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ez*E$ 7Z&)$j9`&J059D*E;%3{*)e'*E"%$#&)(%(%$+*��W9DNK&Z059D*E;X35-/.%?CNK?C3}*);X*)"%$#*E$j9<=)9D;I&Z6x3+9 �m02?C$5$5&Z9<;>3Hg 4S3#@y?1$5&);02?C3+053 ez*E$}NK&);,V (I&Z9D$53 *)es(U*)9D;,023H]t@B?G(%$+?H-C*EN1(%">02?CF�02.%?G=)$2&)(%.^Z�9D;%3+05?\&)Fl*)esL>">9D6DF>9D;%=_980?C7)?H$jVd059DNK?s*E;d05.%?#3%VEgv~[.>?H;k@B?sN1?\&)3+"%$5?CFk02.>?s0+9<N1?T980v02*W*E�}05*4-C*EN1(%">05? &);K&)(>(%$5*\�W9<NK&Z05?(I&Z05. ez*E$|&��W">?H$+V�(%&Z9<$8:u35*E">$5-H?Z]#F%?C3+059D;I&Z0+9<*);`?/g i ?m-\&); 35?C?�05.I&Z0|*E">$|&Z6<=)*E$+9802.%N13n&)$+?35">L%3+02&);,059<&Z6D68Vleu&)3+05?H$102.I&Z; 02.%&Z0K*)e 5y.%?C; &);%F 7 &Z; � �W� � g ~[.%?rNK&Z9D; $+?\&)3+*E; 9D3102.I&Z0K*E">$&Z6D=E*E$j9D05.%N13#F%*Y;%*)0 $5?C�W"M9<$+?1&);,V_-H*)NK(M6<?��mFI&Z02&p3+05$5"%-a02"%$+?H3Cg�4A6<3+*%][email protected].%?o?a�M-H?C(>059D*E;�*)e*E"%$v3j6<?C?C7)? -H*)NK(>">0/&Z0+9<*);w],*E"%$P&Z6D=E*E$j9D05.%N13PF%*Q;%*)0P(U?H$+ez*)$5N ?��M(�?C;%3+987E?S-H*EN1(%">02&Z059D*E;%3�: 3+"%-/.&)3 � .�$5*)02&Z059D*E;K&);%F1"%;Mez*)6<FM9<;%= ?/g .#"%?[05*405.%?s35-\&J6<?s*)eU02.%?A=E$5&)(%.�: $+?H35"M6D0+9<;%=4ez$5*EN 02.%?T6<&)$5=)?059DN1?QF>9 ��?H$+?H;%-C?405*F5y.%?H;r&);%F 7 &); ?/]>@B?Q-\&);%;>*)0AF>9<3j059D;%=E">9D35.rL�?a0q@y?C?H;n02.%?Q-/.I&)$5&)-C05?H$j9<3j059D-H3*)e[05.%?k�M�>?CFl&);%FX9<;,02?C$+7Z&Z6B35-/.%?CN1?H3Hg�7�9<=)"%$5? � g � � F%?C(>9<-a023d&n=E$2&Z(%. 3+.%*�@T9<;%=_05.%?k0qVW(>9D-\&J6?a�M(U?H$j9<N1?H;,02&Z6[$+"%;Mf 0+9<N1?k$5?H3+">68023 *ELM0/&Z9D;%?HF ez$5*EN *E">$405?H3+053Hg_bM.%*�@s; .%?C$5?G&Z$5?k0q@B*_3+?C023}*)e$5?C35">68023C][*E;%?Yez*E$1& � ] � � � eu&)-C?n~<->=�&);>F*);%?Yez*E$d02.%?|32&ZNK?n~<->=�3+05$5?C05-/.%?HF L,V&meu&Z-C02*)$*)eP�%7)?)g 7I$5*EN�02.%?o=E$2&)(>.w]h@B?d-\&);m3+?H? 02.%&Z0#02.>? 059DNK?o$5?H�:">9D$5?CFXez*)$S02.>?1&)F%F>98059D*E;I&Z6x3+6D?H?a7E?-H*)NK(>">0/&Z0+9<*);K9D3B;>?H=)689<=Z9<L>6D?)g -q;k&)F%FM9D0+9<*E;h]:05.%?H$+?A9D3P7E?H$jVd6D98050+6<?AF>9 �h?C$5?C;%-H?AL�?a0q@y?C?H;p05.%?s�>�M?HF&);%F}9<;,02?C$+7Z&Z6M35-/.%?CN1?H3Hg'~[.>9D3�9D3xNK&Z9D;>68VoF>"%?B05*S02.>?Beu&)-a0x02.%&Z0�@B?T&)$+?'6D*W*E�,9<;%=#&Z0�05.%?[&\7)?H$2&Z=E?;:"%NoLU?H$'*)ewbW02?a9<;>?H$'(�*)9D;,023'(�?C$v?HF%=)?)g - eh@B?A.I&)F1-/.%*E3+?H;p05.%?��Sf & �M9D3P*)eU02.%?A=E$2&Z(%.d02*4L�?T02.>?NK&J�W9<N}"%N ;:"%NoLU?H$'*)e^b:02?C9D;%?C$B(U*)9D;:053B(U?H$P?CF%=E?s02.%?C;K@B?S@B*E">6DFp3+?H?s02.I&Z0P05.%?T�>�M?HFG3+-/.%?HN1?.I&)FG&oNo"%-/.|3j6<*�@B?H$[$+"%;%;>9D;%= 059DN1? 02.%&);p02.>?S9D;:05?H$j7)&J6w35-/.>?HN1?)gB~[.>9D3[.%*�@y?a7E?C$H]I@y*)">6<FY.%&�7)?LU?H?H;p&);p">;>eu&Z9D$B-C*EN1(I&)$+9D35*);wg =S*)05? &Z3'@B?C686�]:02.%&Z0B05.%?A-H*EN1(%">02&Z059D*E;K059DNK?A9<;>-H$5?H&)35?C3Bez*E$P02.>?3+05$5?a02-/.%?CFG02?H$+$2&Z9D;wgv~[.>?S059DNd9<;>=o$5?C35">68023'ez*E$P02.%? � � &)F%F>98059D*E;I&Z6�05?H$5$5&Z9D;%3'9D3y3+.%*�@s;p9D;57�9D=E"%$+?

