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Topic: Directed acyclic graph

Related Topics

Graph homomorphism

Graph (data structure)

Planar graph

Graph rewriting

List of graph theory topics

Topological sorting

Cycle space

Graph theory

Adjacency matrix

Bipartite graph

Graph drawing

Complete graph

Adjacency list

Tree rotation

Instruction scheduling

	Directed acyclic graph - Wikipedia, the free encyclopedia
		DAGs appear in models where it doesn't make sense for a vertex to have a path to itself; for example, if an edge u→v indicates that v is a part of u, such a path would indicate that u is a part of itself, which is impossible.
		Among these graphs, the one with the fewest edges is the transitive reduction and the one with the most edges is the transitive closure.
		DAGs can be considered to be a generalization of trees in which certain subtrees can be shared by different parts of the tree.
	en.wikipedia.org /wiki/Directed_acyclic_graph (642 words)

	Graphs
		A graph G= consists of a set of vertices (also known as nodes) V and a set of edges (also known as arcs) E. An edge connects two vertices u and v; v is said to be adjacent to u.
		Graphs are useful for representing networks and maps of roads, railways, airline routes, pipe systems, telephone lines, electrical connections, prerequisites amongst courses, dependencies amongst tasks in a manufacturing system and a host of other data.
		Note that a rooted tree is a special kind of directed graph and that an unrooted tree is a special kind of undirected graph.
	www.csse.monash.edu.au /~lloyd/tildeAlgDS/Graph (1162 words)

	Graph Definitions
		A Graph has a set of Edges usually denoted E. E = {(v1,v2), (v2,v3)} The number of Edges in a graph is E but is somtimes written in equations as just E. A Graph is called Undirected if the edges have no implied direction.
		A value of zero means the given graph has at least one pair of vertices x, y in V such that there is no path connecting x and y.
		Bipartite - a Graph with a set of vertices that can be divided into exactly two non empty subsets such that no edge connects two vertices within a subset and every vertex in one subset has at least one Edge to a vertex in the other subset.
	www.csee.umbc.edu /~squire/reference/graph_def.shtml (820 words)

	Graph
		Moreover, in mathematical graphs, no distinction is made between multiple edges that may be adjacent to a node, so the ports of the Ptolemy II kernel are not needed.
		Acyclic directed graphs, which can be used to model complete partial orders (CPOs) and lattices, are also supported with more specialized algorithms.
		For example, a graph might be constructed that represents data precedences, and a topological sort might be used to generate a schedule.
	ptolemy.eecs.berkeley.edu /papers/98/HMAD/html/graph.html (2035 words)

	graph
		Formally, a graph is a set of vertices and a binary relation between vertices, adjacency.
		Moreover, a mathematical graph is not a comparison chart, nor a diagram with an x- and y-axis, nor a squiggly line on a stock report.
		GraphEd -- Graph Editor and Layout Program (C), graph manipulation (C++, C, Mathematica, and Pascal), build, traverse, top sort, etc. weighted, directed graphs (Java), JGraphT (Java) build, traverse, and display directed and undirected graphs, GEF - Graph Editing Framework (Java) a library to edit and display graphs.
	www.itl.nist.gov /div897/sqg/dads/HTML/graph.html (571 words)

	Graph (mathematics) - Wikipedia, the free encyclopedia
		An edge e = (x,y) is considered to be directed from x to y; y is called the head and x is called the tail of the edge; y is said to be a direct successor of x, and x is said to be a direct predecessor of y.
		A quiver is sometimes said to be simply a directed graph, but in practice it is a directed graph with vector spaces attached to the vertices and linear transformations attached to the arcs.
		Every graph gives rise to a matroid, but in general the graph cannot be recovered from its matroid, so matroids are not truly generalizations of graphs.
	en.wikipedia.org /wiki/Directed_graph (1783 words)

	Introduction to Graphs
		Note that in a directed graph, the edges are arrows (are directed from one node to another) while in the undirected graph the edges are plain lines (they have no direction).
		This means that in a directed graph it is possible to reach a "dead end" (to get to a node from which you cannot leave).
		A directed graph can also be a complete graph; in that case, there must be an edge from every node to every other node.
	www.cs.wisc.edu /~hasti/cs367-common/notes/GRAPH.html (1791 words)

	Topic #30: Directed Acyclic Graphs
		Directed acyclic graphs are directed graphs with no cycles.
		Called dags, they are an important class of graphs, being part tree, part graph, and having many applications, such as those involving precedence among "events".
		The property of dags which is optimal for these problems is their ability to be topologically sorted using depth-first search.
	www.cs.mcgill.ca /~cs251/OldCourses/1997/topic30 (1764 words)

	Directed Acyclic Graph Matcher
		The directed acyclic graph (DAG) matcher is an extension to the indexing and matching framework for hierarchical structures proposed by Shokoufandeh et al.
		The indexing performance is improved by a vote accumulation algorithm that efficiently solves a multiple one-to-one assignment of votes.
		In turn, the matching algorithm is extended by ensuring the satisfaction of all the hierarchical constraints encoded in the graphs.
	www.cs.toronto.edu /~dmac/dagmatcher.html (217 words)

