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### NC Algorithms for the Single Most Vital Edge Problem with Respect to All Pairs Shortest Paths

S Venema
2000 Parallel Processing Letters
For a weighted, undirected graph G = V;E where jV j = n and jEj = m, w e examine the single most vital edge with respect to two measurements related to all-pairs shortest paths APSP.  ...  The Most vital edge with respect to the diameter is the edge lying on such a u , v shortest path which when removed causes the greatest increase in the diameter.  ...  Venema et. al. 10 solved the Single Most Vital Edge problem with respect to an s , t shortest path using this approach. To solve MVE1 and MVE2 we extend the result in 10 as follows.  ...

### NC algorithms for the single most vital edge problem with respect to all pairs shortest paths [chapter]

Sven Venema, Hong Shen, Francis Suraweera
1998 Lecture Notes in Computer Science
For a weighted, undirected graph G = V;E where jV j = n and jEj = m, w e examine the single most vital edge with respect to two measurements related to all-pairs shortest paths APSP.  ...  The Most vital edge with respect to the diameter is the edge lying on such a u , v shortest path which when removed causes the greatest increase in the diameter.  ...  Venema et. al. 10 solved the Single Most Vital Edge problem with respect to an s , t shortest path using this approach. To solve MVE1 and MVE2 we extend the result in 10 as follows.  ...

### NC ALGORITHMS FOR THE SINGLE MOST VITAL EDGE PROBLEM WITH RESPECT TO ALL PAIRS SHORTEST PATHS

SVEN VENEMA, HONG SHEN, FRANCIS SURAWEERA
2000 Parallel Processing Letters
For a weighted, undirected graph G = V;E where jV j = n and jEj = m, w e examine the single most vital edge with respect to two measurements related to all-pairs shortest paths APSP.  ...  The Most vital edge with respect to the diameter is the edge lying on such a u , v shortest path which when removed causes the greatest increase in the diameter.  ...  Venema et. al. 10 solved the Single Most Vital Edge problem with respect to an s , t shortest path using this approach. To solve MVE1 and MVE2 we extend the result in 10 as follows.  ...

### Page 7118 of Mathematical Reviews Vol. , Issue 97K [page]

1997 Mathematical Reviews
| (5-GRIF-SI; Brisbane); Suraweera, Francis (5-GRIF-SI; Brisbane) NC algorithms for the single most vital edge problem with respect to shortest paths. (English summary) Inform. Process.  ...  Summary: “For a weighted, undirected graph G = (VE), the single most vital edge in a network with respect to shortest paths is the edge that, when removed, results in the greatest increase in the shortest  ...

### Page 4201 of Mathematical Reviews Vol. , Issue 2001F [page]

2001 Mathematical Reviews
) NC algorithms for the single most vital edge problem with respect to all pairs shortest paths.  ...  Summary: “For a weighted, undirected graph G = (V, E) where |V|=n and |E|=™m, we examine the single most vital edge with respect to all-pairs shortest paths (APSP) under two different measurements.  ...

### AORM: Fast Incremental Arbitrary-Order Reachability Matrix Computation for Massive Graphs

Sung-Soo Kim, Young-Kuk Kim, Young-Min Kang
2021 IEEE Access
In particular, the proposed method outperforms up to 10 times compared to NetworkX for incremental allpairs shortest paths computation.  ...  Processing a reachability query in large-scale networks using existing methods remains one of the most challenging problems in graph mining.  ...  It is well known that the time complexity of BFS for finding the single-source shortest paths is O(n + m). Then, we can extend this algorithm for all n nodes to compute the all-pair shortest paths.  ...

### Solving Systems of Difference Constraints Incrementally with Bidirectional Search

Jianjun Zhou, Martin Müller
2004 Algorithmica
We propose an incremental algorithm for the problem of maintaining systems of difference constraints.  ...  The major challenge is how to update the solution efficiently after the bidirectional search discovers a region that needs changes.  ...  We thank an anonymous referee for valuable suggestions that significantly improved the presentation of this paper.  ...

