"优秀图与网络算法论文与MCM竞赛总结"

需积分: 0 156 浏览量更新于2024-03-21 收藏 306KB PDF 举报

The 2015 Mathematical Contest in Modeling (MCM) featured a collection of outstanding research papers focusing on graph and network algorithms. Among the 151 papers presented, a diverse range of topics were explored, showcasing innovations and advancements in the field of mathematical modeling. Some of the key themes that emerged from the papers included the development of efficient algorithms for solving complex graph and network problems, the utilization of network analysis to improve communication and transportation systems, and the application of graph theory in various real-world scenarios. The papers presented at the contest demonstrated a deep understanding of graph theory and network algorithms, showcasing the creativity and ingenuity of the participants. From tackling challenging optimization problems to developing novel approaches for analyzing network connectivity, the research papers highlighted the versatility and utility of graph and network algorithms in solving real-world problems. The level of sophistication and complexity displayed in the papers reflected the high caliber of research being conducted in the field of mathematical modeling. Overall, the 2015 MCM contest was a testament to the importance of graph theory and network algorithms in contemporary mathematical research. The participants showcased their analytical skills and problem-solving abilities, demonstrating their ability to tackle complex and challenging problems with innovative solutions. The papers presented at the contest not only contributed to the advancement of mathematical modeling but also highlighted the practical applications of graph and network algorithms in various fields. The contest served as a platform for researchers to exchange ideas, collaborate, and push the boundaries of mathematical knowledge, making valuable contributions to the academic community and beyond.

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

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.”

剩余16页未读，继续阅读

ShenPlanck

粉丝: 951
资源: 343

"优秀图与网络算法论文与MCM竞赛总结"

图与网络算法优秀论文２２1

图与网络算法优秀论文１２1

图与网络算法优秀论文２1

图与网络算法优秀论文９1

图与网络算法优秀论文１３1

图与网络算法优秀论文７1

图与网络算法优秀论文１０1

图与网络算法优秀论文６1

图与网络算法优秀论文２１1

图与网络算法优秀论文５1

最新资源