5 Pages
English
Gain access to the library to view online
Learn more

University of Illinois at Urbana Champaign Spring

Gain access to the library to view online
Learn more
5 Pages
English

Description

University of Illinois at Urbana-Champaign Spring 2007 Math 181 Group F1 Midterm 1. Friday, Feb. 23. No documents allowed. Mobile phones, mp3 players, etc., are also forbidden. The one and only piece of equip- ment you may use is a basic calculator- and you won't need it. NAME 1. (a) Draw a graph with vertices A, B, C and D in which the valence of vertices A and D is 3 and the valence of vertices B and C is 2. (b) Is it possible to draw a graph on the same vertices in which A, B and C have valence 2 and D has valence 3 ? (explain). 2. For each of the graphs below, determine the minimal number of edges that need to be removed to disconnect it.

  • hold no

  • fit decreasing

  • algorithm

  • no documents allowed

  • algorithm when

  • does

  • first-fit algorithm

  • when scheduling


Subjects

Informations

Published by
Reads 20
Language English

Exrait

A B C D A D 3
B C 2
A B C 2 D
3
Friday,erticesdisconnectandFerev1.gFb.23.eloNobdoiscumentsertaltoloweond.181MidtermMobilephones,ofmp3eplayers,hetc.,moarandeandalsooffsoprwbidden.aF1sameGroupwhicvTheonevMathandovnly(explain).pieeaccgraphsedeofmineeedgesquip-needmentryouedmaySpringuseaignisUrbana-Champathebalence2007visice.tIsasicacalculator-(b)aitndossibleyoudrawona'trnephethedvit.inNAMEh,and1.ha(a)eDraalencewandahasgraphalencewith?v2.erticesorsh,theIllinoib,w,oftminimalrumtheandnUniversitybinofwhicthatthetovealenceeofvvtoerticesit.B
1060 3020
A C
65
90
35
8030
40E D
A
mitsneighHovanatEulerthecircuitltonianorWhatnot.nearest-neighIfoneitthedohes,ydrastartingwcostanSameEulerbcircuithamiltonianontothecgraphab;ndifhaitobtaineddotheesn't,oradndansecientt?Eulerizationreplacingoforthealgorithm.graphmanandwuvstoefoimethotgraphtooobtaine,atcirecmiuitcircuitthatbreusesapplyinganearestminimbualgorithm,matn.umibtheerofofhedges.circuit4.b)w,question,elothebbitalgorithmtheywhethersorted-edgesgraphsc)thewofyhcircuitseacouldorhayeinconsiderForderhereapplysabrutea)rFeord3.?1/2
17 4
2
45
6 15
8 6 4
6 71 8
2 4 3
35 23
13 35
ouldbegsitconstructedheusinglengththreeapplyletters?folloowtoedhobmiybrutetndwal'sow.nossibleumeralsst?theb)aYlongoueoutes)wnhaacthmhaoptimaliApplyntoofbninelettersaplatesppartmenpttcomplexesIn(includcomputeitotalnofgtour,thewonewillytakou(inlivnetoin),tandeyforceoulplanoritotovisittheeatourc6.hKruskofalgorithmmantwgraphpropelocandplatesfaerties.IfmixtureitusetaklicenseyesHo,umerals.enaminsomeutey5.a)ourT T1 4
10 13
T7
7
T T2 56 15
T TTT 96 83 12 5 38
T1
3
T7TT 52 5 5 3
T8TT 63 69 4
T
4 2
minimalamounGivbapplyingthetofttimeandneededWhattognishthethecessors)jobheinscthethefollobwingdsituationsa:w,(i)hedulesYooubdon'tcritical-pathknomethowdecreasing-timethemethon?umisbw.ertofConsiderproicessors.r(ii)phThereeloanndescpro(oncessor.w(iii)proThereobtainedareytthewscodulingprodcessorsthe(iv)listTherehedulingared.of(b)path(s)threeprocriticalcessors.(are)estimate8.F(a)orelotdigraphheorder-requiremenorder-requirementhetis7.one9.Youmawhenmm(b)ustonpusingacoksthemfollspannoofwingthewweighotsducedin-tovbinsethatycantreeholdtainnoWhenmorealgothany9lbscompletion:er5lbs,an7lbs,optimal1lb,2lbs,path4lbs,y5lbs,r1lb,dges1thelsalesmanby,enden3lbs,starting6lbs,(c)2lb,n3lbs,a4lbs.c(a)eryUsegraph.thehedulingnext-tlist-proalgorithmithm,torequiredpachkincreasethe(e)walgorithmemoreitgrst-thducetsresults.;Therepresenprotbytheourosolutitedoenalgorithmbsolvingelotraweling(b)problemSameaquestibodepn,tusingthethiscittime.theArst-tidecreasinggalgorithmof(c)graphAgainusttheonsameevquestion,edgeusingathe(d)wscorst-ttasksdecreasingthealgorithm.cessing10.rTdecreasingruetimeorbfalseeac?task(a)yAtheheutime.rTheisticorst-talgorithmnevdousesesbnotxesnecessarilyhptheralgorithm.