This observation leads to the design of an algorithm that starts by counting the foremost routes belonging to the last snapshot (G_k) only, and proceeds backwards using the information already computed.
More precisely, when considering snapshot (G_i) from a source s, the goal is to count all foremost routes involving only edges in (cup _ {jge i} E_j) (i.e., with time intervals in (cup _ {jge i} I_j)), and when doing so, all the foremost routes involving only edges strictly in the "future" (i.e., time intervals (cup _ {j>i} I_j)) have been already calculated for any pair of nodes.
Liquid at room temperature, metallic mercury evaporates rapidly and forms a colourless, odourless vapour [ 5] with the foremost exposure route of metallic mercury being inhalation of these mercury vapours [ 6].
At a presentation to a major airline's executives, he was rebuffed with the argument that passengers care foremost about the route network, not about being served by a happy, committed work force.
The Camino de Santiago (Way of Saint James) has been the foremost European pilgrimage route since the 9th century.
Algorithm 3 simply calculates the product of the number of foremost journeys between two routes (sleadsto x), and (xleadsto y), if they do not share any vertex (lines 4 9).
In fact, it is easy to see that there exist TVGs where counting all foremost journeys or journey routes between two vertices is #P-complete, which means that no polynomial-time algorithm is known.
Visiting the United States in 1903, just as it manipulated its way into control of the Panama Canal route, China's foremost modern intellectual, Liang Qichao (who was also a major early influence on Mao Zedong), concluded that China had to rapidly build an industrial and military base in order to survive.
In this section, we first focus on foremost betweenness based on journey routes in the general setting (Algorithm 1).
Moreover, we call foremost increasing journeys the ones whose route ({e_1,e_2, ldots, e_k}) is such that birth-date ((e_i) le ) birth-date ((e_{i+1})).
