Shortest Path Distance Research Articles

Identification of intrinsic long-range degree correlations in complex networks.

Many real-world networks exhibit degree-degree correlations between nodes separated by more than one step. Such long-range degree correlations (LRDCs) can be fully described by one joint and four conditional probability distributions with respect to degrees of two randomly chosen nodes and shortest path distance between them. While LRDCs are induced by nearest-neighbor degree correlations (NNDCs) between adjacent nodes, some networks possess intrinsic LRDCs which cannot be generated by NNDCs. Here we develop a method to extract intrinsic LRDC in a correlated network by comparing the probability distributions for the given network with those for nearest-neighbor correlated random networks. We also demonstrate the utility of our method by applying it to several real-world networks.

Quantifying the impact of urban road networks on the efficiency of local trips

Abstract City-level circuity factors have been introduced to quantify and compare the directness of vehicular travel across different cities. While these city-level factors help to improve the quality of distance approximation functions for city-wide vehicle movements, more granular factors are needed to obtain accurate shortest path distance approximations for last-mile transportation systems that are typically characterized by local trips. More importantly, local circuity factors encode valuable information about the efficiency and complexity of the urban road network, which can be leveraged to inform policy and practice. In this paper, we quantify and analyze local network circuity leveraging contemporary traffic datasets. Using the city of Sao Paulo as our primary case study and a combination of supervised and un-supervised machine learning methods, we observe significant heterogeneities in local network circuity, explained by dimensional and topological properties of the road network. Locally, real trip distances are about twice as long as distances predicted by the L 1 norm. Results from Sao Paulo are compared to seven additional urban areas in Latin America and the United States. At a coarse-grained level of analysis, we observe similar correlations between road network properties and local circuity across these cities.

Distributed multi-hop routing algorithm for wireless sensor networks

In a Wireless Sensor Network (WSN), routing is the process of finding a cost effective route in terms of power consumption. As an evaluation criterion for the WSN performance, network lifetime is directly affected by the routing method. In a wide variety of WSNs, different techniques are used as routing methods, such as shortest distance path. In this paper, we propose a novel algorithm, optimizing power consumption in WSN nodes, based on the shortest path algorithm. In this approach, the energy level of nodes and their geographical distance from each other contribute to the weight of the connecting path. The proposed algorithm is used as a data dissemination method in WSNs with randomly scattered nodes. We also apply Dijkstra?s shortest path algorithm to the same networks. The results showed that the proposed algorithm increases the network lifetime up to 30 % by preventing nodes with low charge levels from early disconnection.

Network Resilience Assessment via QoS Degradation Metrics

This paper focuses on network resilience to perturbation of edge weight. Other than connectivity, many network applications nowadays rely upon some measure of network distance between a pair of connected nodes. In these systems, a metric related to network functionality is associated to each edge. A pair of nodes only being functional if the weighted, shortest-path distance between the pair is below a given threshold T. Consequently, a natural question is on which degree the change of edge weights can damage the network functionality? With this motivation, we study a new problem, Quality of Service Degradation: given a set of pairs, find a minimum budget to increase the edge weights which ensures the distance between each pair exceeds T. We introduce four algorithms with theoretical performance guarantees for this problem. Each of them has its own strength in trade-off between effectiveness and running time, which are illustrated both in theory and comprehensive experimental evaluation.

Sectorización basada en la teoría de los grafos de redes de distribución de agua potable con una y con múltiples fuentes

A graph theory based methodology for design of water network partitioning is proposed. Both multiple and single source networks are considered. In the first case the partition refers to the definition of isolated sectors, each of them supplied by its own sources. The shortest paths from each water source to each network node are found and each network node is assigned to be supplied exclusively by the source with the shortest path distance to it. The pipes to be closed are the edge separators of such partition. In the second case the partitioning problem refers to a division of the network in relatively small district metering areas (DMAs) each of them fed by a single pipe. A hierarchical tree for the graph is constructed using a breadth-first search. A recursive approach is applied on this tree to find the design flow rates in each pipe summing the demand of descendant nodes. Based on these flow rates the nodes belonging to each DMA are found. The pipes to be closed are defined as the chords between branches of the hierarchical tree lying below the feeding pipe. The procedure has been tested on a real medium city all-pipe water distribution network model.

Refinement of Metrics: Erdős Number, a Case Study

We introduce a concept called refinement and provide two different ways of refining metrics. By applying these methods we produce several refinements of the shortest-path distance on the collaboration graph and hence a couple of new versions of the Erdős number.

