Dynamic Linear Programming in Minimum Spanning Tree Problem
Explore dynamic linear programming formulations for the Minimum Spanning Tree problem, detailing the algorithm steps and arc connections. Witness examples and images illustrating the process and optimization.
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+ + + + + + + + + 10 50 30 70 10 60 30 60 30 Min S t x x x x x x x x x x 12 13 x 24 25 34 35 45 46 56 = . 900 0 0 0 0 = 600 600 0 12 x 13 + + = = x x 12 24 25 + + x x x x 13 34 35 + + = = x x x 24 34 45 x 46 + x x x x 25 35 45 56 900 800 600 600 100 300 400 600 x 46 56 x 12 x 13 x 24 x 25 x 34 x 35 x 45 x 46 x 56 , , , , , , , , x x x x x x x x x 12 13 24 25 34 35 45 46 56
Linear Programming of a Minimum Spanning Tree Problem k E j At each general step of the above algorithm if denoted all of the arc which connected and means that then the following dynamic linear programming can consider as the formulation of Minimum Spanning Tree problem: C k = {( , ) i j | , } E A i C C C k k k k C Min d x l k ij ij ( , ) i j E i dij k . 1 , 1 S t x C N k ij K ( , ) i j E s k {0,1}, ( , ) x i j E j ij k m k C k
Example for formulation of Minimal Spanning Tree + + + + + + 4 6 3 2 + 4 Min S t x x x x x x x 13 x x 14 23 x x 35 x x 45 + . 1 13 14 x 23 35 45 x , , , , {0,1} 13 14 23 35 45
