Help in writing LLR algorithm in matlab

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.

[ana take]

the paper where is the LLR algorithm https://www.google.al/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwjx2_uXobDRAhWBFCwKHeFTBk0QFggaMAA&url=http%3A%2F%2Fwww.ece.rochester.edu%2Fprojects%2Fwcng%2Fpapers%2Fconference%2Fcheng04_mswim.pdf&usg=AFQjCNFkmJ0frzYH0fllrk9TOq4VJ7jXKQ&sig2=ha6-SD5HAc8Hrmds4oPOLA&bvm=bv.142059868,d.bGg

[John D'Errico]

Contact the author of the paper.