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Laplacian matrices of weighted digraphs represented as quantum states

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. ...

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

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 . ...

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

2021
*
arXiv
*
pre-print

., circuits that compute

arXiv:2102.06901v2
fatcat:wdrvmo2xqvd5vl3dhid4stwym4
*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. ...##
###
A Continuous Refinement Strategy for the Multilevel Computation of Vertex Separators
[article]

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 . ...

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

2020
*
arXiv
*
pre-print

Specifically, a GBST is derived from a pair of line

arXiv:1911.06981v3
fatcat:nrccjqux5jdnhkwsv4qi2qwlji
*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 . ...##
###
Collective Tree Spanners in Graphs with Bounded Genus, Chordality, Tree-Width, or Clique-Width
[chapter]

2005
*
Lecture Notes in Computer Science
*

,

doi:10.1007/11602613_59
fatcat:rqadtkwvgbfvdf42wuwloz5vwe
*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. ...##
###
Decomposable edge polytopes of finite graphs
[article]

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. ...

##
###
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]

2010
*
arXiv
*
pre-print

Let H be a fixed

arXiv:1008.1048v2
fatcat:srv5o4kylvf3dfzvgmu32paccq
*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. ...##
###
Rapid mixing of subset Glauber dynamics on graphs of bounded tree-width
[article]

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 ...

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

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. ...

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

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*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 ...

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

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] . ...

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

2015
*
Lecture Notes in Computer Science
*

Previously the directed case was considered by Chung for a probability transition matrix corresponding to a strongly connected

doi:10.1007/978-3-319-21398-9_3
fatcat:mcj6gsu765fzrf3b6igtmjlbae
*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. ...##
###
Multiphase mesh partitioning

2000
*
Applied Mathematical Modelling
*

We consider the load-balancing problems which arise from parallel scientific codes containing

doi:10.1016/s0307-904x(00)00041-x
fatcat:v2bzgy33gneo5pygdol577cqum
*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. ...
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