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Laplacian matrices of weighted digraphs represented as quantum states

Bibhas Adhikari, Subhashish Banerjee, Satyabrata Adhikari, Atul Kumar
2017 Quantum Information Processing  
graphs with complex edge weights and with/without loops.  ...  In this paper, we propose a general weighted directed graph framework for investigating properties of a large class of quantum states which are defined by three types of Laplacian matrices associated with  ...  Figure 9 : 9 Mixed state given by S 4 along with negative weighted loops Now we consider graphs with both positive and negative weighted loops.  ... 
doi:10.1007/s11128-017-1530-1 fatcat:4ycpxy5jsna3dfhzsxfgemogke

A Continuous Refinement Strategy for the Multilevel Computation of Vertex Separators [chapter]

William W. Hager, James T. Hungerford, Ilya Safro
2014 Lecture Notes in Computer Science  
In this paper, we reinforce the bilinear programming approach with a multilevel scheme for learning the structure of the graph.  ...  The Vertex Separator Problem (VSP) on a graph is the problem of finding the smallest collection of vertices whose removal separates the graph into two disjoint subsets of roughly equal size.  ...  Introduction Let G = (V, E) be an undirected graph with vertex set V and edge set E. Vertices are labeled 1, 2, . . ., n. We assign to each vertex a non-negative weight c i ∈ R ≥0 .  ... 
doi:10.1007/978-3-319-09584-4_8 fatcat:d4aar7ed3jg63fkxpil7ht4w2u

Lower Bounds on Dynamic Programming for Maximum Weight Independent Set [article]

Tuukka Korhonen
2021 arXiv   pre-print
., circuits that compute with max and + operations.  ...  For a graph G, an MWIS-circuit of G is a tropical circuit whose inputs correspond to vertices of G and which computes the weight of a maximum weight independent set of G for any assignment of weights to  ...  In particular, note that the edge events E e have non-negative correlation with each other and the vertex set events E A also have non-negative correlation with each other.  ... 
arXiv:2102.06901v2 fatcat:wdrvmo2xqvd5vl3dhid4stwym4

A Continuous Refinement Strategy for the Multilevel Computation of Vertex Separators [article]

William Hager, James Hungerford, Ilya Safro
2013 arXiv   pre-print
In this paper, we reinforce the bilinear programming approach with a multilevel scheme for learning the structure of the graph.  ...  The Vertex Separator Problem (VSP) on a graph is the problem of finding the smallest collection of vertices whose removal separates the graph into two disjoint subsets of roughly equal size.  ...  Introduction Let G = (V, E) be an undirected graph with vertex set V and edge set E. Vertices are labeled 1, 2, . . ., n. We assign to each vertex a non-negative weight c i ∈ R ≥0 .  ... 
arXiv:1311.5930v1 fatcat:yqf6sfxqcnggxj7wvcdork42ry

Parametric Graph-based Separable Transforms for Video Coding [article]

Hilmi E. Egilmez, Oguzhan Teke, Amir Said, Vadim Seregin, Marta Karczewicz
2020 arXiv   pre-print
Specifically, a GBST is derived from a pair of line graphs, whose weights are determined based on two non-negative parameters.  ...  transforms constructed based on DCT-2, DST-7 and DCT-8 in VVC.  ...  So, the edge weights of the graph associated with L are equal to 1, and its non-zero vertex weight is equal to v * c /w * c .  ... 
arXiv:1911.06981v3 fatcat:nrccjqux5jdnhkwsv4qi2qwlji

Collective Tree Spanners in Graphs with Bounded Genus, Chordality, Tree-Width, or Clique-Width [chapter]

Feodor F. Dragan, Chenyu Yan
2005 Lecture Notes in Computer Science  
, and graphs with bounded chordality.  ...  -spanners, any weighted graph with clique-width at most k admits a system of k log 3/2 n collective additive tree (2w)-spanners, and any weighted graph with size of largest induced cycle at most c admits  ...  Our graphs can have (non-negative) weights on edges, w(e), e ∈ E, unless otherwise is specified.  ... 
doi:10.1007/11602613_59 fatcat:rqadtkwvgbfvdf42wuwloz5vwe

Decomposable edge polytopes of finite graphs [article]

Atsushi Funato, Nan Li, Akihiro Shikama
2014 arXiv   pre-print
In particular, we answer two important questions raised in the previous study about 1) the relationship between type I and type II decomposable graphs and 2) description of decomposable graphs.  ...  Edge polytopes is a class of interesting polytope with rich algebraic and combinatorial properties, which was introduced by Ohsugi and Hibi.  ...  We say a graph G is decomposable if edge polytope P G of G is decomposable. A simple graph is a graph with no loops and no multiple edges.  ... 
arXiv:1406.1942v2 fatcat:6k5vfyjgnfa77kwe5mnben244u

Page 5330 of Mathematical Reviews Vol. , Issue 2000h [page]

2000 Mathematical Reviews  
R. (1-XEROX; Palo Alto, CA) Separators in graphs with negative and multiple vertex weights. (English summary) Algorithmica 23 (1999), no. 1, 57-71.  ...  In particular they show that if the vertices of the graph have real-valued weights, which may be positive or negative, then the graph can be divided exactly in half according to weight.  ... 

