of maxflow jt
Transcript of of maxflow jt
Applications of maxflow minent
edge disjointpaths jt Eyenetuork
vertex disjoint paths 1c f't
vertex capacities output max flew
bipartite maximum matchingcasualty integers
MaxMatching
Transform input features in solution F paths inTransform output Max flew
Time in terms oforiginalinputProve correct
Ex ling N ntr pt total input sizen classes Eft n enrollmentr rooms SCI r seatst timeslots Afa t t p availabilityp proctors ACKD T proctorL
is availableEvery class needs scheduling at EmekESS in any examEI exam per room per time slot
Ea.ch onoctoroverseesE5exam
class E capacityschedule set of 4 tuples i j k l room j g 1one per tindforkedavailable
1 or
do I f s
E I t
I
Each class EC jt exam EEthePIIIhas EI exam e inane Iet eachproctor can
exams
onh natch one
Feasibleexam atanytime
Integer flew 2 paths set of successfullyscheduled exams
IS Imax flow in H1 classes
ntr ftp.t2 OCNC En nr Http xp NZ
Time ONE 406USD
TnpleSelec_tionInp_tifinitesetsX1 Xe Xd
representdiscrete resources
for all x c Xi for all I
CCx y for all C Xi yExite for all
Outputtargetset of tuples Cx x xd cXzxXzx xXdSubject to constraints
for each index i each x c Xi appears in Edx tuplesfor each index i
each XE Xi and YE Xi I appear in Echr y tuples
MaxMatchinginput G LUR E X1 L
Outpt max matching Xz R
set of pairsCx y ELxR cC y1 if Xy EE0 if xy E
Ix Cly L
of yOFFIT 4
InX1 Xz Xd
largest complete complete complete maximumvalid set of tuples paths feasible flew
DisjointPat_hCoerTpnti gG Cv.ETgeneralgraphs NP hard
Output min disjointpaths that cover every vertex
b d0 30
08 1 0o oc e with
Intuition We want to assign a successor to as manymatch vertices as possible
a bb e
Iq Path.EE oFIYessorBuild
Reduce to max matching H LUR E
L U
R U Ccopyfind max matching.M
I0 0 paths in G
Oe s paths V M
0 VE timeV V
Projectselection Open pit mininginput dag Etv E U projects
C dependenciesprofit v U su means u can onlybedonefor every vertex after u
Output Subset SEVSE for all u u WES E S
max DCS Festa
a IF Tsf D8 cost
IIPartition V S UT S selectreduce to min cat problem T throw out
toz
8 Build H
a Tsf Tgf computemaxflowf
return P Ift
f OcuE time
p Emax 63,03 Eo Gmpaff.EE Iobhfepend
profit 5 P lls TH claim
Forany XEV cost Cxotcu cG t
yieldCx Izzo toCu Execs u
profitCx yield X costa IZ u
P yield V yield s yieldCt119TH costs yield TP 115TH yield s cost G profit s U