scholarly journals Faster shortest paths in dense distance graphs, with applications

2018 ◽  
Vol 711 ◽  
pp. 11-35
Author(s):  
Shay Mozes ◽  
Yahav Nussbaum ◽  
Oren Weimann
Keyword(s):  
Shortest Paths ◽  
Distance Graphs

scholarly journals Distance closures on complex networks

2015 ◽  
Vol 3 (2) ◽  
pp. 227-268 ◽  
Author(s):  
TIAGO SIMAS ◽  
LUIS M. ROCHA
Keyword(s):  
Complex Networks ◽  
Diffusion Processes ◽  
Shortest Paths ◽  
Approximate Reasoning ◽  
Weighted Graphs ◽  
Dijkstra Algorithm ◽  
Simple Method ◽  
Distance Graphs ◽  
Network Analyses ◽  
Metric Distances

AbstractTo expand the toolbox available to network science, we study the isomorphism between distance and Fuzzy (proximity or strength) graphs. Distinct transitive closures in Fuzzy graphs lead to closures of their isomorphic distance graphs with widely different structural properties. For instance, the All Pairs Shortest Paths (APSP) problem, based on the Dijkstra algorithm, is equivalent to a metric closure, which is only one of the possible ways to calculate shortest paths in weighted graphs. We show that different closures lead to different distortions of the original topology of weighted graphs. Therefore, complex network analyses that depend on the calculation of shortest paths on weighted graphs should take into account the closure choice and associated topological distortion. We characterize the isomorphism using the max-min and Dombi disjunction/conjunction pairs. This allows us to: (1) study alternative distance closures, such as those based on diffusion, metric, and ultra-metric distances; (2) identify the operators closest to the metric closure of distance graphs (the APSP), but which are logically consistent; and (3) propose a simple method to compute alternative path length measures and corresponding distance closures using existing algorithms for the APSP. In particular, we show that a specific diffusion distance is promising for community detection in complex networks, and is based on desirable axioms for logical inference or approximate reasoning on networks; it also provides a simple algebraic means to compute diffusion processes on networks. Based on these results, we argue that choosing different distance closures can lead to different conclusions about indirect associations on network data, as well as the structure of complex networks, and are thus important to consider.

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>

New Results on Edge Rotation Distance Graphs

2016 ◽  
Vol 6 (1) ◽  
pp. 81
Author(s):  
Medha Itagi Huilgol ◽  
Chitra Ramprakash
Keyword(s):  
Distance Graphs

Computer algorithms

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Data Structures ◽  
Analysis Of Algorithms ◽  
Shortest Paths ◽  
Minimum Cut ◽  
Network Data ◽  
Computer Algorithms ◽  
Breadth First Search ◽  
Augmenting Path ◽  
Basic Concepts ◽  
Maximum Flows

This chapter introduces some of the fundamental concepts of numerical network calculations. The chapter starts with a discussion of basic concepts of computational complexity and data structures for storing network data, then progresses to the description and analysis of algorithms for a range of network calculations: breadth-first search and its use for calculating shortest paths, shortest distances, components, closeness, and betweenness; Dijkstra's algorithm for shortest paths and distances on weighted networks; and the augmenting path algorithm for calculating maximum flows, minimum cut sets, and independent paths in networks.

scholarly journals Lower bounds for computing geometric spanners and approximate shortest paths

2001 ◽  
Vol 110 (2-3) ◽  
pp. 151-167 ◽  
Author(s):  
Danny Z. Chen ◽  
Gautam Das ◽  
Michiel Smid
Keyword(s):  
Lower Bounds ◽  
Shortest Paths ◽  
Geometric Spanners

S-packing colorings of distance graphs G(Z,{2,t})

2021 ◽  
Vol 298 ◽  
pp. 143-154
Author(s):  
Boštjan Brešar ◽  
Jasmina Ferme ◽  
Karolína Kamenická
Keyword(s):  
Distance Graphs

Shortest Paths on Cubes

2021 ◽  
Vol 52 (2) ◽  
pp. 121-132
Author(s):  
Richard Goldstone ◽  
Rachel Roca ◽  
Robert Suzzi Valli
Keyword(s):  
Shortest Paths

Density of sets with missing differences and applications

2021 ◽  
Vol 71 (3) ◽  
pp. 595-614
Author(s):  
Ram Krishna Pandey ◽  
Neha Rai
Keyword(s):  
Number Theory ◽  
Asymptotic Density ◽  
Theory Problem ◽  
Distance Graphs ◽  
Positive Integers ◽  
Infinite Set

Abstract For a given set M of positive integers, a well-known problem of Motzkin asks to determine the maximal asymptotic density of M-sets, denoted by μ(M), where an M-set is a set of non-negative integers in which no two elements differ by an element in M. In 1973, Cantor and Gordon find μ(M) for |M| ≤ 2. Partial results are known in the case |M| ≥ 3 including some results in the case when M is an infinite set. Motivated by some 3 and 4-element families already discussed by Liu and Zhu in 2004, we study μ(M) for two families namely, M = {a, b,a + b, n(a + b)} and M = {a, b, b − a, n(b − a)}. For both of these families, we find some exact values and some bounds on μ(M). This number theory problem is also related to various types of coloring problems of the distance graphs generated by M. So, as an application, we also study these coloring parameters associated with these families.

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