lecture27 - CSCI-255 Advanced Data Structures Lecture 27...

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CSCI-255 Advanced Data Structures Lecture 27
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Minimum Spanning Tree • Minimum spanning tree : Given a connected graph G = (V, E) with real-valued edge weights c e , a MST is a subset of the edges T E such that T is a spanning tree whose sum of edge weights is minimized 5 23 10 21 14 24 16 6 4 18 9 7 11 8 5 6 4 9 7 11 8 G = (V, E) T , Σ e T c e = 50
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Applications • MST is a fundamental problem with diverse applications – Network design • telephone, electrical, hydraulic, TV cable, computer, road – Indirect applications • max bottleneck paths • LDPC codes for error correction • image registration with Renyi entropy • learning salient features for real-time face verification • reducing data storage in sequencing amino acids in a protein • model locality of particle interactions in turbulent fluid flows • autoconfig protocol for Ethernet bridging to avoid cycles in a network – Cluster analysis
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Example Application b Suppose each graph vertex represents an electrical outlet in your house. The edge costs represent the amount of wiring you will need to connect the outlets. You want to have them all wired up, but at minimal cost
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v1 v2 v3 v4 v5 v6 v7 The MST is shown with bold red edges. The total edge cost is 16.
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lecture27 - CSCI-255 Advanced Data Structures Lecture 27...

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