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A HypergraphPartitioned Vertex Programming Approach for Largescale Consensus Optimization
"... In modern data science problems, techniques for extracting value from big data require performing largescale optimization over heterogenous, irregularly structured data. Much of this data is best represented as multirelational graphs, making vertexprogramming abstractions such as those of Pregel ..."
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Cited by 1 (1 self)
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In modern data science problems, techniques for extracting value from big data require performing largescale optimization over heterogenous, irregularly structured data. Much of this data is best represented as multirelational graphs, making vertexprogramming abstractions such as those
Pregel: A system for largescale graph processing
 IN SIGMOD
, 2010
"... Many practical computing problems concern large graphs. Standard examples include the Web graph and various social networks. The scale of these graphs—in some cases billions of vertices, trillions of edges—poses challenges to their efficient processing. In this paper we present a computational model ..."
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Cited by 492 (0 self)
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model suitable for this task. Programs are expressed as a sequence of iterations, in each of which a vertex can receive messages sent in the previous iteration, send messages to other vertices, and modify its own state and that of its outgoing edges or mutate graph topology. This vertexcentric approach
Algebraic Graph Theory
, 2011
"... Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area is the investiga ..."
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Cited by 892 (13 self)
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is the investigation of the relation between properties of a graph and the spectrum of its adjacency matrix. A central topic and important source of tools is the theory of association schemes. An association scheme is, roughly speaking, a collection of graphs on a common vertex set which fit together in a highly
Finding the k Shortest Paths
, 1997
"... We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest pat ..."
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Cited by 401 (2 self)
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paths from a given source s to each vertex in the graph, in total time O(m + n log n +kn). We describe applications to dynamic programming problems including the knapsack problem, sequence alignment, maximum inscribed polygons, and genealogical relationship discovery.
Retiming Synchronous Circuitry
 ALGORITHMICA
, 1991
"... This paper describes a circuit transformation called retiming in which registers are added at some points in a circuit and removed from others in such a way that the functional behavior of the circuit as a whole is preserved. We show that retiming can be used to transform a given synchronous circui ..."
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Cited by 376 (3 self)
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circuit into a more efficient circuit under a variety of different cost criteria. We model a circuit as a graph in which the vertex set Visa collection of combinational logic elements and the edge set E is the set of interconnections, each of which may pass through zero or more registers. We give an 0(V
Vertex
"... Abstract. The structural semantics of UMLbased metamodeling were recently explored[1], providing a characterization of the models adhering to a metamodel. In particular, metamodels can be converted to a set of constraints expressed in a decidable subset of firstorder logic, an extended Horn logic. ..."
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. We augment the constructive techniques found in logic programming, which are also based on an extended Horn logic, to produce constructive techniques for reasoning about models and metamodels. These methods have a number of practical applications: At the metalevel, it can be decided if a (composite
A userprogrammable vertex engine
 In Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (ACM SIGGRAPH 2001
"... In this paper we describe the design, programming interface, and implementation of a very efficient userprogrammable vertex engine. The vertex engine of NVIDIA’s GeForce3 GPU evolved from a highly tuned fixedfunction pipeline requiring considerable knowledge to program. Programs operate only on a ..."
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Cited by 194 (1 self)
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In this paper we describe the design, programming interface, and implementation of a very efficient userprogrammable vertex engine. The vertex engine of NVIDIA’s GeForce3 GPU evolved from a highly tuned fixedfunction pipeline requiring considerable knowledge to program. Programs operate only on a
A Pivoting Algorithm for Convex Hulls and Vertex Enumeration of Arrangements and Polyhedra
, 1990
"... We present a new piv otbased algorithm which can be used with minor modification for the enumeration of the facets of the convex hull of a set of points, or for the enumeration of the vertices of an arrangement or of a convex polyhedron, in arbitrary dimension. The algorithm has the following prope ..."
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Cited by 223 (29 self)
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(nd) space. The v vertices in a simple arrangement of n hyperplanes in R d can be found in O(n²dv) time and O(nd) space complexity. The algorithm is based on inverting finite pivot algorithms for linear programming.
Approximate Graph Coloring by Semidefinite Programming.
 In Proceedings of 35th Annual IEEE Symposium on Foundations of Computer Science,
, 1994
"... Abstract. We consider the problem of coloring kcolorable graphs with the fewest possible colors. We present a randomized polynomial time algorithm that colors a 3colorable graph on n vertices with min{O(⌬ 1/3 log 1/2 ⌬ log n), O(n 1/4 log 1/2 n)} colors where ⌬ is the maximum degree of any vertex ..."
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Cited by 210 (7 self)
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vertex. Besides giving the best known approximation ratio in terms of n, this marks the first nontrivial approximation result as a function of the maximum degree ⌬. This result can be generalized to kcolorable graphs to obtain a coloring using min{O(⌬ 1Ϫ2/k log 1/2 ⌬ log n), O(n 1Ϫ3/(kϩ1) log 1/2 n
Results 1  10
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112,290