The Random f-Graph Process

Balińska, Krystyna T.; Quintas, Louis V.

doi:10.1016/s0167-5060(08)70398-4

Cited by 6 publications

(5 citation statements)

References 7 publications

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“…For the experiments in this paper we generate a random graph from the model in [44] with maximum degree equal to 4, and vary the graph order from 50 to 350…”

Section: Other Random Graph Modelsmentioning

confidence: 99%

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Graph Matching: Relax at Your Own Risk

Lyzinski

Fishkind

Fiori

et al. 2016

IEEE Trans. Pattern Anal. Mach. Intell.

118

124

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Graph matching—aligning a pair of graphs to minimize their edge disagreements—has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and connectomics. Its attention can be partially attributed to its computational difficulty. Although many heuristics have previously been proposed in the literature to approximately solve graph matching, very few have any theoretical support for their performance. A common technique is to relax the discrete problem to a continuous problem, therefore enabling practitioners to bring gradient-descent-type algorithms to bear. We prove that an indefinite relaxation (when solved exactly) almost always discovers the optimal permutation, while a common convex relaxation almost always fails to discover the optimal permutation. These theoretical results suggest that initializing the indefinite algorithm with the convex optimum might yield improved practical performance. Indeed, experimental results illuminate and corroborate these theoretical findings, demonstrating that excellent results are achieved in both benchmark and real data problems by amalgamating the two approaches.

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“…For the experiments in this paper we generate a random graph from the model in [44] with maximum degree equal to 4, and vary the graph order from 50 to 350…”

Section: Other Random Graph Modelsmentioning

confidence: 99%

“…For the experiments in this paper we generate a random graph from the model in [44] vertices. Figure 7 shows the comparison of the different techniques and initializations for these graphs, across a range of bit-flipping parameters p ∈ [0, 1].…”

Section: Other Random Graph Modelsmentioning

confidence: 99%

Graph Matching: Relax at Your Own Risk

Lyzinski

Fishkind

Fiori

et al. 2016

IEEE Trans. Pattern Anal. Mach. Intell.

118

124

View full text Add to dashboard Cite

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“…We call this procedure the Random f-Graph Process with nonuniform edge probabilities (R*f- GP) of order n . This is in contrast to the Random f-Graph Process (Rf-GP) of order n in which the edges that are added are selected with uniform probability (see ref ).…”

Section: Introductionmentioning

confidence: 99%

“…The bounded degree restriction f < n − 1 introduces difficulties of a type different than those encountered in the Random Graph Process. The interest in random graphs with bounded degree and in particular in the context of the R f -GP and R* f -GP follows from their natural occurrence in network reliability theory and in chemistry and physics applications. , The R* f -GP is related to chemical applications in the sense that the nonuniform edge probability reflects the condition that a vertex of lower degree emanates a greater attraction for bonding. Many of the questions posed in these models are the same, for example, those related to evolution such as hitting times and structure properties of the random graphs at various points in the evolution.…”

Section: Introductionmentioning

confidence: 99%

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A Kinetic Approach to the Random f-Graph Process with Nonuniform Edge Probabilities

Balińska¹,

Galina²,

Quintas³

et al. 1996

J. Chem. Inf. Comput. Sci.

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Starting with n labeled vertices and no edges, introduce edges, one at a time, so as to obtain a sequence of graphs each having no vertex of degree greater than f. The latter are called f-graphs. At each step the edge to be added is selected from among those edges whose addition would not violate the f-degree restriction and with probability proportional to the product of the respective numbers of available sites at the vertices of the potential edge. We call this procedure the Random f-Graph Process with nonuniform edge probabilities (R*f-GP) of order n. This is in contrast to the Random f-Graph Process (Rf-GP) of order n in which the edges that are added are selected with uniform probability. Using the Law of Mass Action, chemists have derived the degree distribution of the vertices in a graph generated by the R*f-GP. Here we apply a differential equation technique to obtain this degree distribution.

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