Page 107: people.scs.carleton.calanthier/cv/phdThesis.pdf · 2004. 5. 5. · CUDg[cjP Fi FifT_cX jGF JSj QZ_]^J^boFqboX f CEDGF HTNGnGn-X fTC [cjGV \IX jxpgVGFIjP\IF CUDG[7CzCUDGFy_ Dg[l FZHEDGX

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Average Number of Steiner Points per Edge

1,012 Face Unweighted TIN

FixInt

FixSlvIntSlv

Chen and Han

0

1

2

3

4

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6

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Tim

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Average Number of Steiner Points per Edge

1,012 Face Unweighted TIN (Stretched Heights)

FixInt

FixSlvIntSlv

Chen and Han

0

5

10

15

20

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30

35

40

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Tim

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Average Number of Steiner Points per Edge

5,000 Face Unweighted TIN (Random Heights)

FixInt

FixSlvIntSlv

Chen and Han

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Tim

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Average Number of Steiner Points per Edge

5,000 Face Unweighted TIN (Random Heights)

FixInt

FixSlvIntSlv

Chen and Han

0

10

20

30

40

50

60

70

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Tim

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Average Number of Steiner Points per Edge

5,000 Face Unweighted TIN (Random Stretched Heights)

FixInt

FixSlvIntSlv

Chen and Han

0

20

40

60

80

100

120

140

160

180

200

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Tim

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Average Number of Steiner Points per Edge

10,082 Face Unweighted TIN

FixInt

FixSlvIntSlv

Chen and Han

0

50

100

150

200

250

300

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Tim

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Average Number of Steiner Points per Edge

10,082 Face Unweighted TIN (Stretched Heights)

