The inverse shortest paths problem with upper bounds on shortest paths costs

1997 ◽  
pp. 156-171 ◽  
Author(s):  
D. Burton ◽  
W. R. Pulleyblank ◽  
Ph. L. Toint
Keyword(s):  
Shortest Paths ◽  
Upper Bounds

scholarly journals Lower and upper bounds of shortest paths in reachability graphs

2004 ◽  
Vol 2004 (57) ◽  
pp. 3023-3036 ◽  
Author(s):  
P. K. Mishra
Keyword(s):  
Petri Nets ◽  
Shortest Path ◽  
Petri Net ◽  
Free Choice ◽  
Shortest Paths ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Marked Graphs ◽  
Marked Graph

We prove the following property for safe marked graphs, safe conflict-free Petri nets, and live and safe extended free-choice Petri nets. We prove the following three results. If the Petri net is a marked graph, then the length of the shortest path is at most(|T|−1)⋅|T|/2. If the Petri net is conflict free, then the length of the shortest path is at most(|T|+1)⋅|T|/2. If the petrinet is live and extended free choice, then the length of the shortest path is at most|T|⋅|T+1|⋅|T+2|/6, whereTis the set of transitions of the net.

A Path Based Algorithm for Solve the Hazardous Materials Transportation Bilevel Problem

2012 ◽  
Vol 253-255 ◽  
pp. 1082-1088
Author(s):  
José Fernando Camacho Vallejo ◽  
Rafael Muñoz Sánchez
Keyword(s):  
Mathematical Program ◽  
Transportation Network ◽  
Shortest Paths ◽  
Hazardous Materials ◽  
Upper Bounds ◽  
Government Agency ◽  
Population Exposure ◽  
Hazardous Materials Transportation ◽  
Total Cost ◽  
Upper Level

In this work we consider the problem of determining a set of optimal tolls on the arcs of a multicommodity transportation network. The problem is formulated as a bilevel mathematical program where the upper level consists in a government agency that regulate the traffic of the dangerous materials by imposing tolls on arcs of the network trying to minimize the risk for the population in the case when an accident occurs to the carriers, while the lower level is represented by a group of carriers traveling on shortest paths with respect to a generalized travel cost. So, the problem can be seen in a simplistic form as find the equilibrium between tolls that minimize the population exposure to the risk and tolls that are convenient for the shippers. The paper applies a path based algorithm to solve a bi-level multi-commodity optimal toll setting ‘hazmat’ problem. The algorithm consists in find upper bounds for the tolls considering the total cost and the risk associated to a particular path. We made several experiments and the results are shown in this work.

scholarly journals Notes on the betweenness centrality of a graph

2012 ◽  
Vol 62 (1) ◽  
pp. 1-12 ◽  
Author(s):  
S. Gago ◽  
J. Hurajová ◽  
T. Madaras
Keyword(s):  
Betweenness Centrality ◽  
Average Distance ◽  
Shortest Paths ◽  
Upper Bounds

AbstractThe betweenness centrality of a vertex of a graph is the portion of the shortest paths between all pairs of vertices passing through a given vertex. We study upper bounds for this invariant and its relations to the diameter and average distance of a graph.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

eMap: A Web Application for Identifying and Visualizing Electron or Hole Hopping Pathways in Proteins

2019 ◽  
Author(s):  
Ruslan N. Tazhigulov ◽  
James R. Gayvert ◽  
Melissa Wei ◽  
Ksenia B. Bravaya
Keyword(s):  
Web Application ◽  
Shortest Paths ◽  
Coarse Grained ◽  
Decay Parameter ◽  
Electron Hole ◽  
Web Based ◽  
Aromatic Amino Acid Residue ◽  
Pathways Model ◽  
Visualization Tools ◽  
Effective Decay

<p>eMap is a web-based platform for identifying and visualizing electron or hole transfer pathways in proteins based on their crystal structures. The underlying model can be viewed as a coarse-grained version of the Pathways model, where each tunneling step between hopping sites represented by electron transfer active (ETA) moieties is described with one effective decay parameter that describes protein-mediated tunneling. ETA moieties include aromatic amino acid residue side chains and aromatic fragments of cofactors that are automatically detected, and, in addition, electron/hole residing sites that can be specified by the users. The software searches for the shortest paths connecting the user-specified electron/hole source to either all surface-exposed ETA residues or to the user-specified target. The identified pathways are ranked based on their length. The pathways are visualized in 2D as a graph, in which each node represents an ETA site, and in 3D using available protein visualization tools. Here, we present the capability and user interface of eMap 1.0, which is available at https://emap.bu.edu.</p>

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

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