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### Decremental All-Pairs ALL Shortest Paths and Betweenness Centrality [chapter]

Meghana Nasre, Matteo Pontecorvi, Vijaya Ramachandran
2014 Lecture Notes in Computer Science
We consider the all pairs all shortest paths (APASP) problem, which maintains the shortest path dag rooted at every vertex in a directed graph G = (V, E) with positive edge weights.  ...  Thus for graphs with a constant number of shortest paths between any pair of vertices, our algorithm maintains APASP and BC scores in amortized time O(n 2 • log n) under decremental updates, regardless  ...  Discussion We have presented an efficient decremental algorithm to maintain all-pairs all shortest paths (APASP).  ...

### Decremental All-Pairs ALL Shortest Paths and Betweenness Centrality [article]

Meghana Nasre and Matteo Pontecorvi and Vijaya Ramachandran
2014 arXiv   pre-print
We consider the all pairs all shortest paths (APASP) problem, which maintains the shortest path dag rooted at every vertex in a directed graph G=(V,E) with positive edge weights.  ...  Thus for graphs with a constant number of shortest paths between any pair of vertices, our algorithm maintains APASP and BC scores in amortized time O(n^2 \log n) under decremental updates, regardless  ...  Discussion We have presented an efficient decremental algorithm to maintain all-pairs all shortest paths (APASP).  ...

### Fully Dynamic Betweenness Centrality [chapter]

Matteo Pontecorvi, Vijaya Ramachandran
2015 Lecture Notes in Computer Science
For graphs with ν * = O(n), our algorithms match the fully dynamic all pairs shortest paths (APSP) bounds of Demetrescu and Italiano [8] and Thorup [28] for unique shortest paths, where ν * = n − 1.  ...  We present fully dynamic algorithms for maintaining betweenness centrality (BC) of vertices in a directed graph G = (V, E) with positive edge weights.  ...  To compute BC, however, we need all the SPs for each pair of vertices (all pairs all shortest paths -APASP ).  ...

### Efficient computation of distance labeling for decremental updates in large dynamic graphs

Yongrui Qin, Quan Z. Sheng, Nickolas J. G. Falkner, Lina Yao, Simon Parkinson
2016 World wide web (Bussum)
Shortest path computation is one of the most fundamental operations for managing and analyzing large graphs.  ...  In this paper, we focus on the problem of computing the shortest path distance in dynamic graphs, particularly on decremental updates (i.e., edge deletions).  ...  For online social networks, the shortest path distance can be used to measure the closeness centrality between users [22, 23] .  ...

### Faster Algorithms for Mining Shortest-Path Distances from Massive Time-Evolving Graphs

Mattia D'Emidio
2020 Algorithms
Computing shortest-path distances is a fundamental primitive in the context of graph data mining, since this kind of information is essential in a broad range of prominent applications, which include social  ...  Standard algorithms for shortest paths (e.g., Dijkstra's) do not scale well with the graph size, as they take more than a second or huge memory overheads to answer a single query on the distance for large-scale  ...  If the above condition holds, then L k−1 already contains a hub vertex for pair (v k , u) ((u, v k ), respectively) and for all pairs (v k , x) such that there exists a shortest path between v k and x  ...

### An Analysis of Email-Eu-Core Network

A. Bharali
2018 International Journal of Scientific Research in Mathematical and Statistical Sciences
This communication network displays small-world (SW) properties with an average path length of 2.0834 and a clustering coefficient of 0.372, and it also exhibits assortative mixing on degree of nodes,  ...  A study of the robustness of Email-Eu-Core network is also carried out for random and targeted node failures.  ...  Shortest path: There exists a set of paths between any given pair of nodes.  ...

### A Faster Algorithm for Fully Dynamic Betweenness Centrality [article]

Matteo Pontecorvi, Vijaya Ramachandran
2015 arXiv   pre-print
We present a new fully dynamic algorithm for maintaining betweenness centrality (BC) of vertices in a directed graph G=(V,E) with positive edge weights.  ...  We achieve an amortized O((ν^*)^2 ^2 n) time per update, where n = |V| and ν^* bounds the number of distinct edges that lie on shortest paths through any single vertex.  ...  all SPs for each pair of vertices (all pairs all shortest paths -APASP ).  ...

### Partially Dynamic Algorithms for Distributed Shortest Paths and their Experimental Evaluation

Serafino Cicerone, Gianlorenzo D'Angelo, Gabriele Di Stefano, Daniele Frigioni, Alberto Petricola
2007 Journal of Computers
In this paper, we study the dynamic version of the distributed all-pairs shortest paths problem.  ...  In particular, it is able to concurrently update shortest paths and in many cases its convergence is quite fast.  ...  centralized Dijkstra's algorithm for shortest paths on every node.  ...

