rsmt40.ps

生成直角Steiner树的程序包

%!PS-Adobe-3.0
%%Creator: Steiner Tree Version 3.1
%%Copyright: Copyright (c) 1998, 2001 by David M. Warme
%%LanguageLevel: 1
%%DocumentNeededResources: font Times-Roman
%%DocumentSuppliedResources: procset SteinerTreeProcs 2.0 0
%%EndComments
%%BeginProlog
%%BeginProcSet: SteinerTreeProcs 2.0 0
/LabelTerminals	0		def	% set non-zero to label terminals
/inch { 72 mul } def
/PaperWidth	8.5 inch	def
/PaperHeight	11 inch		def
/BigBoxSize	7 inch		def
/SmallBoxSize	2 inch		def
/SmallBoxHeight	SmallBoxSize	def
/SmallBoxWidth	SmallBoxSize	def
/BoxHeight	BigBoxSize	def
/BoxWidth	BigBoxSize	def
/MinX		0		def
/MaxX		1		def
/MinY		0		def
/MaxY		1		def
/BoxMode	0		def	% (0 ==> big plot, 1 ==> small plots)
/SmallBoxCount	0		def
/TermRadius	1 32 div inch	def
/LineWidth	currentlinewidth	def

% Define the clipping region to be the inside edge of the box.

/ClipHeight	BigBoxSize LineWidth sub def
/ClipWidth	ClipHeight def

% Define the plotting region so that points plotted at the extremes will
% exactly meet the edge of the clipping region.  (Reduce by the terminal
% radius on each side.)

/PlotHeight	ClipHeight TermRadius 2 mul sub def
/PlotWidth	ClipWidth  TermRadius 2 mul sub	def
/XlateX { MinX sub MaxX MinX sub div PlotWidth mul } def
/XlateY { MinY sub MaxY MinY sub div PlotHeight mul } def
/XlateXY { exch XlateX exch XlateY } def
/Dup2 { dup 3 -1 roll dup 4 1 roll exch } def
/Swap2 { 4 2 roll } def
% define the two fonts we will use:
%	- one for numbering the terminals
%	- one for printing the plot's title
/TermNumPointsize	8	def
/TitlePointsize		15	def
/TermNumFont
	/Times-Roman findfont TermNumPointsize scalefont
def
/UseTermNumFont { TermNumFont setfont } def
/TitleFont
	/Times-Roman findfont TitlePointsize scalefont
def
/UseTitleFont { TitleFont setfont } def
/DefineTerminals {
	/NumTerms exch def
	/TermX NumTerms array def
	/TermY NumTerms array def
	/TermIndex 0 def
} def
/DT {
	TermY TermIndex 3 -1 roll put
	TermX TermIndex 3 -1 roll put
	/TermIndex TermIndex 1 add def
} def
/SetAxes {	% minx maxx miny maxy
	/MaxY exch def
	/MinY exch def
	/MaxX exch def
	/MinX exch def
} def
/PTString	12 string	def
/Plot_Terminals {
	LabelTerminals 0 eq {
		% Display terminals, no labels
		0 1 NumTerms 1 sub {			% i
			dup				% i i
			TermX exch get exch		% x i
			TermY exch get
			newpath
			XlateXY
			TermRadius 0 360 arc fill
		} for
	}
	{	% Display terminals, with labels
		0 1 NumTerms 1 sub {			% i
			dup				% i i
			PTString cvs exch dup		% str i i
