Team #39160
•
Each office manager within an office of four positions supervises every other position within that
office and also supervises the office manager in every directly connected office one level down in
the tree structure given in the problem statement.
• If office
contains two divisions, the office manager of
division
as well as the division manager of division
supervises the office manager in every directly connected o
given tree structure.
•
Each division manager of a division
We turn our attention to an example showing this hierarchical structure on a smaller scale. Figure 1
depicts a subset
of our multilayer network representing ICM. Specifically, we have depicted the
connections between the positions in the research and networks offices given in the problem statement.
relation. Two nodes in this layer are in an edge if and only if they are in the same office, but not in the
same division. Of mild interest is that this is a complete bipartite graph due to the nature of the relation
being represented.
The top layer represents the “works closely with” relation. Two nodes in this layer are connected by an
edge if and only if they are either in the same four position office or in the same division, so this layer of
the network is the disjoint union of cli
position office are the complement of the complete bipartite graph representing that office.
2.1.3 Treating Objects L
ike
We now define a Person
, for the purpose of our models, as an in
Each Person has some immutable attributes:
Figure
1
Each office manager within an office of four positions supervises every other position within that
office and also supervises the office manager in every directly connected office one level down in
the tree structure given in the problem statement.
contains two divisions, the office manager of
supervises the six other positions in
as well as the division manager of division
within
. The office manager of
supervises the office manager in every directly connected o
ffice one level down from
Each division manager of a division
supervises the six other positions in .
We turn our attention to an example showing this hierarchical structure on a smaller scale. Figure 1
of our multilayer network representing ICM. Specifically, we have depicted the
connections between the positions in the research and networks offices given in the problem statement.
The bottom layer of the figure shows a tree
representing the direct com
mand structure described
above. The node labeled 0 represents the office
manager of the research office. Since this office
manager supervises the other positions in the
research office, we draw edges to nodes 1, 2, and 3,
which represent those positions. T
also supervises the networks office manager, so we
draw an edge from node 0 to node 4, where node 4
represents the networks office manager. The
networks office manager, in turn, supervises the six
positions in division
within the netw
well as the division manager of division
draw edges from node 4 to nodes 5
draw edges from node 11, which represents the
division manager of the networks office, to nodes
12-17.
The middle layer represents the
“works loosely with”
relation. Two nodes in this layer are in an edge if and only if they are in the same office, but not in the
same division. Of mild interest is that this is a complete bipartite graph due to the nature of the relation
The top layer represents the “works closely with” relation. Two nodes in this layer are connected by an
edge if and only if they are either in the same four position office or in the same division, so this layer of
the network is the disjoint union of cli
ques. The cliques representing the two divisions of the fourteen
position office are the complement of the complete bipartite graph representing that office.
ike
People
, for the purpose of our models, as an in
stance of a Python class called “Person.”
Each Person has some immutable attributes:
Page 4 of 17
Each office manager within an office of four positions supervises every other position within that
office and also supervises the office manager in every directly connected office one level down in
supervises the six other positions in
. The office manager of
also
ffice one level down from
in the
We turn our attention to an example showing this hierarchical structure on a smaller scale. Figure 1
of our multilayer network representing ICM. Specifically, we have depicted the
connections between the positions in the research and networks offices given in the problem statement.
The bottom layer of the figure shows a tree
mand structure described
above. The node labeled 0 represents the office
manager of the research office. Since this office
manager supervises the other positions in the
research office, we draw edges to nodes 1, 2, and 3,
which represent those positions. T
his office manager
also supervises the networks office manager, so we
draw an edge from node 0 to node 4, where node 4
represents the networks office manager. The
networks office manager, in turn, supervises the six
within the netw
orks office as
well as the division manager of division
. Thus, we
draw edges from node 4 to nodes 5
-11. Similarly, we
draw edges from node 11, which represents the
division manager of the networks office, to nodes
“works loosely with”
relation. Two nodes in this layer are in an edge if and only if they are in the same office, but not in the
same division. Of mild interest is that this is a complete bipartite graph due to the nature of the relation
The top layer represents the “works closely with” relation. Two nodes in this layer are connected by an
edge if and only if they are either in the same four position office or in the same division, so this layer of
ques. The cliques representing the two divisions of the fourteen
position office are the complement of the complete bipartite graph representing that office.
stance of a Python class called “Person.”
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