Lecture23_NetworkFlows2 Friday, October 23, 2020 1:44 PM Recap: • Flowvalue:|f|=f(s,V). • Cut: Any partition (S, T) of V such that s ∈ S and t ∈ T. • Lemma. | f | = f (S, T) for any cut (S, T). • Corollary. | f | 0. • Augmenting path: Any path from s to […]
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Lecture18_ShortestPaths2 Tuesday, October 20, 2020 4:21 PM Unweighted graph Suppose that w(u, v) = 1 for all (u, v) ∈ E. Can Dijkstra’s algorithm be improved? The PQ we have does not have to be a true PQ. Reason: whenever we found a new improved path, we change the key value or the distance. Therefore,
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22.1-6 We start at the position (1, 1) of the adjacency matrix and move to neighboring positions based on the value at the current position. If the value of the current position (i, j) is 1, there’s an edge from i to j, so that i cannot be the universal sink and we move to
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22.1-6 We start at the position (1, 1) of the adjacency matrix and move to neighboring positions based on the value at the current position. If the value of the current position (i, j) is 1, there’s an edge from i to j, so that i cannot be the universal sink and we move to
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Systems, Networks & Concurrency 2019 Distributed Syst8ems Uwe R. Zimmer – The Australian National University [Bacon1998] [Schneider1990] Bacon, J Schneider, Fred Concurrent Systems Implementing fault-tolerant services using the state machine approach: a tutorial ACM Computing Surveys 1990 vol. 22 (4) pp. 299-319 Addison Wesley Longman Ltd (2nd edition) 1998 [Ben2006] Ben-Ari, M [Tanenbaum2001] Principles of
March 5, 2009 4 March 5, 2009 5 March 5, 2009 6 Analysis of Algorithms Recall from previous Lecture • Flow value: | f | = f (s, V). Max-flow, min-cut theorem Proof (continued) Ford-Fulkerson max-flow Ford-Fulkerson max-flow LECTURE 26-27 • Cut: Any partition (S, T) of V such that s ∈ S Network Flows
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Lecture22_NetworkFlows1 Wednesday, October 21, 2020 3:31 PM Matching problem Flow Networks Definition. A flow network is a directed graph G = (V, E) with two distinguished vertices: a source s and a sink t. Each edge (u, v) ∈ E has a nonnegative capacity c(u, v). If (u, v) ∉ E, then c(u, v) =
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BenOr Rand After Exam Mopup Radu Nicolescu Department of Computer Science University of Auckland 30 Oct 2020 1/12 BenOr Rand After Exam 1 BenOr 2 Randomisation 3 Life after 711 4 Exam 2/12 BenOr Rand After Exam BenOr • BenOr 1983: “Theorems” but NO proof: F < • Lynch 1996: Proof F < N/3 •
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COT5405 Analysis of Algorithms LECTURE 14-15 Dynamic Programming vs Greedy Algorithms • MatrixChain Multiplication • Activity Selection Problem • Optimal substructure • Greedy Selection • Knapsack Problem Prof. Alper Üngör COT5405 Analysis of Algorithms 1 Matrix Chain Multiplication Given a sequence (chain) of n matrices A1, A2,…, An, where Ai is a pi-1×pi matrix Compute
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DFS ClassicalDFS CidonDFS§1 CidonDFS§2 Bellman-Ford MIS Search Fundamentals Radu Nicolescu Department of Computer Science University of Auckland 12 Aug 2020 1/35 DFS ClassicalDFS CidonDFS§1 CidonDFS§2 Bellman-Ford MIS 1 Distributed DFS and BFS 2 ClassicalDFS 3 CidonDFS §1 4 CidonDFS §2 5 Bellman-Ford algorithm 6 Maximal Independent Set 2/35 DFS ClassicalDFS CidonDFS§1 CidonDFS§2 Bellman-Ford MIS Distributed
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