	Biopathways Graph Data Manager (BGDM)
		I have broad interests in graphs, their role in databases and knowledge representation, graph algorithms (esp. parallel graph algorithms) for biology (phylogenetic tree construction, NMR peak assignment, shotgun sequence assembly, etc.), and graph grammars (for modeling graph query languages, evolution of biopathways, schema evolution and integration).
		graph composition (e.g., of directed graphs) connects matching outputs (e.g., chemical compounds) from one graph to the corresponding inputs of a second directed graph.
		Graph matchings attempt to match entire graphs and are the graph analogs of global sequence alignments.
	hpcrd.lbl.gov /staff/olken/graphdm/graphdm.htm (7829 words)

	Sensei's Library: Directed Acyclic Graph
		The graphs are directed because there is a sense of forwardness as more moves are played.
		They are acyclic because positions can't repeat in most rule sets according to Super-Ko rules (Ko Rules).
		Charles Matthews: In cyclic positions taxonomy the consequences of dropping the 'acyclic' condition, for local positions on a sub-board, are explored mathematically.
	senseis.xmp.net /?DirectedAcyclicGraph (159 words)

	blender3d.org :: Dependency Graph (Site not responding. Last check: 2007-10-20)
		Once the DAG is built, it can be queried to show which object depends on another, and also to find an order of evaluation that respects all dependancies, as long as there is no cycles in them.
		Although DAG can be used in many areas in Blender, for now we will restrict our discussion to the signalling of Object updates by the animation system or other tools in Blender.
		The first use of the DAG is to presort the list of Objects in a scene in dependency order, assuring calculations for updates happen without lag.
	www.blender3d.org /cms/Dependency_Graph.633.0.html (873 words)

	Physics - Martin Baker
		The tree and DAG are similar, except that in the DAG the branches may possibly grow back together.
		Directed means that the parent-child relationship is one-way, Acyclic means that there cant be loops, i.e.
		The scene graph contains 'nodes' such as shape, light, camera, etc. The relationships between the parent and child is known as an edge, but this terminology could be confusing in this context as the term 'edge' is used when we are talking about mesh shapes.
	www.euclideanspace.com /threed/scenegraph/index.htm (612 words)

	Method for representing a directed acyclic graph of worlds using an assumption-based truth maintenance system - Patent ...
		1 is an illustration of a directed acyclic graph of worlds in a knowledge base constructed in accordance with the invention.
		2 is an illustration of a graph of assertions, assumptions and justifications.
		3 is an illustration of a directed acyclic graph of worlds in a knowledge base constructed in accordance with the invention for showing merge ambiguity.
	www.freepatentsonline.com /4918621.html (7654 words)

	System and method for serializing lazy updates in a distributed database without requiring timestamps - Patent 6381609
		A sink node is a node in a directed acyclic copy graph that does not have a directed edge to another node in the directed acyclic copy graph.
		The problem of ensuring execution serializability of a copy graph is that existing approaches use lazy replication protocols that guarantee serializability if and only if the undirected graph obtained from a copy graph is acyclic.
		A sink node is a node in a directed acyclic copy graph that does not have a directed edge to another node in the directed acyclic-copy graph.
	www.freepatentsonline.com /6381609.html (5112 words)

	Directed Acyclic Graph (Site not responding. Last check: 2007-10-20)
		A DirectedAcyclicGraph is a DirectedGraph with no circuits, often abbreviated DAG.
		For example, ({A, B}, {(A, B), (B, A)}) and ({A, B, C}, {(A, B), (B, C), (C, A)}) both contain circuits, whereas ({A, B, C}, {(A, B), (B, C), (A, C)}) is acyclic.
		A very common use of DAGs is to represent expressions in a compiler or interpreter.
	c2.com /cgi/wiki?DirectedAcyclicGraph (440 words)

	Document filtering via directed acyclic graphs (US5873081)
		Each node in the DAG includes pointers to any successor nodes thereof, the terms in the queries are embedded as source nodes in the graph, and the operators embedded as internal nodes.
		When a document is received, the document is evaluated against the nodes in the DAG by comparing the relevant terms in the document with the source nodes in the DAG representative thereof.
		For each term that matches a source node, the internal successor node of the matched source node is evaluated based on the logical operator represented by the successor node and truth information of the predecessor nodes thereto, thereby determining a truth value of the internal successor node.
	www.delphion.com /details?pn10=US05873081 (388 words)

	Boost Graph Library: Topological Sort
		The graph must be a directed acyclic graph (DAG).
		The graph type must be a model of Vertex List Graph.
		Read/Write Property Map and its key type must be the graph's vertex descriptor type and the value type of the color map must model ColorValue.
	www.boost.org /libs/graph/doc/topological_sort.html (229 words)

	The Graph ADT
		A graph is a structure composed of a set of vertices and edges that connect the vertices.
		Given the graph in Example 1, the vertices can be represented as V = {A, B, C, D} and the edges as E = {AB, AC, BC, BD, CD, BA, CA, CB, DC, DB}.
		Example 3 is also a graph with parallel edges and self-loops.
	www.cis.cau.edu /123/notes/GraphADT.htm (1136 words)