FixInt

FixSlvIntSlv

Chen and Han

7�9D=E"%$+? � g � � � �Q$5&)(%.%3A35.%*�@T9D;%=Y&\7E?C$2&)=)? -H*EN1(%"M0/&Z0+9<*E;n059DN1? :u9D;_3+?H-H*);%F%3+?[ez*E$S3j98�r3+?C6D?H-C05?HF02?C$5$5&Z9<;>3Hg

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Tim

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Average Number of Steiner Points per Edge

1,012 Face Unweighted TIN (Normal(N) and Stretched(S))

Fix (N)Int (N)

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Fix (S)Intl (S)

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7�9D=E"%$+? � g � � � �{$2&)(>. 35.>* @T9D;%=m02.>?k0qVW(>9D-\&Z6y$5"%;%;M9<;%=_0+9<N1?k-/.I&)$2&Z-C02?C$+9D3+0+9<-C31ez*)$405.%?p02?C3+05?HF02?C$5$5&Z9<;>3'">3+9D;%=}05.%?T�>�M?HFG&Z;%FK9D;,02?C$+7Z&Z6�35-/.>?HN1?H3yez*)$v;%*E$5NK&Z6Y:Y=(?x&);%F13+05$5?C05-/.%?HF9: bC?x02?H$+$2&Z9D;%3Cg

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�{?C050+9<;>=GLI&)-/�n02*p05.%? 35(%&);%;%?C${35-/.%?CNK?C3H]�@B?d-\&);m;%*�@ ?a�>&)Nd9D;%? 02.>?C9D$#-H*EN1(%"M0/&Z0+9<*E;_0+9<N1?Zg4S6802.>*E"%=E.p05.%? (%&Z02.Y&Z-H-H">$2&)-aVk9D3[$5?CF%"%-C?HFG@s.%?C;G02.%?#3+(I&)$+35?#3+(I&);%;%?C$[=E$5&)(%.%3y&)$5?S"%35?CFw]>02.>?$5">;%;>9D;%=}0+9<N1?S&Z6<3+*oF%?C-H$+?\&)3+?H3[3j9<;%-C?S05.%?H$+? &)$+?A6D?H3+3B?CF%=E?C3B9D;k02.>?S=E$5&)(%.wg�7�9<=)"%$5? � g �E� 35.%*�@s302.>?k$+"%;%;>9D;%=r0+9<N1?1ez*E${02.%?102?C3+053o-H*)$5$5?C35(U*E;%F>9D;%=n02*r05.%?K=E$2&)(>.%3Q*)e 7�9D=E"%$+? � g � � gki ?k-H&);35?C?S05.I&Z0'02.%?A35(I&Z;%;%?H$+3["%3j9<;%=}02.%?s6`&Z$5=E?C$B-C*E;%?S&);%=)6D? .I&\7)? LU?C0505?H$'$5"%;>;>9<;>=o059DN1?A05.I&Z0'02.%*[email protected]&Z686D?H$[-C*E;%?{&);>=)6<?C3Hg -q;Geu&)-a0\]:@y?{3+?H? 05.I&Z0B02.%?#=)$2&)(%.p35.I&)(U? =)*M?C3yez$5*EN �+�:"I&ZF%$2&Z0+9<- �02* �j689<;>?\&)$��k3j9<;%-C?}05.%?};:"%N}L�?C$S*Zet=E$5&)(%.n?HF%=E?C3 LU?H-C*EN1?H3S689D;%?\&)$�:z059DNK?C3#&1-H*E;>3+0/&Z;:0+?y@s.>?H;35(%&);%;%?C$53#&Z$5?4"%35?CFwg[i ?}&Z6D35*k35?H?Q02.%&Z0S05.%?H$+?49D3s6D98050+6<?4F>9 �h?C$5?H;>-H?d&)=E&Z9<;nLU?C0q@B?H?H;_05.%?Q�>�M?HF&);%F|9D;:05?H$j7)&J6^35-/.%?CNK?C3Hg

Page 109: people.scs.carleton.calanthier/cv/phdThesis.pdf · 2004. 5. 5. · CUDg[cjP Fi FifT_cX jGF JSj QZ_]^J^boFqboX f CEDGF HTNGnGn-X fTC [cjGV \IX jxpgVGFIjP\IF CUDG[7CzCUDGFy_ Dg[l FZHEDGX

