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SEARCHING AND PEBBLING
, 1986
"... We relate the search number of an undirected graph G with the minimum and maximum of the progressive pebble demands of the directed acyclic graphs obtained by orienting (7. Towards this end, we introduce nodesearching, a slight variant of searching, in which an edge is cleared by placing searchers ..."
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Cited by 99 (1 self)
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We relate the search number of an undirected graph G with the minimum and maximum of the progressive pebble demands of the directed acyclic graphs obtained by orienting (7. Towards this end, we introduce nodesearching, a slight variant of searching, in which an edge is cleared by placing searchers
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning under uncertainty, sensorbased planning, visibility, decisiontheoretic planning, game theory, information spaces, reinforcement learning, nonlinear systems, trajectory planning, nonholonomic planning, and kinodynamic planning.
A Separator Theorem for Planar Graphs
, 1977
"... Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which ..."
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Cited by 465 (1 self)
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Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which finds such a partition A, B, C in O(n) time.
Technological pedagogical content knowledge: A framework for teacher knowledge
, 2006
"... Research in the area of educational technology has often been critiqued for a lack of theoretical grounding. In this article we propose a conceptual framework for educational technology by building on Shulman’s formulation of "pedagogical content knowledge" and extend it to the phenomenon ..."
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Cited by 374 (17 self)
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Research in the area of educational technology has often been critiqued for a lack of theoretical grounding. In this article we propose a conceptual framework for educational technology by building on Shulman’s formulation of "pedagogical content knowledge" and extend it to the phenomenon of teachers integrating technology into their pedagogy. This framework is the result of 5 years of work on a program of research focused on teacher professional development and faculty development in higher education. It attempts to capture some of the essential qualities of teacher knowledge required for technology integration in teaching, while addressing the complex, multifaceted, and situated nature of this knowledge. We argue, briefly, that thoughtful pedagogical uses of technology require the development of a complex, situated form of knowledge that we call Technological Pedagogical Content Knowledge (TPCK). In doing so, we posit the complex roles of, and interplay among, three main components of learning environments: content, pedagogy, and technology. We argue that this model has much to offer to discussions of technology integration at multiple levels: theoretical, pedagogical, and methodological. In this article, we describe the theory behind our framework, provide examples of our teaching approach based upon the framework, and illustrate the methodological contributions that have resulted from this work. The important thing in science is not so much to obtain new facts as to discover new ways of thinking about them. —Sir William Henry Bragg The advent of digital technology has dramatically changed routines and practices in most arenas of human work. Advocates of technology in education often envisage similar dramatic changes in the process of teaching
Pebbling and Optimal Pebbling in Graphs
, 2007
"... Given a distribution of pebbles on the vertices of a graph G, a pebbling move takes two pebbles from one vertex and puts one on a neighboring vertex. The pebbling number Π(G) is the least k such that for every distribution of k pebbles and every vertex r, a pebble can be moved to r. The optimal pebb ..."
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Given a distribution of pebbles on the vertices of a graph G, a pebbling move takes two pebbles from one vertex and puts one on a neighboring vertex. The pebbling number Π(G) is the least k such that for every distribution of k pebbles and every vertex r, a pebble can be moved to r. The optimal
The Hero with a Thousand Faces
, 1972
"... Botiingen Foundation, andpttt.!.,.: b % / ,.,;:,c,m B<,.ik.*, second ..."
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Cited by 353 (0 self)
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Botiingen Foundation, andpttt.!.,.: b % / ,.,;:,c,m B<,.ik.*, second
Synthesizing Natural Textures
 In ACM Symposium on Interactive 3D Graphics
"... We present a simple texture synthesis algorithm that is wellsuited for a specific class of naturally occurring textures. This class includes quasirepeating patterns consisting of small objects of familiar but irregular size, such as flower fields, pebbles, forest undergrowth, bushes and tree branc ..."
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Cited by 314 (0 self)
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We present a simple texture synthesis algorithm that is wellsuited for a specific class of naturally occurring textures. This class includes quasirepeating patterns consisting of small objects of familiar but irregular size, such as flower fields, pebbles, forest undergrowth, bushes and tree
Graph Pebbling
, 2008
"... A graph is a mathematical object that contains a set of vertices and edges, where an edge connects any two vertices. In the plane, a graph can be represented by points (vertices) and lines connecting the points (edges). Given a graph we consider placing some number of pebbles on the vertices, and de ..."
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A graph is a mathematical object that contains a set of vertices and edges, where an edge connects any two vertices. In the plane, a graph can be represented by points (vertices) and lines connecting the points (edges). Given a graph we consider placing some number of pebbles on the vertices
A Partial KArboretum of Graphs With Bounded Treewidth
 J. Algorithms
, 1998
"... The notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies. This survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class. Also, some mutual relations between such classes ..."
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Cited by 328 (34 self)
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The notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies. This survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class. Also, some mutual relations between such classes are discussed.
Results 1  10
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