a study on minimal spanning tree on network flow

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@ IJTSRD | Available Online @ www ISSN No: 245 Inte R A Study on Minim Vivek S 1 Ass Sri Krishna Adithya Coll ABSTRACT In this paper we discussed the characteristic and application of mini tree and how it is applied on network a we solved some real life problems. KEYWORD: Network flow, Nodes, L spanning tree INTRODUCTION Trees are nothing more than restricted ty just with many more rules to follow. A tr be a graph, but not all graphs will be tree also referred to as a node, a junction, a or an 0 simplex. Instead of shortest span may wish to find a longest spanning tre be interested the trees with other desi and constraints. Such as, a spanni specified maximum degree or diameter. Characteristics: We are given the nodes of a netwo link instead we are given the p between node pairs and the len potential link. It is desired to choose enough pot such a way that there is a part conn nodes of the network. That is no node is left out unconnect The choosen links must provide a each pair of node in such a way length of these links is a minimum. Application of minimal spanning Tree Telecommunication networks: In information super highway applicati becomes, more important telecommunication network are hig w.ijtsrd.com | Volume – 2 | Issue – 5 | Jul-Aug 56 - 6470 | www.ijtsrd.com | Volum ernational Journal of Trend in Sc Research and Development (IJT International Open Access Journ mal Spanning Tree on Networ S 1 , Dhivya Dharshini S 2 , Megala R 2 sistant Professor, 2 B.Sc Mathematics lege of Arts and Science, Coimbatore, Tamil Na concept the imal spanning areas, and also Links, Minimal ypes of graphs, ree will always es. A vertex is a point 0 – cell nning tree, one ee or one may ired properties ing tree with ork but not the potential links ngth for each tential links in necting all the ted. path between that the total e: n these age of ion in this area as many ghly expensive with is very important to o finding minimum spanning Power Transmission Net voltage power transmission Pipeline Network: To co destination. Transportation Network minimum cost. Algorithm: Step 1: start with any given nearest distinct node. Tick a been connected. Step 2: Identify the un conne a connected node and then con Step 3: Repeat step2 untill a The resulting network is guar spanning tree they may be tie node or the closest unconnecte break the ties arbitrarily the a an optimal solution. General Problem: The Midwest TV cable comp providing cable services t development areas. The figure tv linkages among the five are shown on each branch. economical cable network for 2018 Page: 1893 me - 2 | Issue 5 cientific TSRD) nal rk Flow adu, India optimize their designs by g trees for them. twork: To provide high n lines. onnect sources to a no of k: To provide links at n node. Connect it to the all the nodes that have ect node that is closest to nnect these two nodes. all nodes are connected. ranteed to be a minimal es for the nearest distinct ed node. In such a cases algorithm will still yield pany is in the process of to five new housing e below depict potential eas. The cable miles are Determine the most the Midwest Company.

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In this paper we discussed the concept the characteristic and application of minimal spanning tree and how it is applied on network areas, and also we solved some real life problems. Vivek S | Dhivya Dharshini S | Megala R "A Study on Minimal Spanning Tree on Network Flow" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-5 , August 2018, URL: https://www.ijtsrd.com/papers/ijtsrd15794.pdf Paper URL: http://www.ijtsrd.com/mathemetics/applied-mathematics/15794/a-study-on-minimal-spanning-tree-on-network-flow/vivek-s

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  • @ IJTSRD | Available Online @ www.ijtsrd.com

    ISSN No: 2456

    International

    Research

    A Study on Minimal Spanning Tree Vivek S

    1Assistant ProfessorSri Krishna Adithya College of Arts a

    ABSTRACT In this paper we discussed the concept the characteristic and application of minimal spanning tree and how it is applied on network areas, and also we solved some real life problems.

    KEYWORD: Network flow, Nodes, Links, Minimal spanning tree

    INTRODUCTION Trees are nothing more than restricted types of graphs, just with many more rules to follow. A tree will always be a graph, but not all graphs will be treesalso referred to as a node, a junction, a point 0 or an 0 simplex. Instead of shortest spanning may wish to find a longest spanning tree or one may be interested the trees with other desired properties and constraints. Such as, a spanning tree with specified maximum degree or diameter. Characteristics: We are given the nodes of a network but not the

    link instead we are given the potential links between node pairs and the length for each potential link.

