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    Can anyone tell me to understand the following code?I don't understand which is the function of A in the following algorithhm: A is the set of links or the set of link lifetimes? I have to write this code in matlab.



    LLR SELECTION ALGORITHM
    In the previous section, we investigate the distributions of
    link lifetime and route lifetime based on some fundamental
    mobility models. The study on the route lifetime distribu-
    tions tells us that despite the higher complexity, a deter-
    ministic routing design for LLR is more suitable for real life
    scenarios than a probabilistic scheme. In this section, we will
    study how to determine long lifetime routes between a pair
    of nodes given a random network snapshot. We first provide
    a polynomial time algorithm to determine the longest life-
    time routes at different route lengths from all the possible
    routes between the source and the destination. Using this
    algorithm, we are able to gather statistical results on the
    achievable maximum route lifetime improvement in random
    networks.
    Here, we put N nodes randomly in a circle of unit ra-
    dius centered at location (0,0). A source node S is placed
    at (x s ,0) and a destination node D is placed at (x d ,0). All
    the nodes have the same transmission range R t . Nodes are
    assigned a speed uniformly distributed in [s min ,s max ] and
    a moving direction uniformly distributed in [0,2π]. At time
    0, S chooses a route to D, and at time T, the route is bro-
    ken. We are interested in the statistical results of following
    metrics.
    1. The longest route lifetime and its route length.
    2. The longest route lifetime of the shortest path. This is
    the best case among all the shortest paths.
    3. The shortest route lifetime of the shortest routes. This
    is the worst case for all the shortest paths.
    4. The longest route lifetime at route lengths between the
    longest and the shortest route length and their correspond-
    ing lifetimes. This metric will be further studied in the next
    section to compare with the lifetime of random shortest-path
    routes.
    The following algorithm is proposed to discover qualified
    long lifetime routes within a polynomial time. The basic
    idea of this algorithm is to first sort all the links based on
    their weights: link lifetime in this case. Then we add the
    links in a descending order and adjust route lengths between
    each pair of nodes one by one. Meanwhile, we keep a record
    (s i , theta i )
    (s j , theta j )
    i
    j
    (x i ,y i )
    (x j ,y j )
    Figure 4: The geometry to calculate link lifetime.
    for all the route length changes and their corresponding life-
    time changes for the source-destination pair. After every
    link is added, we will have a complete record of any lifetime
    changes between the source-destination pair.
    We are only interested in the lifetime and length of the
    path between the source node S and the sink node D. The
    arc set A is sorted in descending order by the lifetime c[i,j]
    of the link composed of nodes i and j. Given a snapshot of
    the network, if the link distance between node i and node
    j is shorter than the transmission range, their link lifetime
    c[i,j] is determined as in Fig. 4 and equation 5.
    D 2 (t) =[(x i + s i cosθ i t) − (x j + s j sincosθ j t)] 2
    + [(y i + s i sinθ i t) − (y j + s j sinθ j t)] 2
    (5)
    By solving D(t) = R t , we will have the link lifetime t as-
    signed to c[i,j]. Notice that when the network snapshot is
    given, all the node location and speed information is deter-
    ministic.
    We denote an edge as e or a link between node i and
    j as e[i,j] if node i and j are connected. d[i,j] is the hop
    distance between nodes i and j. d prev is the last route length
    recorded between the pair. The Long Lifetime Route (LLR)
    selection algorithm is shown in Algorithm 1.



    Data: A, initial c[i,j] for each link
    Result: Record of the longest lifetime achievable for routes
    with different hop distances {d[S,D], c[S,D]}
    begin
    S := ∅;S := A; d prev = ∞;
    for all node pairs [i,j] ∈ N N do
    d[i,j] := ∞; pred[i,j] := 0;
    end
    for all nodes i ∈ N do d[i,i] := 0;
    while |S| 6= A do
    let e[i,j] ∈ S for which c[i,j] = max{c(e),e ∈ S};
    S := S
    S {[i,j]}; S := S − {[i,j]};
    d[i,j] = d[j,i] = 1;
    for each [m,n] ∈ N N do
    if d[m,n] > d[m,i] + d[i,j] + d[j,n] then
    d[m,n] := d[m,i] + d[i,j] + d[j,n] and
    pred[m,n] := i;
    end
    if d[m,n] > d[m,j] + d[j,i] + d[i,n] then
    d[m,n] := d[m,j] + d[j,i] + d[j,n] and
    pred[m,n] := j;
    end
    end
    if d[S,D] < d prev then
    d prev = d[S,D] and record {d[S,D],c[S,D]}
    end
    end
    end
    Algorithm 1: LLR selection algorithm.

  • #2
    Originally posted by ina View Post
    Can anyone tell me to understand the following code?I don't understand which is the function of A in the following algorithhm: A is the set of links or the set of link lifetimes? I have to write this code in matlab.