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Average Number of Steiner Points per Edge

9,799 Face Unweighted TIN (Africa)

FixInt

FixSlvIntSlv

0

0.5

1

1.5

2

2.5

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Tim

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Average Number of Steiner Points per Edge

9,788 Face Unweighted TIN (North America)

FixInt

FixSlvIntSlv

0

0.2

0.4

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0.8

1

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Tim

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Average Number of Steiner Points per Edge

9,944 Face Unweighted TIN (Australia)

FixInt

FixSlvIntSlv

0

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Tim

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Average Number of Steiner Points per Edge

9,778 Face Unweighted TIN (Brazil)

FixInt

FixSlvIntSlv

0

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1

1.5

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2.5

0 1 2 3 4 5 6

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Tim

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Average Number of Steiner Points per Edge

9,817 Face Unweighted TIN (Europe)

FixInt

FixSlvIntSlv

0

0.2

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1

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Tim

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Average Number of Steiner Points per Edge

9,690 Face Unweighted TIN (Greenland)

FixInt

FixSlvIntSlv

0

0.5

1

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Tim

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Average Number of Steiner Points per Edge

10,952 Face Unweighted TIN (Italy)

FixInt

FixSlvIntSlv

0

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0.4

0.5

0.6

0.7

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Average Number of Steiner Points per Edge

2,854 Face Unweighted TIN (Japan)

FixInt

FixSlvIntSlv

0

0.5

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Tim

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Average Number of Steiner Points per Edge

9,839 Face Unweighted TIN (Madagascar)

FixInt

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0

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1

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Average Number of Steiner Points per Edge

9,781 Face Unweighted TIN (NorthWest Territories)

FixInt

FixSlvIntSlv

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Average Number of Steiner Points per Edge

10,082 Face Unweighted TIN using Fixed Scheme with Spanners

1 degree5 degree

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Average Number of Steiner Points per Edge

10,082 Face Unweighted TIN using Interval Scheme with Spanners

1 degree5 degree

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Computation Time

Accuracy/Runtime Tradeoff for Spanner Graphs using Fixed Scheme

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Computation Time

Accuracy/Runtime Tradeoff for Spanner Graphs using Interval Scheme

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1,012 Face Weighted TIN

FixInt

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1,012 Face Weighted TIN (Stretched Heights)

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4250

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Average Number of Steiner Points per Edge

5,000 Face Weighted TIN (Random Heights)

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30000

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Average Number of Steiner Points per Edge

5,000 Face Weighted TIN (Random Stretched Heights)

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1820

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Average Number of Steiner Points per Edge

10,082 Face Weighted TIN

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11000

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Average Number of Steiner Points per Edge

10,082 Face Weighted TIN (Stretched Heights)

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1,012 Face Weighted TIN (Stretched Heights)

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5,000 Face Weighted TIN (Random Heights)

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0

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5,000 Face Weighted TIN (Random Stretched Heights)

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10,082 Face Weighted TIN

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FixSlvIntSlv

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Average Number of Steiner Points per Edge

10,082 Face Weighted TIN (Exagerated Heights)

FixInt

FixSlvIntSlv

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Pat

h C

ost

Average Number of Steiner Points per Edge

5,000 Face Slope Weighted TIN (Random Heights)

FixInt

FixSlvIntSlv

30000

35000

40000

45000

50000

55000

0 1 2 3 4 5 6

Pat

h C

ost

Average Number of Steiner Points per Edge

5,000 Face Slope Weighted TIN (Random Stretched Heights)

FixInt

FixSlvIntSlv

1650

1700

1750

1800

1850

1900

1950

0 1 2 3 4 5 6

Pat

h C

ost

Average Number of Steiner Points per Edge

5,000 Face Random Weighted TIN (Random Heights)

FixInt

FixSlvIntSlv

2500

3000

3500

4000

4500

5000

5500

6000

0 1 2 3 4 5 6

Pat

h C

ost

Average Number of Steiner Points per Edge

5,000 Face Random Weighted TIN (Random Stretched Heights)

FixInt

FixSlvIntSlv

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