underlying graph functions to accelerate their execution is a topic of intense effort industry-wide. graph functions merged with SPARQL provide a new mechanism by which third-party graph-algorithm developers may expose their algorithms to widespread use.

关键词： graph analytics SPARQL scalability graph algorithms

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Immortalgraph: A System for Storage and Analysis of Temporal graphs

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ACM TRANSACTIONS ON STORAGE 2015年第3期11卷 14-14页

作者： Miao, Youshan Han, Wentao Li, Kaiwei Wu, Ming Yang, Fan Zhou, Lidong Prabhakaran, Vijayan Chen, Enhong Chen, Wenguang Univ Sci & Technol China Hefei 230026 Peoples R China

Temporal graphs that capture graph changes over time are attracting increasing interest from research communities, for functions such as understanding temporal characteristics of social interactions on a time-evolving social graph. Immortalgraph is a storage and execution engine designed and optimized specifically for temporal graphs. Locality is at the center of Immortalgraph's design: temporal graphs are carefully laid out in both persistent storage and memory, taking into account data locality in both time and graph-structure dimensions. Immortalgraph introduces the notion of locality-aware batch scheduling in computation, so that common "bulk" operations on temporal graphs are scheduled to maximize the benefit of in-memory data locality. The design of Immortalgraph explores an interesting interplay among locality, parallelism, and incremental computation in supporting common mining tasks on temporal graphs. The result is a high-performance temporal-graph system that is up to 5 times more efficient than existing database solutions for graph queries. The locality optimizations in Immortalgraph offer up to an order of magnitude speedup for temporal iterative graph mining compared to a straightforward application of existing graph engines on a series of snapshots.

关键词： Design algorithms Concurrent computing temporal graph graph algorithms

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