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A combinatorial Laplacian with vertex weights
, 1996
"... One of the classical results in graph theory is the matrixtree theorem which asserts that the determinant of a cofactor of the combinatorial Laplacian is equal to the number of spanning trees in a graph (see [1, 7, 11, 15]). The usual notion of the combinatorial Laplacian for a graph involves edge ..."
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Cited by 30 (3 self)
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weights. Namely, a Laplacian L for G is a matrix with rows and columns indexed by the vertex set V of G, andthe(u, v)entry of L, for u, v in G, u � = v, is associated with the edgeweight of the edge (u, v). It is not so obvious to consider Laplacians with vertex weights (except for using some symmetric
Vertex Weighted Steiner Tree Games
, 1996
"... We introduce a variant of the minimum cost spanning tree game in which the players receive a reward if they are connected to a central supplier. The game is called a vertex weighted Steiner tree (VWST) game. The problem is to distribute the total profit in a VWST game (defined as the sum of the rewa ..."
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Cited by 1 (0 self)
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We introduce a variant of the minimum cost spanning tree game in which the players receive a reward if they are connected to a central supplier. The game is called a vertex weighted Steiner tree (VWST) game. The problem is to distribute the total profit in a VWST game (defined as the sum
ALGORITHMS FOR VERTEXWEIGHTED MATCHING IN GRAPHS
, 2009
"... A matching M in a graph is a subset of edges such that no two edges in M are incident on the same vertex. Matching is a fundamental combinatorial problem that has applications in many contexts: highperformance computing, bioinformatics, network switch design, web technologies, etc. Examples in th ..."
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Cited by 3 (0 self)
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, and to coarsen graphs in multilevel graph partitioning algorithms. In the first part of this thesis, we develop exact and approximation algorithms for vertex weighted matchings, an understudied variant of the weighted matching problem. We propose three exact algorithms, three half approximation algorithms
Motionadaptive transforms based on vertexweighted graphs
 in Proc. of the IEEE Data Compression Conference
, 2013
"... Motion information in image sequences connects pixels that are highly correlated. In this paper, we consider vertexweighted graphs that are formed by motion vector information. The vertex weights are defined by scale factors which are introduced to improve the energy compaction of motionadaptive t ..."
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Cited by 3 (3 self)
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Motion information in image sequences connects pixels that are highly correlated. In this paper, we consider vertexweighted graphs that are formed by motion vector information. The vertex weights are defined by scale factors which are introduced to improve the energy compaction of motion
Minimal invariant sets in a vertexweighted graph
 THEORETICAL COMPUTER SCIENCE
, 2006
"... A weighting of vertices of a graph is admissible if there exists an edge weighting such that the weight of each vertex equals the sum of weights of its incident edges. Given an admissible vertex weighting of a graph, an invariant set is an edge set such that the sum of the weights of its edges is th ..."
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Cited by 2 (2 self)
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A weighting of vertices of a graph is admissible if there exists an edge weighting such that the weight of each vertex equals the sum of weights of its incident edges. Given an admissible vertex weighting of a graph, an invariant set is an edge set such that the sum of the weights of its edges
AllPairs Bottleneck Paths in Vertex Weighted Graphs
 In Proc. of SODA, 978–985
, 2007
"... Let G = (V, E, w) be a directed graph, where w: V → R is an arbitrary weight function defined on its vertices. The bottleneck weight, or the capacity, of a path is the smallest weight of a vertex on the path. For two vertices u, v the bottleneck weight, or the capacity, from u to v, denoted c(u, v), ..."
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Cited by 9 (1 self)
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Let G = (V, E, w) be a directed graph, where w: V → R is an arbitrary weight function defined on its vertices. The bottleneck weight, or the capacity, of a path is the smallest weight of a vertex on the path. For two vertices u, v the bottleneck weight, or the capacity, from u to v, denoted c(u, v
Maximum VertexWeighted Matching in Strongly Chordal Graphs
"... Given a graph G = (V; E) and a real weight for each vertex of G, the vertexweight of a matching is defined to be the sum of the weights of the vertices covered by the matching. In this paper we present a linear time algorithm for finding a maximum vertexweighted matching in a strongly chordal grap ..."
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Given a graph G = (V; E) and a real weight for each vertex of G, the vertexweight of a matching is defined to be the sum of the weights of the vertices covered by the matching. In this paper we present a linear time algorithm for finding a maximum vertexweighted matching in a strongly chordal
Deducing Vertex Weights from Empirical Occupation Times
, 2009
"... We consider the following problem arising from the study of human problem solving: Let G be a vertexweighted graph with marked “in ” and “out ” vertices. Suppose a random walker begins at the invertex, steps to neighbors of vertices with probability proportional to their weights, and stops upon rea ..."
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We consider the following problem arising from the study of human problem solving: Let G be a vertexweighted graph with marked “in ” and “out ” vertices. Suppose a random walker begins at the invertex, steps to neighbors of vertices with probability proportional to their weights, and stops upon
Separators in Graphs with Negative and Multiple Vertex Weights
 ALGORITHMICA
, 1992
"... A separator theorem for a class of graphs asserts that every graph in the class can be divided approximately in half by removing a set of vertices of specified size. Nontrivial separator theorems hold for several classes of graphs, including graphs of bounded genus and chordal graphs. We show t ..."
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Cited by 12 (2 self)
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that any separator theorem implies various weighted separator theorems. In particular, we show that if the vertices of the graph have realvalued weights, which may be positive or negative, then the graph can be divided exactly in half according to weight. If k unrelated sets of weights are given
A bracket polynomial for graphs. III. Vertex weights
, 2009
"... In earlier work the Kauffman bracket polynomial was extended to an invariant of marked graphs, i.e., looped graphs whose vertices have been partitioned into two classes (marked and not marked). The markedgraph bracket polynomial is readily modified to handle graphs with weighted vertices. We presen ..."
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Cited by 2 (2 self)
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In earlier work the Kauffman bracket polynomial was extended to an invariant of marked graphs, i.e., looped graphs whose vertices have been partitioned into two classes (marked and not marked). The markedgraph bracket polynomial is readily modified to handle graphs with weighted vertices. We
Results 1  10
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