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Math Help - minimize the number of Base Stations used by the using the independent set and graph

  1. #1
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    minimize the number of Base Stations used by using independent set and graph theory

    In cellular planning, we have to list the set of available locations for BS. And in any radio network design (RND) we need to maximize the coverage and minimize the # of used BS. So, if we denote the set of all possible available BS locations by M, and set of all potentially covered locations by L. In order to meet our objective we are searching for M' that belongs to M such that |M'| is minimum and such that |Neighbors(M',E)| is maximum, where Neighbors(M',E)= {u belongs to L| there exists v that belongs to M', (u,v) belong to E}.

    So, my question is that how can we explain the last equation and what do we mean by neighbors as a function of M' and E ??

    thanks.
    Last edited by yaso; October 31st 2010 at 11:29 AM. Reason: edit the typos in the title
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  2. #2
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    Quote Originally Posted by yaso View Post
    In cellular planning, we have to list the set of available locations for BS. And in any radio network design (RND) we need to maximize the coverage and minimize the # of used BS. So, if we denote the set of all possible available BS locations by M, and set of all potentially covered locations by L. In order to meet our objective we are searching for M' that belongs to M such that |M'| is minimum and such that |Neighbors(M',E)| is maximum, where Neighbors(M',E)= {u belongs to L| there exists v that belongs to M', (u,v) belong to E}.

    So, my question is that how can we explain the last equation and what do we mean by neighbors as a function of M' and E ??

    thanks.
    How about instead you explain how you can extremise two objectives simultaneously? That is how do you balance the number an extra base station against 1000 extra locations covered?

    CB
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    Thanks CaptainBlack,,, and can you please elaborate more about the your idea?
    is it really used in determing the optimal number and location of BSs in network planning?
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    Quote Originally Posted by yaso View Post
    Thanks CaptainBlack,,, and can you please elaborate more about the your idea?
    is it really used in determing the optimal number and location of BSs in network planning?
    Optimisation always comes down to optimising a single objective. In this case that could be a weighted sum of the number of base stations and the coverage, or something like finding the minimum number of base stations to give an acceptable level of coverage, or ..

    Also:

    Neighbors(M',E)= {u belongs to L| there exists v that belongs to M', (u,v) belong to E}

    Means the set of all locations that are acceptably close to a base station in M'. It is a slightly odd notation in that:

    1. This and some other stuff in your post imply that the set of locations is discrete.
    2. The set of locations is in some way uniform

    CB
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  5. #5
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    Thanks alot CaptainBlack ,,, now I got the idea
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