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Time diffusion synchronization (TDP) [32] supports the synchronization of a whole network. Initially, a set of master nodes so-called leaders is elected. For external synchronization, these nodes must have access to a global time. This is not required for internal synchronization, where masters are initially unsynchronized. Master nodes then broadcast a request message containing their current time, and all receivers send back a reply message. Using these round-trip measurements, a master node calculates and broadcasts the average message delay and standard deviation. Receiving nodes record these data for all leaders. Then they turn themselves into so-called diffused leaders and repeat the procedure. The average delays and standard deviations are summed up along the path from the masters. The diffusion procedure stops at a given number of hops from the masters. All nodes have now received from one or more masters m the time hm at the initial leader, the accumulated message delay Dm, and the accumulated standard deviation bm . A clock estimate is computed as Smvm(hm Dm), where the weights vm are inversely proportional to the standard deviation bm. After all nodes have updated their clocks, new masters are elected and the procedure is repeated until all node clocks have converged to a common time. In a simulation with 200 static nodes with 802.11 radios and a delay of 5 seconds between consecutive synchronization rounds, the deviation of time across the network dropped to 0.6 second after about 200 seconds. 7.6 EVALUATION STRATEGIES



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the situation in which all stations utilize a uniform transmission range R, and there is no interference Thus, the transmission of a station v will be received by all stations within a Euclidean distance R of v In these graphs, there is an edge between nodes u and v if and only if the Euclidean distance between stations u and v does not exceed R An example of a unit disk graph model of a wireless multihop network and a nominal schedule are shown in Figure 161 In that figure, there is a link between a pair of stations if and only if the circles of radius R/2 centered at the pair of stations intersect, including being tangent The slots assigned to the stations are the numbers inside the brackets.





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Regardless of the graph model utilized, if there is an edge between nodes u and v, then u is a one-hop neighbor/neighbor of v and likewise v is a neighbor of u The degree of a node is the number of neighbors The degree of a network is the maximum degree of the nodes in the network The distance-2 neighbors of a node include all of its one-hop neighbors and the one-hop neighbors of its one-hop neighbors The two-hop neighbors of a node are those nodes that are distance-2 neighbors, but are not one-hop neighbors The unit subset of node u consists of u and its distance-2 neighbors The distance-2 degree D(u) of u is the number of distance-2 neighbors of u, and the distance-2 degree D of a network, is the maximum distance-2 degree of the nodes in the network.

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The cost of each tile t is derived from the minimal span of a channel assignment for (G, t) plus a link-up cost of connecting the assignment to a following tile This link-up cost is calculated using the assumption that the same assignment will be repeated The cost of a tile cover y is defined as c(y) = t T y(t)c(t) The minimal cost of a tile cover of a weighted, constrained graph (G, w) will be denoted by (G, w) In order to derive lower bounds from tile covers, it must be established that for the graphs and constraints under consideration S(G, w) (G, w) k.

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Relevant to broadcast scheduling is distance-2 coloring [22, 13] of a graph G = (V, E), where the problem is to produce an assignment of colors C : V 1, 2, such that no two nodes are assigned the same color if they are distance-2 neighbors An optimal coloring is a coloring utilizing a minimum number of colors A distance-2 coloring algorithm is said to color nodes in a greedy fashion (ie, greedily) if when coloring a node, the color.

GNSS SD w (3,4,5) Pseudolites SD w (3,4) GNSS DD w (2,4,5) Pseudolites DD w (2,4)

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