Race conditions mean that we cannot guarantee that the value stored in our firing time variable truly represents the minimum over all firing events.
Hence, ∀(x 0,y 0) in A, (int _{{P}^{ast }}mathcal {C} (x s),y(s))mathrm {d}s) is minimum over all possible paths from (x 0,y 0) to sinks if and only if (int _{A}mathcal {C} (x,y left |mathbf {D} x,y right |mathrm {d}xmathrm {d}y) is minimum over all possible vector fields for a given ρ.
Hence, ∀v in A, (sum limits _{v^{prime } in llbracket {{P}^{ast }}rrbracket }mathcal {C} (x_{v^{prime }},y_{v^{prime }})) is minimum over all possible paths from v to sinks if and only if (sum limits _{v,textt {in}, A}mathcal {C} (x_{v},y_{v})left |mathbf {D}(x_{v},y_{v})right |) is minimum over all possible vector fields for a given ρ.
An important problem that commonly arises in areas such as internet traffic-flow analysis, phylogenetics and electrical circuit design, is to find a representation of any given metric D on a finite set by an edge-weighted graph, such that the total edge length of the graph is minimum over all such graphs.
By taking the minimum over all ({j in I_{n}}) such that ({j ne i}), we obtain d_{i}bigl(T^{(N)}(x bigr) ge psi_{N}bigl(E x bigr) d_{i}(x) >0 (5.14) which implies that (T^{(N)}(x)) has distinct components.
Finally, one simple way to approximate the ML distance and LLRs is by selecting the minimum over all t in (28) and (31), respectively: begin{array}{cc}{d}^{mathrm{ML}}& approx underset{t=1,cdots kern0.3em,T}{ min}left({d}_t^{mathrm{WL}}right),kern2em {varLambda}_{n,k}^{mathrm{ML}}approx underset{t=1,cdots kern0.3em,T}{ min}left({varLambda}_{n,k,t}^{mathrm{WL}}right).end{array} (32).
The optimal product-requirement communication spanning tree is the spanning tree with minimum total routing cost summed over all pairs of vertices.
Turning first to the prediction of potential reservoirs: with ε vi |mj) in hand, for a given vector vi, we can construct a ranked list, from maximum to minimum value, of ε vi |mj), over all pairs (vi,mj), i.e., a ranking of the links of a given node according to their strength.
Asterisks indicate normalization between minimum and maximum over all regimens compared.
We further denote by D s (resp. D g ) the absolute minimum APDD over all S- (resp.
A data routing algorithm has been proposed to maximize the minimum lifetime over all nodes in WSN In [15].
