An Exact Algorithm for Solving Difficult Detailed Routing Problems Kolja Sulimma
Wolfgang Kunz
J. W. Goethe-Universität Frankfurt
J. W. Goethe-Universität Frankfurt
[email protected]
[email protected]
ABSTRACT
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2. ALGORITHM
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/,e z KG HQBDFR'G H%FBIILG \K I,JQMA,T7DHjMILKM8NLMvT;NLMODNjILKM0NNLM8t HVIjNLG A8ILG B+FHB+F%ILKMXRB+\+C M\HelBNJM8pTE%gC M+"T|RB+\CM8\~QM\G FFG F\ B+FTF>B"AADgG M,RIjN.T7A0xwA,T7FBFC]SMF!R?B+FTFM8E%gIqSvB+FMTF!R Y G AMJY1M0NLHLTe}F&E%B+HVI[ABC DE%FH{ILKM F DEQM0N/B7O!gB+HjHjG QCMRB+\C M\+H G HCM8HjHXILKTFhj7 2.3 Channel width minimization
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3. IMPLEMENTATION
=MWG E%gCM8E%MF"ILM,R|ILKNLMMY1M8NLHjG B+FHlB7O{ILKMTC \+B7NLG]ILKEve}qE%gC M8t E%MF"I.T7ILG BF f DHjM8H[TKTHjK|HjM8IILBXHVILBNLMJILKMlHjM8IB7OIjN.T7A0xUT7HjHjG \+Ft E%MF"ILHed}qE%gC ME%M8F I.T;ILG B+Fn?DHjM8H[TWKM,T7gUHVIjNLDA8ILDNLM ILKT7I/TC C B;kH BOM0pT7A8IYGTE%G FGE%G ®,T;ILG B+FwT7F!RHjBE%M|KMDNLG HVILG AUNLDF"ILG E%MZG Et gNLB;Y1M8E%MF"ILHeU}qE%gCM8E%MF"I.T7ILG B+F?¯DHjMHnE~DC]ILG Y+T7CDM,RwRM8AG HjGBF RGT7\N.TE%HnILB(NLMgNLM8HjMF"InILKMHjM0I&BOJIjN.T7A0x?T7HjHjG \+FE%M8F ILHUQ"S?G]ILH A.K!T7N.T7A8ILM8NLG HVILG AUOPDFA8ILG B+F{e }qF=TC CG E%gC ME%MF"I.T;ILGBFH|TvIjN.TA.x=T7HjHjG\FE%MF"I~G H~HVILB7NLM,R'TH TFvT7NjN.TS(BO[hG F"ILM\M8NLHGF(ILKMnN.T7F\+MUB7O°~ILB|hkG]ILKILKMUYTC DM
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dRB+\C M\+HEDHVIXKT;Y+M C MHjHWILK!T7Fh8i ¹ `PhL¹+c0iIjN.T7A0x(THjHjG \FE%MF"ILHe #G]ILKnILKGH{G E%gC ME%MF"I.T;ILGBFnQMFA0KE6T7NLx H!kG]ILK|DgZILBºIjN.TA.x H ABDCRQMnNLBDILM,R(GFvT~NLM,THjBF!T7QC M|TE%B+DF"IWBO[ILG E%M+e
3.2 Implementation B
}FILKGHUG E%gCM8E%MF"I.T7ILG B+FwIjN.TA.x?THjHjG \FE%MF"ILHUT;NLMHVILBNLM,RG F TnKMTgDHjGF\nILKMF DE~QM8N[BO{Y GTH FMMRM,R~ILBUA0NLM,T7ILMILKMIjN.T7A0x THjHjG \FE%MF"ITH~ILKM6x1M8S"e z N.T7A0x=THjHjG \+FE%MF"ILH|kG]ILK'C MHjHY GTH T7NLMZgNLB"AMHjHjMR y NLHVI, NLMHjDC ILG F\G FvT&NLB+DILG F\~kG]ILKvT|E%GFG EDE F DE~QM8NB7OUY G@T7He z KG H6gNLB RDAMH6TA8G NLA8DG]I6ILK!T7I6KTH6C B,kM8N gB,kM8NvAB+FHjDE%gILG BF¸TF!R#HjE6T7CC M8NwRMCTS¸RDMILB'ILKMC B,kM8N NLMHjG HVI.TFAM&TFRA,T7g!TA8G I.T7FAMUB7O[ILKMZkG]NLMHXT7HXkJMC C/T7HT~QM8IjILM8N SG MCR#RDNLG F\E6TF DOPTA8ILDNLGF\e£»G FGE%G ®G F\'ILKM?FDEQM8N6B7O Y GTHXE%G\K"IZT7C HjB(NLMHjDC]IZG F?THjE6TC C M8NZC@TS"BDIG]OlA8B+E%g!T7A8ILG B+FvG H DHjMRTHXTgBHVIjtugNLB"AMHjHjG F\%HVILMgde f H/TWKM8DNLG HVILG ANLDF"ILGE%M[BgILG E%G ®,T7ILG BFnILKM THjHjG \+FE%MF"ILH{kJM8NLM FB7IJgNLB"AMHjHjM,R6ABCDE%F%Q"SABCDE%FQDIJG F(T&RMgILKt y NLHVI E6T7Ft FM0N,e z KG HG H[TWC BI/ObTHVILM0NGF&E6T7F SZA,THjM8H[QMA,TDHjMlILKM8NLMlDHjD!T7CC]S T7NLM~T%C BInB7OJgBHjHjG QC MBgILG E6TC{NLB+DILG F\+HZOBNUT%\GY+MF?gNLB+QC ME G FHVI.T7FAMTFRILKMTC \+B7NLG ILKE¼A,T7F'HVILB+g'THHjB"B+FTHILKM y NLHVI B+FMnG HXOB+DF!RG FHVILM,T+RB7O[MF DE%M0N.T7ILG F\|ILKME½T7C C§e
3.3 Implementation C
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