			TermX exch get exch		% str x i
			TermY exch get			% str x y
			newpath
			XlateXY
			Dup2
			TermRadius 0 360 arc fill
			moveto TermRadius 3 mul dup neg rmoveto
			UseTermNumFont
			show
		} for
	} ifelse
} def
% n T ==> Xn Yn, get coordinates of terminal n.
/T {
	dup
	TermX exch get exch
	TermY exch get
} def
% Draw a line segment.
/S {
	newpath
	XlateXY
	moveto
	XlateXY
	lineto
	stroke
} def
% Draw a corner.  First point is incident to vertical segment.
% Second point is incident to horizontal segment.
/C {	% x1 y1 x2 y2
	newpath
	% x1 y1 x2 y2 -> x1 y1 x1 y2 x2 y2
	4 -1 roll dup 5 1 roll exch dup 4 -1 roll exch
	XlateXY
	moveto
	XlateXY
	lineto
	XlateXY
	lineto
	stroke
} def
/BeginPlot {
	FlushSmallPlot
	gsave
	PaperWidth BoxWidth sub 2 div
	 PaperHeight BoxHeight sub 2 div
	  translate
	newpath
	0 0 moveto
	BoxWidth 0 lineto
	BoxWidth BoxHeight lineto
	0 BoxHeight lineto
	closepath
	stroke
	gsave
	% establish a clipping region at the inside edge of the box
	LineWidth 2 div dup moveto
	ClipWidth 0 rlineto
	0 ClipHeight rlineto
	ClipWidth neg 0 rlineto
	closepath
	clip
	% establish the origin for the plotting region
	LineWidth 2 div TermRadius add
	 dup
	  translate
} def
/EndPlot {
	grestore
	newpath
	UseTitleFont
	0 0 moveto
		dup stringwidth pop BigBoxSize exch sub 2 div
		TitlePointsize -2 mul
	rmoveto
	show
	grestore
	showpage
} def
/BeginSmallPlot {
	gsave
	.75 inch SmallBoxCount 3 mod SmallBoxWidth .5 inch add mul add
	  .75 inch 3 SmallBoxCount 3 idiv sub SmallBoxHeight .5 inch add mul add
	    translate
	SmallBoxWidth BoxWidth div
	 SmallBoxHeight BoxHeight div
	  scale
	newpath
	0 0 moveto
	BoxWidth 0 lineto
	BoxWidth BoxHeight lineto
	0 BoxHeight lineto
	closepath
	stroke
	gsave
	% establish a clipping region at the inside edge of the box
	LineWidth 2 div dup moveto
	ClipWidth 0 rlineto
	0 ClipHeight rlineto
	ClipWidth neg 0 rlineto
	closepath
	clip
	% establish the origin for the plotting region
	LineWidth 2 div TermRadius add
	 dup
	  translate
} def
/EndSmallPlot2 {
	grestore
	newpath
	UseTitleFont
	0 0 moveto
		dup stringwidth pop BigBoxSize exch sub 2 div
		TitlePointsize -2 mul
	rmoveto
	show
	grestore
	/SmallBoxCount SmallBoxCount 1 add def
	SmallBoxCount 12 ge {
		FlushSmallPlot
	} if
} def
/FlushSmallPlot {
	SmallBoxCount 0 gt {
		showpage
		/SmallBoxCount	0 def
	} if
} def
/PT {
	dup				% i i
	TermX exch get exch		% x i
	TermY exch get
	newpath
	XlateXY
	TermRadius 0 360 arc fill
} def
%%EndProcSet
%%EndProlog