    It is desired to choose enough potential links in such a way that there is a part connecting all the nodes of the network.

    That is no node is left out unconnected. The choosen links must provide a path between

    each pair of node in such a way that the total length of these links is a minimum.

    Application of minimal spanning Tree: Telecommunication networks: In these age of

    information super highway application in this area becomes, more important as many telecommunication network are highly expensive

    @ IJTSRD | Available Online @ www.ijtsrd.com | Volume 2 | Issue 5 | Jul-Aug 2018

    ISSN No: 2456 - 6470 | www.ijtsrd.com | Volume

    International Journal of Trend in Scientific

    Research and Development (IJTSRD)

    International Open Access Journal

    n Minimal Spanning Tree on Network Flow

    Vivek S1, Dhivya Dharshini S2, Megala R2 Assistant Professor, 2B.Sc Mathematics

    Sri Krishna Adithya College of Arts and Science, Coimbatore, Tamil Nadu

    In this paper we discussed the concept the characteristic and application of minimal spanning tree and how it is applied on network areas, and also

    Network flow, Nodes, Links, Minimal

    Trees are nothing more than restricted types of graphs, just with many more rules to follow. A tree will always

    trees. A vertex is ode, a junction, a point 0 cell

    or an 0 simplex. Instead of shortest spanning tree, one may wish to find a longest spanning tree or one may be interested the trees with other desired properties and constraints. Such as, a spanning tree with

    We are given the nodes of a network but not the link instead we are given the potential links between node pairs and the length for each

    It is desired to choose enough potential links in that there is a part connecting all the

    That is no node is left out unconnected. The choosen links must provide a path between each pair of node in such a way that the total

    l spanning Tree: In these age of

    information super highway application in this area becomes, more important as many telecommunication network are highly expensive

    with is very important to optimize their designs by finding minimum spanning trees for them.

    Power Transmission Network: voltage power transmission lines.

    Pipeline Network: To connect sources to a no of destination.

    Transportation Network:minimum cost.

    Algorithm: Step 1: start with any given node. Connect it to the nearest distinct node. Tick all the nodes that have been connected. Step 2: Identify the un connect node that is closest to a connected node and then connect these two nodes.Step 3: Repeat step2 untill all nodes aThe resulting network is guaranteed to be a minimal spanning tree they may be ties for the nearest distinct node or the closest unconnected node. In such a cases break the ties arbitrarily the algorithm will still yield an optimal solution. General Problem: The Midwest TV cable company is in the process of providing cable services to five new housing development areas. The figure below depict potential tv linkages among the five areas. The cable miles are shown on each branch. Determine the meconomical cable network for the Midwest

    Aug 2018 Page: 1893

    6470 | www.ijtsrd.com | Volume - 2 | Issue 5

    Scientific

    (IJTSRD)

    International Open Access Journal

    n Network Flow

    Tamil Nadu, India

    with is very important to optimize their designs by nimum spanning trees for them.

    Power Transmission Network: To provide high voltage power transmission lines.

    To connect sources to a no of

    Transportation Network: To provide links at

    with any given node. Connect it to the nearest distinct node. Tick all the nodes that have

    Identify the un connect node that is closest to a connected node and then connect these two nodes.

    Repeat step2 untill all nodes are connected. The resulting network is guaranteed to be a minimal spanning tree they may be ties for the nearest distinct node or the closest unconnected node. In such a cases break the ties arbitrarily the algorithm will still yield

    The Midwest TV cable company is in the process of providing cable services to five new housing development areas. The figure below depict potential tv linkages among the five areas. The cable miles are shown on each branch. Determine the most economical cable network for the Midwest Company.

  • International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456-6470

    @ IJTSRD | Available Online @ www.ijtsrd.com | Volume 2 | Issue 5 | Jul-Aug 2018 Page: 1894

    SOLUTION Step 1: We start with node 1.Connected to the nearest distinct node 2.color node 1 and 2 as both are now connected

    Step 2: identify the unconnected node that is closest to a connected node. The unconnected node closest to either nodes 1 or 2 is node 5. So, we connect node 2 to node 5 and color it to indicate that is connected node.

    Step 3: the unconnected node closest any colored node is node 4.So we connected to node 4 to node 2.