The reach, metric distortion, geodesic convexity and the variation of tangent spaces

In this paper we discuss three results. The first two concern general sets of positive reach: we first characterize the reach of a closed set by means of a bound on the metric distortion between the distance measured in the ambient Euclidean space and the shortest path distance measured in the set. Secondly, we prove that the intersection of a ball with radius less than the reach with the set is geodesically convex, meaning that the shortest path between any two points in the intersection lies itself in the intersection. For our third result we focus on manifolds with positive reach and give a bound on the angle between tangent spaces at two different points in terms of the reach and the distance between the two points.

Upper Bounds on Liouville First‐Passage Percolation and Watabiki's Prediction

AbstractGiven a planar continuum Gaussian free field h𝒰 in a domain 𝒰 with Dirichlet boundary condition and any δ > 0, we let be a real‐valued smooth Gaussian process where is the average of h𝒰 along a circle of radius δ with center v. For γ > 0, we study the Liouville first‐passage percolation (in scale δ), i.e., the shortest path distance in 𝒰 where the weight of each path P is given by . We show that the distance between two typical points is for all sufficiently small but fixed γ > 0 and some constant c* > 0. In addition, we obtain similar upper bounds on the Liouville first‐passage percolation for discrete Gaussian free fields, as well as the Liouville graph distance, which roughly speaking is the minimal number of euclidean balls with comparable Liouville quantum gravity measure whose union contains a continuous path between two endpoints. Our results contradict some reasonable interpretations of Watabiki's prediction (1993) on the random distance of Liouville quantum gravity at high temperatures.© 2019 Wiley Periodicals, Inc.

Air Cushion Vehicle (ACV): History Development and Maglev Comparison

This paper will present the ACV working principle and a review of the past research developments of high-speed ACV trains and their efforts in countries like, Brazil, France, Germany, Italy, United Kingdom, and United States, and the low-speed ACV trains, revealing why the former did not match the expectations and failed, while the latter have been prospered and purchase a well-established market niche in short distance paths.
 Finally, this study will promote a direct comparison between the two technologies, ACV and MagLev, with advantages and disadvantages of each one. The ACV development will bring important insights to the research of MagLev trains from a technical and economic perspective, learning with errors of the ACV, that did not enable any high-speed projects to flourish, and, on other hand, the comparative success of the urban ACV, as a complete commercial solution, like the MagLev trains.

Network Resilience Assessment via QoS Degradation Metrics

This paper focuses on network resilience to perturbation of edge weight. Other than connectivity, many network applications nowadays rely upon some measure of network distance between a pair of connected nodes. In these systems, a metric related to network functionality is associated to each edge. A pair of nodes only being functional if the weighted, shortest-path distance between the pair is below a given threshold T. Consequently, a natural question is on which degree the change of edge weights can damage the network functionality? With this motivation, we study a new problem, Quality of Service Degradation : given a set of pairs, find a minimum budget to increase the edge weights which ensures the distance between each pair exceeds T . We introduce four algorithms with theoretical performance guarantees for this problem. Each of them has its own strength in trade-off between effectiveness and running time, which are illustrated both in theory and comprehensive experimental evaluation.

HoTPiG: a novel graph-based 3-D image feature set and its applications to computer-assisted detection of cerebral aneurysms and lung nodules.

A novel image feature set named histogram of triangular paths in graph (HoTPiG) is presented. The purpose of this study is to evaluate the feasibility of the proposed HoTPiG feature set through two clinical computer-aided detection tasks: nodule detection in lung CT images and aneurysm detection in head MR angiography images. The HoTPiG feature set is calculated from an undirected graph structure derived from a binarized volume. The features are derived from a 3-D histogram in which each bin represents a triplet of shortest path distances between the target node and all possible node pairs near the target node. First, the vessel structure is extracted from CT/MR volumes. Then, a graph structure is extracted using an 18-neighbor rule. Using this graph, a HoTPiG feature vector is calculated at every foreground voxel. After explicit feature mapping with an exponential-χ2 kernel, each voxel is judged by a linear support vector machine classifier. The proposed method was evaluated using 300 CT and 300 MR datasets. The proposed method successfully detected lung nodules and cerebral aneurysms. The sensitivity was about 80% when the number of false positives was three per case for both applications. The HoTPiG image feature set was presented, and its high general versatility was shown through two medical lesion detection applications.