	Boost Graph Library: Directed Acyclic Graph Shortest Paths
		The graph object on which the algorithm will be applied.
		The edge descriptor type of the graph needs to be usable as the key type for the weight map.
		The vertex descriptor type of the graph needs to be usable as the key type of the distance map.
	www.boost.org /libs/graph/doc/dag_shortest_paths.html (906 words)

	Directed Acyclic Word Graphs
		A Directed Acyclic Word Graph, or DAWG, is a data structure that permits extremely fast word searches.
		It's a Directed graph because you can only move in a specific direction between two nodes.
		In other words, you can move from A to B, but you can't move from B to A. It's Acyclic because there are no cycles.
	www.wutka.com /dawg.html (1389 words)

	Topological Sorting
		A topological sort of a directed acyclic graph is an ordering on the vertices such that all edges go from left to right.
		Only an acyclic graph can have a topological sort, because a directed cycle must eventually return home to the source of the cycle.
		A directed graph is a DAG if and only if no back edges are encountered during a depth-first search.
	www2.toki.or.id /book/AlgDesignManual/BOOK/BOOK2/NODE70.HTM (299 words)

	Directed Acyclic Graphs (DAGS)
		For example, a DAG may be used to represent common subexpressions in an optimising compiler.
		A DAG can be used to represent prerequisites in a university course, constraints on operations to be carried out in building construction, in fact an arbitrary partial-order `
		Note that no order is imposed between `roof' and `brick-work', but the plaster cannot be applied until the walls are there for it to stick to and the roof exists to protect it.
	www.csse.monash.edu.au /~lloyd/tildeAlgDS/Graph/DAG (720 words)

	Directed Acyclic Graph Manager (Site not responding. Last check: 2007-10-20)
		A directed acyclic graph (DAG) can be used to represent a set of programs where the input, output, or execution of one or more programs is dependent on one or more other programs.
		An input file defined prior to submission describes the DAG, and a Condor submit description file for each program in the DAG is used by Condor.
		The DAG itself is defined by the contents of a DAGMan input file.
	www.cs.wisc.edu /condor/dagman (226 words)

	directed acyclic word graph (Site not responding. Last check: 2007-10-20)
		Definition: (1) A directed acyclic graph representing the suffixes of a given string in which each edge is labeled with a character.
		Crochemore and R. Verin, Direct Construction of Compact Directed Acyclic Word Graphs, 8th Annual Symposium, CPM 97, Aarhus, Denmark, 116-129, 1997.
		Paul E. Black, "directed acyclic word graph", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology.
	www.nist.gov /dads/HTML/directedAcyclicWordGraph.html (252 words)

	NSDL Metadata Record -- Acyclic Digraph -- from MathWorld
		An acyclic digraph is a directed graph containing no directed cycles, also known as a directed acyclic graph or a "DAG." Every acyclic digraph has at least one node of outdegree 0.
		The numbers of acyclic digraphs on n = 1, 2,...
		Robinson, R. "Counting Unlabeled Acyclic Digraphs." In Combinatorial Mathematics V (Melbourne 1976).
	nsdl.org /mr/697053 (173 words)

	Directed Acyclic Subsequence Graph (Site not responding. Last check: 2007-10-20)
		Tronicek, Directed Acyclic Subsequence Graph for multiple texts, Technical Report, IGM-99-??, Institut Gaspard-Monge, 1999, 19 pages.
		The subsequence matching problem is to decide, for given strings S and T, whether S is a subsequence of T.
		The automaton is called Directed Acyclic Subsequence Graph (DASG) and we present an algorithm for its building.
	www-igm.univ-mlv.fr /~mac/REC/99-DASG.html (196 words)

	Definition of a Gröbner Graph
		We begin by stating the following definition in which we define a Gröbner graph to encapsulate the observations of §.
		Definition 12.7 Let G = (V,E) be a graph and v be a vertex of G. We will say that v is a starting vertex if T(v,G) is the empty set.
		Other subgraphs of a Gröbner graph may be Gröbner, but the above mentioned subgraphs can be seen to be Gröbner from purely graph-theoretic arguments.
	math.ucsd.edu /~ncalg/StrategyPaper/node70.html (409 words)

	directed acyclic graph (Site not responding. Last check: 2007-10-20)
		Definition: A directed graph with no path that starts and ends at the same vertex.
		Also known as DAG, acyclic directed graph, oriented acyclic graph.
		Paul E. Black, "directed acyclic graph", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology.
	www.nist.gov /dads/HTML/directAcycGraph.html (93 words)

	3.1 Storing everything in a Directed Acyclic Graph (DAG)
		Everything, even numbers and strings, is stored as nodes of a Directed Acyclic Graph (DAG).
		The following excerpt from an input file creates the graph shown in figure 3.1 (you can alse use the Graph-Editor (2.5) for exploring the created graph):
		Variables are just substitutes for nodes of the DAG, and can be used at any place where a graph node is expected.
	gul.sourceforge.net /viewdog-manual/node11.html (174 words)

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