    LLR SELECTION ALGORITHM
    In the previous section, we investigate the distributions of
    link lifetime and route lifetime based on some fundamental
    mobility models. The study on the route lifetime distribu-
    tions tells us that despite the higher complexity, a deter-
    ministic routing design for LLR is more suitable for real life
    scenarios than a probabilistic scheme. In this section, we will
    study how to determine long lifetime routes between a pair
    of nodes given a random network snapshot. We first provide
    a polynomial time algorithm to determine the longest life-
    time routes at different route lengths from all the possible
    routes between the source and the destination. Using this
    algorithm, we are able to gather statistical results on the
    achievable maximum route lifetime improvement in random
    networks.
    Here, we put N nodes randomly in a circle of unit ra-
    dius centered at location (0,0). A source node S is placed
    at (x s ,0) and a destination node D is placed at (x d ,0). All
    the nodes have the same transmission range R t . Nodes are
    assigned a speed uniformly distributed in [s min ,s max ] and
    a moving direction uniformly distributed in [0,2π]. At time
    0, S chooses a route to D, and at time T, the route is bro-
    ken. We are interested in the statistical results of following
    metrics.
    1. The longest route lifetime and its route length.
    2. The longest route lifetime of the shortest path. This is
    the best case among all the shortest paths.
    3. The shortest route lifetime of the shortest routes. This
    is the worst case for all the shortest paths.
    4. The longest route lifetime at route lengths between the
    longest and the shortest route length and their correspond-
    ing lifetimes. This metric will be further studied in the next
    section to compare with the lifetime of random shortest-path
    routes.
    The following algorithm is proposed to discover qualified
    long lifetime routes within a polynomial time. The basic
    idea of this algorithm is to first sort all the links based on
    their weights: link lifetime in this case. Then we add the
    links in a descending order and adjust route lengths between
    each pair of nodes one by one. Meanwhile, we keep a record
    (s i , theta i )
    (s j , theta j )
    i
    j
    (x i ,y i )
    (x j ,y j )
    Figure 4: The geometry to calculate link lifetime.
    for all the route length changes and their corresponding life-
    time changes for the source-destination pair. After every
    link is added, we will have a complete record of any lifetime
    changes between the source-destination pair.
    We are only interested in the lifetime and length of the
    path between the source node S and the sink node D. The
    arc set A is sorted in descending order by the lifetime c[i,j]
    of the link composed of nodes i and j. Given a snapshot of
    the network, if the link distance between node i and node
    j is shorter than the transmission range, their link lifetime
    c[i,j] is determined as in Fig. 4 and equation 5.
    D 2 (t) =[(x i + s i cosθ i t) − (x j + s j sincosθ j t)] 2
    + [(y i + s i sinθ i t) − (y j + s j sinθ j t)] 2
    (5)
    By solving D(t) = R t , we will have the link lifetime t as-
    signed to c[i,j]. Notice that when the network snapshot is
    given, all the node location and speed information is deter-
    ministic.
    We denote an edge as e or a link between node i and
    j as e[i,j] if node i and j are connected. d[i,j] is the hop
    distance between nodes i and j. d prev is the last route length
    recorded between the pair. The Long Lifetime Route (LLR)
    selection algorithm is shown in Algorithm 1.



    Data: A, initial c[i,j] for each link
    Result: Record of the longest lifetime achievable for routes
    with different hop distances {d[S,D], c[S,D]}
    begin
    S := ∅;S := A; d prev = ∞;
    for all node pairs [i,j] ∈ N N do
    d[i,j] := ∞; pred[i,j] := 0;
    end
    for all nodes i ∈ N do d[i,i] := 0;
    while |S| 6= A do
    let e[i,j] ∈ S for which c[i,j] = max{c(e),e ∈ S};
    S := S
    S {[i,j]}; S := S − {[i,j]};
    d[i,j] = d[j,i] = 1;
    for each [m,n] ∈ N N do
    if d[m,n] > d[m,i] + d[i,j] + d[j,n] then
    d[m,n] := d[m,i] + d[i,j] + d[j,n] and
    pred[m,n] := i;
    end
    if d[m,n] > d[m,j] + d[j,i] + d[i,n] then
    d[m,n] := d[m,j] + d[j,i] + d[j,n] and
    pred[m,n] := j;
    end
    end
    if d[S,D] < d prev then
    d prev = d[S,D] and record {d[S,D],c[S,D]}
    end
    end
    end
    Algorithm 1: LLR selection algorithm.
    In the given code there are figures. Please provide the figures.

    Comment


    • #3
      the link
      https://www.google.al/url?sa=t&rct=j...T-NzKAZiL8nC5w

      Comment


      • #4
        Originally posted by forum-admin View Post

        In the given code there are figures. Please provide the figures.
        here are the figures.I need to know how to write and solve in matlab the lifetime of each node
        Attached Files

        Comment

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