Faster Shortest Path Algorithm for H-Minor Free Graphs with Negative Edge Weights [article]

Christian Wulff-Nilsen
2010 arXiv   pre-print
Let H be a fixed graph and let G be an H-minor free n-vertex graph with integer edge weights and no negative weight cycles reachable from a given vertex s.  ...  We present an algorithm that computes a shortest path tree in G rooted at s in Õ(n^4/3 L) time, where L is the absolute value of the smallest edge weight.  ...  Let H be a fixed graph and let G be an H-minor free n-vertex graph with integer edge weights and no negative weight cycles reachable from a given vertex s.  ... 
arXiv:1008.1048v2 fatcat:srv5o4kylvf3dfzvgmu32paccq

Rapid mixing of subset Glauber dynamics on graphs of bounded tree-width [article]

Magnus Bordewich, Ross J. Kang
2011 arXiv   pre-print
With a canonical paths argument, we demonstrate that the chains defined within this framework mix rapidly upon graphs of bounded tree-width.  ...  This extends known results on rapid mixing for the Tutte polynomial, the adjacency-rank (R_2-)polynomial and the interlace polynomial.  ...  For fixed λ > 0, we say that the weight function w is vertex λ-multiplicative, if for any G = (V, E) and K a vertex cut that separates sets V 1 and V 2 with respect to G, we havê λ −|K| ≤ w(G[V 1 ])w(G  ... 
arXiv:1102.3635v1 fatcat:ozlhoeao4fekzovwtyrknsfjwq

Multiple-source multiple-sink maximum flow in planar graphs [article]

Yahav Nussbaum
2010 arXiv   pre-print
In this paper we show an O(n^(3/2) log^2 n) time algorithm for finding a maximum flow in a planar graph with multiple sources and multiple sinks.  ...  However, the standard reduction does not preserve the planarity of the graph, and it is not known how to generalize existing maximum flow algorithms for planar graphs to the multiple-source multiple-sink  ...  Acknowledgments The author would like to thank Haim Kaplan and Christian Wulff-Nilsen for their comments on the paper.  ... 
arXiv:1012.4767v2 fatcat:hynvnq23jvchvinx5xp3onnqay

Rapid Mixing of Subset Glauber Dynamics on Graphs of Bounded Tree-Width [chapter]

Magnus Bordewich, Ross J. Kang
2011 Lecture Notes in Computer Science  
With a canonical paths argument, we demonstrate that the chains defined within this framework mix rapidly upon graphs of bounded tree-width.  ...  The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes  ...  For fixed λ > 0, we say that the weight function w in (9) is vertex λmultiplicative, if for any G = (V, E) and K a vertex cut that separates sets V 1 and V 2 with respect to G, we havê λ −|K| ≤ w(G[V 1  ... 
doi:10.1007/978-3-642-22006-7_45 fatcat:34jyin2e2rgurfegnhdevtobri

Subset Glauber Dynamics on Graphs, Hypergraphs and Matroids of Bounded Tree-Width

Magnus Bordewich, Ross J. Kang
2014 Electronic Journal of Combinatorics  
With a canonical paths argument, we demonstrate that the chains defined within this framework mix rapidly upon graphs, hypergraphs and matroids of bounded tree-width.This extends known results on rapid  ...  We show that Glauber dynamics for a very wide class of polynomials mixes rapidly on graphs of bounded tree-width, including many cases in which the Glauber dynamics does not mix rapidly for all graphs.  ...  Note that |K| is at most the vertex-separation . Clearly, K is a vertex cut separating V 1 and V 2 with respect to G and also with respect to the graphs G[I], G[F ], G[H], G [C] .  ... 
doi:10.37236/4195 fatcat:amjdhchrdzfs3leyuavc3uhgaa

Cheeger Inequalities for General Edge-Weighted Directed Graphs [chapter]

T.-H. Hubert Chan, Zhihao Gavin Tang, Chenzi Zhang
2015 Lecture Notes in Computer Science  
Previously the directed case was considered by Chung for a probability transition matrix corresponding to a strongly connected graph with weights induced by a stationary distribution.  ...  In particular, we obtain higher-order Cheeger Inequalities for the following scenarios: (1) The underlying graph needs not be strongly connected. (2) The weights can deviate (slightly) from a stationary  ...  Given an undirected graph with non-negative edge weights, the weight of a vertex is the sum of the weights of its incident edges.  ... 
doi:10.1007/978-3-319-21398-9_3 fatcat:mcj6gsu765fzrf3b6igtmjlbae

Multiphase mesh partitioning

C. Walshaw, M. Cross, K. McManus
2000 Applied Mathematical Modelling  
We consider the load-balancing problems which arise from parallel scientific codes containing multiple computational phases, or loops over subsets of the data, which are separated by global synchronisation  ...  The technique is tested on several examples of meshes, both real and artificial, containing multiple computational phases and it is demonstrated that our method can achieve high quality partitions where  ...  Separator theory for graphs with multiple weights A separator for a graph is a small set of vertices or edges whose removal divides the graph into disjoint pieces of approximately equal size.  ... 
doi:10.1016/s0307-904x(00)00041-x fatcat:v2bzgy33gneo5pygdol577cqum
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