### NC approximation algorithms for 2-connectivity augmentation in a graph [chapter]

Weifa Liang, George Havas
1997 Lecture Notes in Computer Science
We devise NC approximation algorithms for the optimal 2-edge connectivity and the optimal 2-vertex connectivity augmentation problems by delivering solutions within (1 + In no)(1 + e) times optimum and  ...  Given an undirected graph G = (V, E0) with IVI--n, and a feasible set E of m weighted edges on V, the optimal 2-edge (2-vertex) connectivity augmentation problem is to find a subset S* __ E such that G  ...  Let the shortest path between bl and bk, denoted by Pbl,bk, be the shortest among these 1-1 shortest paths, 2 < k < 1.  ...

### Multicasting in cognitive radio networks: Algorithms, techniques and protocols

2014 Journal of Network and Computer Applications
Multicasting in CRNs is a challenging problem due to the dynamic nature of spectrum opportunities available to the SUs.  ...  In this paper, we provide a self-contained tutorial on algorithms and techniques useful for solving the multicast problem, and then provide a comprehensive survey of protocols that have been proposed for  ...  The famous Dijkstra algorithm used for solving the shortest path tree (SPT) problem is an example greedy algorithm.  ...

### New lower and upper bounds for shortest distance queries on terrains

Manohar Kaul, Raymond Chi-Wing Wong, Christian S. Jensen
2015 Proceedings of the VLDB Endowment
As shortest-path computation, an integral element of query processing, is inherently expensive on terrains, a key approach to enabling efficient query processing is to reduce the need for exact shortest-path  ...  To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/4.0/. For any use beyond those covered by this license, obtain permission by emailing info@vldb.org.  ...  is at most 7 times the optimal shortest surface path  ...

### PiP-X: Online feedback motion planning/replanning in dynamic environments using invariant funnels [article]

Mohamed Khalid M Jaffar, Michael Otte
2022 arXiv   pre-print
A volumetric funnel-graph is constructed using sampling-based methods, and an optimal funnel-path from robot configuration to a desired goal region is then determined by computing the shortest-path subtree  ...  We combine concepts from sampling-based methods, nonlinear systems analysis and control theory to create a single framework that enables feedback motion re-planning for any general nonlinear dynamical  ...  ACKNOWLEDGMENTS The authors are grateful to the Robot Locomotion Group at MIT for providing an open-source software distribution for computing funnels.  ...

### Modularity-based Backbone Extraction in Weighted Complex Networks [article]

Stephany Rajeh and Marinette Savonnet and Eric Leclercq and Hocine Cherifi
2022 arXiv   pre-print
The so-called "modularity vitality backbone" removes nodes with the lower contribution to the network's modularity.  ...  Coarse-graining merges similar nodes to reduce the network size, while filter-based methods remove nodes or edges according to a specific statistical property.  ...  Previous works on modularity vitality centrality has proved to assign high scores to the most influential nodes [32] . Algorithm.  ...

### On Short Paths Interdiction Problems: Total and Node-Wise Limited Interdiction

Leonid Khachiyan, Endre Boros, Konrad Borys, Khaled Elbassioni, Vladimir Gurvich, Gabor Rudolf, Jihui Zhao
2007 Theory of Computing Systems
In contrast, the short paths total interdiction problem is known to be NPhard.  ...  This is known as the short paths interdiction problem.  ...  We proceed with a negative observation. It is well known that the standard shortest path problem is in NC, that is it can be efficiently solved in parallel.  ...

### On Short Paths Interdiction Problems: Total and Node-Wise Limited Interdiction

Leonid Khachiyan, Endre Boros, Konrad Borys, Khaled Elbassioni, Vladimir Gurvich, Gabor Rudolf, Jihui Zhao
2007 Theory of Computing Systems
In contrast, the short paths total interdiction problem is known to be NPhard.  ...  This is known as the short paths interdiction problem.  ...  We proceed with a negative observation. It is well known that the standard shortest path problem is in NC, that is it can be efficiently solved in parallel.  ...

### MODECP: A Multi-Objective Based Approach for Solving Distributed Controller Placement Problem in Software Defined Network

Chenxi Liao, Jia Chen, Kuo Guo, Shang Liu, Jing Chen, Deyun Gao
2022 Sensors
Moreover, compared with the genetic algorithm and random placement algorithm, the proposed algorithm performs better with low latency, high security, low load rate, and low link overhead.  ...  In the controller placement stage, an improved multi-objective differential evolution algorithm is proposed to search for controllers' positions and assign switches to controllers reasonably.  ...  The shortest path length is the combination of the number of hops of the shortest path and the length of the single-hop physical link.  ...
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