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# Facility Location Problem & Migration in Networks

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• 1. Facility Location Problem & MigrationSpeaker: Vasileios KomianosSupervisor: Konstantinos OikonomouIonian University, Dept. of Informatics, PostgraduateFor the course: Distributed Networks & Algorithms
• 2. Facility Location Problem• Problem concerning optimal placement of facilities in order to minimize communication costs.• Decision space: network.• Objective function: median.• Two solutions: – locally optimum, – global optimum.
• 3. Global Optimum • Suppose global information is known, specify the location for facility 0 minimizing total cost.Servicedemand Connection cost
• 4. Global Optimum Communication Cost* Matrix At 0 At 1 At 2 At 3 At 4 At 5 At 6Node 0 0 0,07 0,29 0,18 0,18 0,36 0,07Node 1 0,12 0 0,57 0,40 0,25 0,68 0,11Node 2 0,29 0,37 0 0,11 0,48 0,10 0,36Node 3 0,20 0,29 0,12 0 0,42 0,21 0,29Node 4 0,15 0,13 0,38 0,29 0 0,44 0,09Node 5 0,03 0,04 0,01 0,01 0,05 0 0,04Node 6 0,05 0,05 0,26 0,1 0,07 0,31 0Total Cost 0,86 0,98 1,65 1,19 1,49 2,12 0,99Minimum total cost is 0,86 when facility 0 is hosted at node 0.*Communication Cost = connection cost × service demand
• 5. Local Optimum• Facility tracks service demands and their origin.• Calculates demands in case it moves to another node.• Moves to node where remote demands are minimized.• If any movement is to increase the remote demands will not be carried out.
• 6. Local OptimumExample, facility 0 is hosted atnode 5:1. Demands from nodes: • N3 = 2,837673 • N2 = 0,544883 • N5 = 0,0567132. If facility moves to node 2: N3 demands + N5 demands = 2,894383. If facility moves to node 3: N2 demands + N5 demands = 0,601596 4. Facility moves to node 3
• 7. Local OptimumFacility 0 is now located at node 3:1. Demands from nodes: • node 0 = 2,214109 • node 2 = 0,544883 • node 3 = 0,623564 • node 5 = 0,0567132. If facility moves to node 2: N0 demands + N3 demands = 2,8376733. If facility moves to node 5: 4. If facility moves to node 0: N3 demands + N0 demands Demands = N3 + N2 = 2,837673 + N55 = 1,22516 5. Facility moves to node 0
• 8. Local OptimumFacility 0 is now located at node 0:1. Demands from nodes: • node 1 = 0,844266 • node 3 = 1,22516 • node 4 = 0,437587 • node 6 = 0,3834422. If facility moves to node 1: N0 demand + N3 + N4 + N6 = 2,595003 5. If facility moves to node 6:3. If facility moves to node 3: 3,055827 N0 + N1 + N4 + N6 6. Any migration would increase =2,214109 the cost so facility remains at4. If facility moves to node 4: node 0 which in this case happens 2,452868 to be global optimum as well.