Efficient Benders decomposition for distance-based critical node detection problem

This paper addresses the critical node detection problem which seeks a subset of nodes for removal in order to maximize the disconnectivity of the residual graph with respect to a specific distance-based measure, namely the Wiener index. Such a measure is defined based on the all-pair shortest path distances in the residual graph so that the longer the total length of shortest paths, the greater the value of the disconnectivity measure. In the literature, a mixed integer linear programming model and an exact iterative-based method have been presented for this problem; however, both approaches become very time-consuming on graphs having large diameter and non-unit edge lengths. To overcome this shortcoming, in this paper, we present a new formulation for the problem and solve it by Benders decomposition algorithm. We improve the performance of Benders algorithm by several techniques (including analytical calculation of dual variables, generation of good-quality initial optimality cuts, considering master's optimality cuts as lazy constraints, etc.) to reduce the total running time. The extensive computational experiments on instances, taken from the literature or generated randomly, confirm the effectiveness of the new approaches.

Fully Dynamic 2-Hop Cover Labeling

The 2-hop Cover labeling of a graph is currently the best data structure for answering shortest-path distance queries on large-scale networks, since it combines low query times, affordable space occupancy, and reasonable preprocessing effort. Its main limit resides in not being suited for dynamic networks since, after a network change, (1) queries on the distance can return incorrect values and (2) recomputing the labeling from scratch yields unsustainable time overhead. In this article, we overcome this limit by introducing the first decremental algorithm able to update 2-hop Cover labelings under node/edge removals and edge weight increases . We prove the new algorithm to be (1) correct, i.e., after each update operation queries on the updated labeling return exact values; (2) efficient with respect to the number of nodes that change their distance as a consequence of a graph update; and (3) able to preserve the minimality of the labeling, a desirable property that impacts on both query time and space occupancy. Furthermore, we provide an extensive experimental study to demonstrate the effectiveness of the new method. We consider it both alone and in combination with the unique known incremental approach (Akiba et al. 2014), thus obtaining the first fully dynamic algorithm for updating 2-hop Cover labelings under general graph updates. Our experiments show that the new dynamic algorithms are orders of magnitude faster than the from-scratch approach while at the same time being able to preserve the quality of the labeling in terms of query time and space occupancy, thus allowing one to employ the 2-hop Cover labeling approach in dynamic networks with practical performance.

Unconstrained and Curvature-Constrained Shortest-Path Distances and Their Approximation

We study shortest paths and their distances on a subset of a Euclidean space, and their approximation by their equivalents in a neighborhood graph defined on a sample from that subset. In particular, we recover and extend the results of Bernstein et al. (Graph approximations to geodesics on embedded manifolds, Tech. Rep., Department of Psychology, Stanford University, 2000). We do the same with curvature-constrained shortest paths and their distances, establishing what we believe are the first approximation bounds for them.

Object recognition based on critical nodes

In recent decades, the need for efficient and effective image search from large databases has increased. In this paper, we present a novel shape matching framework based on structures common to similar shapes. After representing shapes as medial axis graphs, in which nodes show skeleton points and edges connect nearby points, we determine the critical nodes connecting or representing a shape’s different parts. By using the shortest path distance from each skeleton (node) to each of the critical nodes, we effectively retrieve shapes similar to a given query through a transportation-based distance function. To improve the effectiveness of the proposed approach, we employ a unified framework that takes advantage of the feature representation of the proposed algorithm and the classification capability of a supervised machine learning algorithm. A set of shape retrieval experiments including a comparison with several well-known approaches demonstrate the proposed algorithm’s efficacy and perturbation experiments show its robustness.

Ggenealogy: An R Package for Visualizing Genealogical Data

This paper introduces ggenealogy (Rutter, Vanderplas, and Cook 2019), a developing R software package that provides tools for searching through genealogical data, generating basic statistics on their graphical structures using parent and child connections, parsing and performing calculations on branches of interest, and displaying the results. It is possible to draw the genealogy in relation to variables related to the nodes, and to determine and display the shortest path distances between the nodes. Production of pairwise distance matrices and genealogical diagrams constrained on generation are also available in the visualization toolkit. The tools are being tested on a dataset with milestone cultivars of soybean varieties (Hymowitz, Newell, and Carmer 1977) as well as on a web-based database of the academic genealogy of mathematicians (North Dakota State University and American Mathematical Society 2010). The latest stable package version is available in source and binary form on the Comprehensive R Archive Network (CRAN).