### A BRIEF SURVEY ON DISTRIBUTED GRAPH ALGORITHMS FOR SHORTEST DISTANCE

V. Jenifer
2019 Zenodo
Number of relative studies namely Graph pattern matching, Spatially Induced Linkage Cognizance (SILC), Snowball Algorithm, GREEDY-SNDOP, APSP and Efficient incremental algorithms are discussed and evaluate  ...  This paper aims to present a brief survey on graph theory based on Shortest Distances in Dynamic Graphs techniques in which the goal is to minimize the amount of work needed to re-optimize the solution  ...  In dynamic all pairs shortest paths, the query DISTANCE(X, Y) can ask for the shortest distance between any pair of vertices X and Y, while in dynamic single source shortest paths, there is a fixed source  ...

### New Techniques and Fine-Grained Hardness for Dynamic Near-Additive Spanners [article]

Thiago Bergamaschi, Monika Henzinger, Maximilian Probst Gutenberg, Virginia Vassilevska Williams, Nicole Wein
2021 arXiv   pre-print
Our new algebraic techniques and spanner algorithms allow us to also obtain (1) a new fully dynamic algorithm for All-Pairs Shortest Paths (APSP) with update and path query time O(n^1.9); (2) a fully dynamic  ...  Maintaining and updating shortest paths information in a graph is a fundamental problem with many applications.  ...  asks for the shortest path tree from a fixed vertex. (3) The All-Pairs Shortest Paths (APSP) problem asks for the shortest path between every vertex pair.  ...

### Efficient algorithms for updating betweenness centrality in fully dynamic graphs

Min-Joong Lee, Sunghee Choi, Chin-Wan Chung
2016 Information Sciences
Betweenness centrality of a vertex (edge) in a graph is a measure for the relative participation of the vertex (edge) in the shortest paths in the graph.  ...  Betweenness centrality is widely used in various areas such as biology, transportation, and social networks.  ...  , betweenness centrality was determined by computing the number of shortest paths between all pairs, and then summing up pair-dependencies of all pairs [22] .  ...

### A Brief Survey on Distributed Graph Algorithms for Shortest Distance

JENIFER.V
2021 Zenodo
Number of relative studies namely Graph pattern matching, Spatially Induced Linkage Cognizance (SILC), Snowball Algorithm, GREEDY-SNDOP, APSP and Efficient incremental algorithms are discussed and evaluate  ...  This paper aims to present a brief survey on graph theory based on Shortest Distances in Dynamic Graphs techniques in which the goal is to minimize the amount of work needed to re-optimize the solution  ...  In dynamic all pairs shortest paths, the query DISTANCE(X, Y) can ask for the shortest distance between any pair of vertices X and Y, while in dynamic single source shortest paths, there is a fixed source  ...

### A Survey of Shortest-Path Algorithms [article]

Amgad Madkour, Walid G. Aref, Faizan Ur Rehman, Mohamed Abdur Rahman, Saleh Basalamah
2017 arXiv   pre-print
A shortest-path algorithm finds a path containing the minimal cost between two vertices in a graph.  ...  There is no one general algorithm that is capable of solving all variants of the shortest-path problem due to the space and time complexities associated with each algorithm.  ...  All-Pairs Shortest-Path (APSP) The all-pairs shortest-paths algorithms reports the distances between any two vertices in a graph.  ...

### Faster Betweenness Centrality Updates in Evolving Networks [article]

Elisabetta Bergamini, Henning Meyerhenke, Mark Ortmann, Arie Slobbe
2017 arXiv   pre-print
Betweenness centrality is a well-known measure which quantifies the importance of a node based on the fraction of shortest paths going though it.  ...  For betweenness, several dynamic algorithms have been proposed over the years, targeting different update types (incremental- and decremental-only, fully-dynamic).  ...  On the contrary, for every node pair (s, t) for which either d(s, t) or σ st has been affected by the insertion, all the nodes in the new shortest paths and the ones in the old shortest paths between s  ...

### Improved Algorithms for Decremental Single-Source Reachability on Directed Graphs [chapter]

Monika Henzinger, Sebastian Krinninger, Danupon Nanongkai
2015 Lecture Notes in Computer Science
In this paper we simplify the previous algorithm using new algorithmic ideas and achieve an improved running time of Õ((m^7/6 n^2/3, m^3/4 n^5/4 + o(1), m^2/3 n^4/3+o(1) + m^3/7 n^12/7+o(1))).  ...  presented the first algorithm for maintaining the set of nodes reachable from a source node in a directed graph that is modified by edge deletions with o(mn) total update time, where m is the number of edges and  ...  There are decremental algorithms for maintaining single-source reachability and strongly connected components with constant query time and expected total update timê O(m 2/3 n 4/3 + m 3/7 n 12/7 ) that  ...
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