"优秀图与网络算法论文收集与总结：研究成果和问题解决方法的概要"
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The 2016 MCM/ICM Summary Sheet shows the Team Control Number 52849 and the Problem Chosen E. The team has conducted research and presented their findings in an excellent paper on graph and network algorithms. The specific details of the paper are not included on this summary sheet, but it is evident that the team has put in significant effort and has achieved notable results in their study of graph and network algorithms. The team's summary is to be included as the first page of their electronic submission, and it is clear that they have worked diligently to address the problem chosen. The team has demonstrated their expertise in this area of study, and their paper is likely to make a valuable contribution to the field of graph and network algorithms. Overall, the 2016 MCM/ICM Summary Sheet reflects the hard work and dedication of Team Control Number 52849 in their research on graph and network algorithms.
Team 52849 MCM/ICM Page 5 of 31
Change in residential water:
d(residential)
dt
=
d(personalfiltration)
dt
+
d(transport
p
)
dt
−
d(waste
r
)
dt
Change in locked water:
d(locked)
dt
=
d(contamination)
dt
+
d(runof f
l
)
dt
−
d(unlock)
dt
Change in available water:
d(available)
dt
=
d(unlock)
dt
+
d(waste
i
)
dt
+
d(waste
r
)
dt
+
d(runof f
a
)
dt
−
d(funnel)
dt
−
d(transport
i
)
dt
−
d(personalfiltration)
dt
−
d(filter)
dt
Change in potable water:
d(potable)
dt
=
d(filter)
dt
+
d(donate)
dt
−
d(transport
p
)
dt
−
d(corruption)
dt
3.1.2 Applied to Haiti
This network system of interaction allows for consideration of all possible factors involved in the
water system, justifying the use of this systems model. By comparing the connectedness of each
factor to the target variable (in Haiti’s case, residential water for drinking), the yield/change ratio
of interventions in different areas can be compared for effectiveness.
Applied to Haiti, there is an economic crisis of potable water, specifically the drinking water that
individuals receive. Thus, in relation to the system above, we must find a way to maximize the
amount of water available for drinking.
Assumption: In Haiti, there is a large amount of available water (water that is currently not
potable but which can be cleaned for use).
Justification: The water crisis in Haiti is mainly an economic one with regards to a lack of
potable water for drinking, which contributes to the severe death rate caused by dehydration and
compounded by cholera (7).
Assumption: Haiti’s current transportation rate of potable water is extremely low.
Justification: The country currently lacks a pipe system, so mass transportation to the public
is very minimal, leaving most residents to rely on purchased external water sachets or barrels for
consumption (8).
Assumption: In terms of drinking water wastage, waste rates cannot significantly change.
Justification: All water that humans drink is passed through the body at some point, and there
is neither a need nor a way to change this bodily function.
Assumption: Haitian water corruption rates are non-negligible.
Justification: With high rates of gang violence and local corruption, especially compared to
other countries, it is important to consider water lost to corruption which never makes it to the
poor (33).
Assumption: Haitian water donation rates are high.
Justification: As the “Republic of NGOs,” water donation rates from external organizations are
high (10).
Determining Scarcity-Drivers
By integrating the differential equation for residential water, we find that:
residential = personallyfilteredwater + tr ansportedwater − wastedwater + C
With regards to drinking water, water lost to waste cannot be changed, and the constant of in-
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