Spatio-temporal Networks: Modeling, Storing, and Querying Temporally-Detailed Roadmaps - Space-Time Integration in Geography and GIScience - page 85

Tabl e 6. 3 Examples of operators in the accessor category

at_time

at_all_time at_earliest

Node get(node,time) get_node(node) get_node_earliest(node,time)

Edge getEdge(node1,node2,time) get_edge(node1,node2) get_edge_earliest(node1,

node2,time)

Route getRoute(node1,node2,time) getRoute(node1,node2) get_route_earliest(node1,

node2,time)

Route getSP_Route(node1,node2,

time)

getSP_Route(node1,
node2)

Flow get_max_Flow(node1,node2,

time)

get_max_Flow(node1,
node2)

Graph get_Graph(time) get_Graph() -

etc. and (2) the operator categories which consist of accessors, modifiers and
predicates. A representative set of operators for each operator category is provided
in Tables 6.3 , 6.4 and 6.5 .

6.10 STN Operations

Tab le 6.3 lists a representative set of 'access' operators. For example, the operator
getEdge(node1,node2,time) returns the edge properties of the edge from node 1 to
node 2, such as the edge identifier (if any) and associated parameters at the specified
time instant. For example operator getEdge(N1,N2,1) on the time-aggregated graph
shown in Fig. 6.5 would return the attribute value of the edge N1 N2 at t D 1,
that is (1, 0.5). Similarly, get_edge(node1,node2) returns the edge properties for
the entire time interval. In Fig. 6.5 , the operator get_edge(N1,N2) would result in
((1,0.5),(1,0.5), 1 ). get_edge_earliest(N3,N4,2) returns the earliest time instant at
which the edge N3 N4 is present after t D 2 (that is t D 3).
Tab le 6.4 shows a set of modifier operators that can be applied to the time
aggregated graphs. We can also define two predicates on the time-aggregated graph.

exists_at_time_t: This predicate checks whether the entity exists at the start time
instant t .
exists_after_time_t: This predicate checks whether the entity exists at a time
instant after t .

Tab le 6.5 illustrates these operators. For example, node v is adjacent to node u at
any time t if and only if the edge ( u , v ) exists at time t asshowninthetable. exists
(N1,N2,1) on the time aggregated graph in Fig. 6.7 returns a “true” since the edge
N1-N2 exists at t D 1.