Sven Venema

NC algorithms for the single most vital edge problem with respect to shortest paths

Abstract For a weighted, undirected graph G = (V,E), 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 distance between two nodes s and t. We give a sequential algorithm for the Single Most Vital Edge problem on weighted and undirected graphs. Our algorithm has a time complexity O(mα(m,n)), where n = ¦ V ¦, m = ¦ E ¦ , and α(m,n) is a functional inverse of Ackermanns function. This algorithm eliminates the inherent sequentiality of the algorithm due to Malik et al. We also obtain a set of parallel algorithms running in O(log n) time using m processors and O(m) space on the CRCW PRAM, in O(log n) time using mn log n CREW processors and O(m + n log m) space, and in O(log n) time using mn log n EREW processors and O(mn) respectively. These are the first NC algorithms for solving this problem on the PRAM.

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

For a weighted, undirected graph G = (V, E) where |V| = n and |E| = m, we examine the single most vital edge with respect to two measurements related to all-pairs shortest paths (APSP). The first measurement considers only the impact of the removal of a single edge from the APSP on the shortest distance between each vertex pair. The second considers the total weight of all the edges which make up the APSP, that is, calculate the sum of the distance between each vertex pair after the deletion of a tree edge. We give a sequential algorithm for this problem, and show how to obtain an NC algorithm running in O(log n) time using mn2 processors and O(mn2) space on the MINIMUM CROW PRAM. Given the shortest distance between each pair of vertices u and v, the diameter of the graph is defined as the longest of these distances. 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. We show how to modify the above algorithm to solve this problem using the same time and number of processors. Both algorithms compare favourably with the straightforward solution which simply recalculates the all pairs shortest path information.

Peer Observation as a Collaborative Vehicle for Innovation in Incorporating Educational Technology into Teaching

We provide a case study using peer review and observation of teaching (PRO-Teaching) as a vehicle to develop both a scholarly approach to teaching as well as providing a framework to gather data for ongoing change to facilitate scholarship of learning and teaching.

Collaborative Supervision of Machine Learning as a Tool for Web-Based Education: A Teaching and Learning Triangle

Machine-learning applications often suffer bottlenecks due to inefficiency in the human-machine interface. A novel architecture design has been developed to allow expert supervisors to collaborate and cooperate in real-time to alleviate the effects of the bottleneck. Replacing supervisors with students, this architecture also allows for supervised training and collaborative learning of students as well as machine learners. Our attempts to provide Web-based courses to distance learners have highlighted the need for more effective use of the medium for education and appropriate tools to provide the necessary richness of experience. We present our design and an example application to demonstrate how we address some of the shortfalls present in Web-based, distance education.

Collaborative supervision of machine vision systems: Breaking a sequential bottleneck in the supervised learning process

This paper describes a computer vision system in the context of exploiting parallelism. The key contribution is a description of a network design that breaks a long-standing bottleneck in the supervision phase of the vision process. The proposed solution draws from and contributes to the disciplines of machine learning, computer vision and collaborative editing. The significance of the solution is that it provides the means by which complex visual tasks such as mammography can be learned by an artificial vision system.

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

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. The first measurement considers only the impact of the removal of a single edge from the APSP on the shortest distance between each vertex pair. The second considers the total weight of all the edges which make up the APSP, that is, calculate the sum of the distance between each vertex pair after the deletion of any edge belonging to a shortest path. We give a sequential algorithm for this problem, and show how to obtain an NC algorithm running in O(log n) time using mn2 processors and O(mn2) space on the MINIMUM CRCW PRAM. Given the shortest distance between each pair of vertices u and v, the diameter of the graph is defined as the longest of these distances. 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. We show how to modify the above algorithm to solve this problem using the same time and number of processors. Both algorithms compare favourably with the straightforward solution which simply recalculates the all pairs shortest path information.