    Step 4: The unconnected node closest to colored node is node 6. So we connect node 6 to node 4.

    Step 5: The unconnected node closest to colored node is node 3. So we connect node 3 to node.

    Step 6: All nodes are now connected. Thus, the minimal spnning tree provides an optimal solution. The most economical cable network i.e. the minimal spanning tree for the Midwest Company given by the links connecting the node pairs as indicated.

    1-2-5; 2-4-6; 1-3.

    The minimum cable miles needed for this spanning tree is given by

    Z = 1+3+4+3+5 = 16 miles.

    PROBLEMS Consider the following network where the number on links represent actual distance between the corresponding nodes. Find the minimal spanning tree

  • International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456-6470

    @ IJTSRD | Available Online @ www.ijtsrd.com | Volume 2 | Issue 5 | Jul-Aug 2018 Page: 1895

    Step 1: We start with node O. connect it to the nearest distinct node A. Colour the nodes O and A as both are

    now connected nodes.

    Step 2: Identify the unconnected node that is closest to a connected node. The unconnected node closest to

    either node O or node A is node B. So, we connect node A to node B and colour it to indicate that is

    connected node.

    Step 3: The unconnected node closest to any coloured

    node is node C. So, we connect node C to node B.

    Step 4: The unconnected node closest to any coloured

    node is node E. So, we connect node E to node B.

    Step 5: The unconnected node closest to a coloured node is node D. So, we connect node D to node E.

    Step 6: The unconnected node closest to coloured node is node T. So, we connect node T to node D.

    Step 7: All nodes are connected .Thus the minimal

    spanning tree provide an optimal solution.

    The most economical cable network, i.e. the minimal spanning tree for network is given by the link connecting the node pairs as indicated :

    O-A-B-C; B-E-D-T

    The minimal cable miles needed for this spanning tree is

    Z = 4+1+2+4+1+6 = 18 miles The management of city information park desires to determine which road telephone cable should be install to connect all 7 work station with a minimal total length of the cable .Node and distance of potential links are given in the network below . Use the minimal spanning tree algorithm to find the most economical cable tree:

  • International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456-6470

    @ IJTSRD | Available Online @ www.ijtsrd.com | Volume 2 | Issue 5 | Jul-Aug 2018 Page: 1896

    Step 1: We start with node O. connect it to the nearest distinct node A .Colour the nodes O and A as both are

    now connected nodes.

    Step 2: Identify the unconnected node that is closest to a connected node. The unconnected node closest to

    either node O or node A is node B. So, we connect node A to node B and colour it to indicate that is

    connected node.

    Step 3: The unconnected node closest to any coloured

    node is node C. So, we connect node C to node B.

    Step 4: The unconnected node closest to any coloured

    node is node E. So, we connect node E to node B.

    Step 5: The unconnected node closest to a coloured node is node D. So, we connect node D to node E.

    Step 6: The unconnected node closest to coloured node is node T. So, we connect node T to node D.

    Step 7: All nodes are connected .Thus the minimal

    spanning tree provide an optimal solution.

    The most economical cable network, i.e. the minimal spanning tree for network is given by the link connecting the node pairs as indicated:

    O-A-B-C; B-E-D-T The minimal cable miles needed for this spanning tree is

    Z = 2+2+1+3+1+5 = 14 miles

    Conclusions: These problems can be expressed and solved elegantly as graph theory problems involving connected and weighted digraph. From a practical point of view, all these problems are trivial if the network is small. Many real life situation however

  • International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456-6470

    @ IJTSRD | Available Online @ www.ijtsrd.com | Volume 2 | Issue 5 | Jul-Aug 2018 Page: 1897

    consist of huge networks, and therefore it is important to look at these network problems in terms of solving them on computers. Reference: 1. KANTI SWARUP, P.K.GUPTA MAN MOHAN,

    Operations Research

    2. NARSINGH DEO, Graph Theory with applications to engineering and computer science.

    3. PRIM, R. C.,shortest connection networks and some generalization: Bell system tech.

    4. P. R.VITTAL, Introduction of Operation Research

    5. BATTERSBY, A. network analysis for planning and scheduling, New York.

    6. FULKER SON, D. R. Flow networks and combinational operation research.