Local Search Yields Approximation Schemes for $k$-Means and $k$-Median in Euclidean and Minor-Free Metrics

We give the first polynomial-time approximation schemes (PTASs) for the following problems: (1) uniform facility location in edge-weighted planar graphs; (2) $k$-median and $k$-means in edge-weighted planar graphs; and (3) $k$-means in Euclidean space of bounded dimension. Our first and second results extend to minor-closed families of graphs. All our results extend to cost functions that are the $p$th power of the shortest-path distance. The algorithm is local search, where the local neighborhood of a solution $S$ consists of all solutions obtained from $S$ by removing and adding $1/\varepsilon^{\Theta(1)}$ centers.

Uncertain Graph Sparsification

Uncertain graphs are prevalent in several applications including communications systems, biological databases, and social networks. The ever increasing size of the underlying data renders both graph storage and query processing extremely expensive. Sparsification has often been used to reduce the size of deterministic graphs by maintaining only the important edges. However, adaptation of deterministic sparsification methods fails in the uncertain setting. To overcome this problem, we introduce the first sparsification techniques aimed explicitly at uncertain graphs. The proposed methods reduce the number of edges and redistribute their probabilities in order to decrease the graph size, while preserving its underlying structure. The resulting graph can be used to efficiently and accurately approximate any query and mining tasks on the original graph. An extensive experimental evaluation with real and synthetic datasets illustrates the effectiveness of our techniques on several common graph tasks, including clustering coefficient, page rank, reliability, and shortest path distance.

Shortest path distance vs. least directional change: Empirical testing of space syntax and geographic theories concerning pedestrian route choice behaviour

Existing knowledge on the impact of built environment (BE) on route choice behaviour is doubtful due to an unresolved tension between two schools of thought. One represented BE geographically and found that most people tend to choose the shortest route. The other represented BE topologically and showed that least directional change is a key determinant of route choice. How do pedestrians make a trade-off between these two factors in route choice? This question is answered using walking route data of 178 pedestrians in Brisbane, Australia. Their reported routes were examined against the corresponding shortest path and least directional change routes using the percent overlap method. The effects of 25 additional BE factors were also estimated in a conditional logit model. The results reveal that: (a) Together distance and direction are likely to explain 53% of route choice decisions; (b) Individually, distance and direction are likely to explain 34% and 46% of route choice decisions respectively; (c) 28% of the chosen routes satisfied both distance and direction criteria. These findings confirm the claims of both schools, but also point that the least directional change route is a preferred option, and that pedestrians tend to minimise both criteria if they can.

Clustering approaches for visual knowledge exploration in molecular interaction networks

BackgroundBiomedical knowledge grows in complexity, and becomes encoded in network-based repositories, which include focused, expert-drawn diagrams, networks of evidence-based associations and established ontologies. Combining these structured information sources is an important computational challenge, as large graphs are difficult to analyze visually.ResultsWe investigate knowledge discovery in manually curated and annotated molecular interaction diagrams. To evaluate similarity of content we use: i) Euclidean distance in expert-drawn diagrams, ii) shortest path distance using the underlying network and iii) ontology-based distance. We employ clustering with these metrics used separately and in pairwise combinations. We propose a novel bi-level optimization approach together with an evolutionary algorithm for informative combination of distance metrics. We compare the enrichment of the obtained clusters between the solutions and with expert knowledge. We calculate the number of Gene and Disease Ontology terms discovered by different solutions as a measure of cluster quality.Our results show that combining distance metrics can improve clustering accuracy, based on the comparison with expert-provided clusters. Also, the performance of specific combinations of distance functions depends on the clustering depth (number of clusters). By employing bi-level optimization approach we evaluated relative importance of distance functions and we found that indeed the order by which they are combined affects clustering performance.Next, with the enrichment analysis of clustering results we found that both hierarchical and bi-level clustering schemes discovered more Gene and Disease Ontology terms than expert-provided clusters for the same knowledge repository. Moreover, bi-level clustering found more enriched terms than the best hierarchical clustering solution for three distinct distance metric combinations in three different instances of disease maps.ConclusionsIn this work we examined the impact of different distance functions on clustering of a visual biomedical knowledge repository. We found that combining distance functions may be beneficial for clustering, and improve exploration of such repositories. We proposed bi-level optimization to evaluate the importance of order by which the distance functions are combined. Both combination and order of these functions affected clustering quality and knowledge recognition in the considered benchmarks. We propose that multiple dimensions can be utilized simultaneously for visual knowledge exploration.