 % ./bb
 % Args:
 % Phase 1: 0.00 seconds

%%BeginSetup

0 10000 0 10000 SetAxes

40 DefineTerminals
	1857	2738	DT
	2894	8773	DT
	1463	5183	DT
	6905	8268	DT
	3221	2457	DT
	3473	730	DT
	2983	4045	DT
	5486	5208	DT
	815	6755	DT
	1875	934	DT
	606	7576	DT
	6045	4078	DT
	9323	8669	DT
	7952	2547	DT
	303	8201	DT
	6131	4811	DT
	7871	9452	DT
	854	1630	DT
	5468	655	DT
	7539	7194	DT
	2588	3671	DT
	5319	3872	DT
	4004	3636	DT
	8823	9370	DT
	2183	4813	DT
	4853	437	DT
	8935	5346	DT
	8461	2389	DT
	2920	9868	DT
	4339	473	DT
	8222	1895	DT
	9336	5659	DT
	5826	447	DT
	8995	3322	DT
	3337	1432	DT
	7140	4825	DT
	7970	3168	DT
	1959	6377	DT
	8240	6048	DT
	953	5905	DT

%%EndSetup

 % initialize_constraint_pool: 0.00 seconds.
 % Constraint pool initialized with:
 %	1	Total degree rows	94	coeffs.
 %	40	Cutset rows		271	coeffs.
 %	0	Incompatibility rows	0	coeffs.
 %	70	2-terminal SEC rows	269	coeffs.
 %	109	Total rows in pool	41	in LP
 % @PMEM 109 rows, 1 blocks, 1797 nzfree, 0 nzwasted, 2536 nztotal
 % build_initial_formulation: 0.00 seconds.
% Resuming node 0
  % @PAP adding 41 rows, 365 nz to LP
  % @PL 41 rows, 94 cols, 459 nonzeros, 12 slack, 29 tight.
  % @PAP adding 11 rows, 32 nz to LP
  % @PL 52 rows, 94 cols, 491 nonzeros, 14 slack, 38 tight.
  % @PAP adding 10 rows, 48 nz to LP
  % @PL 62 rows, 94 cols, 539 nonzeros, 16 slack, 46 tight.
  % @PAP adding 6 rows, 14 nz to LP
  % @PL 68 rows, 94 cols, 553 nonzeros, 20 slack, 48 tight.
  % @PAP adding 7 rows, 34 nz to LP
  % @PL 75 rows, 94 cols, 587 nonzeros, 24 slack, 51 tight.
  % @PAP adding 4 rows, 20 nz to LP
  % @PL 79 rows, 94 cols, 607 nonzeros, 22 slack, 57 tight.
  % @PAP adding 2 rows, 8 nz to LP
  % @PL 81 rows, 94 cols, 615 nonzeros, 22 slack, 59 tight.
  % @PAP adding 1 rows, 3 nz to LP
  % @PL 82 rows, 94 cols, 618 nonzeros, 25 slack, 57 tight.
  % @PAP adding 3 rows, 10 nz to LP
  % @PL 85 rows, 94 cols, 628 nonzeros, 22 slack, 63 tight.
  % Node 0 LP 1 Solution, length = 41795.500000, 0.00 0
 % 6 fractional variables
 % @LO 0.00 41795.50000000000000000000 99.9000000000
 % @LN 0.00 41795.50000000000000000000 99.9000000000
 % @UO 0.00 44473.00000000000000000000 6.0205068244
 % @UN 0.00 44473.00000000000000000000 6.0205068244
 % @cutset: 5 connected components.
 % initially 10 congested vertices:
 % find_congested_components found 2 components:
 %	component 0:	6 verts,	8 edges
 %	component 1:	3 verts,	3 edges
 % @D deleting 22 slack rows
  % @PAP adding 32 rows, 470 nz to LP
 % @PMEM 141 rows, 1 blocks, 1295 nzfree, 0 nzwasted, 2536 nztotal
  % @PL 95 rows, 94 cols, 951 nonzeros, 28 slack, 67 tight.
  % @PAP adding 1 rows, 2 nz to LP
  % @PL 96 rows, 94 cols, 953 nonzeros, 22 slack, 74 tight.
  % Node 0 LP 2 Solution, length = 44290.000000, 0.00/0.01/0.00/0.00/0.00/0.00/0.00 32
 % 0 fractional variables
 % @UO 0.01 44473.00000000000000000000 6.0205068244
 % @UN 0.01 44290.00000000000000000000 5.6321968842
  % *     0     0    44290.0000    44290.0000
 % @LO 0.01 41795.50000000000000000000 5.6321968842
 % @LN 0.01 44290.00000000000000000000 0.0000000000

 % Certificate of solution:
 % @C	2588	2738
 % @C	1959	5183
 % @C	7539	8268
 % @C	7871	9370
 % @C	4004	3872
 % @C	6045	4811
 % @C	953	6377
 % @C	7970	2547
 % @C	8222	2389
 % @C	606	8201
 % @C	1857	1630
 % @C	2588	4045
 % @C	4853	447
 % @C	5468	447
 % @C	7970	3322
 % @C	7970	4825
 % @C	8240	5346
%%Page: 1 1
BeginPlot
	Plot_Terminals
 % fs3: 0 20 4
	0 T	2588	2738	S
	2588	2738	20 T	S
	2588	2738	4 T	C
 % fs4: 2 37 24
	2 T	1959	5183	S
	1959	5183	37 T	S
	1959	5183	24 T	C
 % fs5: 3 19 16 23
	3 T	7539	8268	S
	7539	8268	19 T	S
	7539	8268	7871	9370	C
	7871	9370	16 T	S
	7871	9370	23 T	S
 % fs10: 6 22 21
	6 T	4004	3872	C
	4004	3872	22 T	S
	4004	3872	21 T	S
 % fs11: 7 11 15
	7 T	6045	4811	C
	6045	4811	11 T	S
	6045	4811	15 T	S
 % fs13: 8 39 37
	8 T	953	6377	C
	953	6377	39 T	S
	953	6377	37 T	S
 % fs16: 13 36 30 27
	13 T	7970	2547	S
	7970	2547	36 T	S
	7970	2547	8222	2389	C
	8222	2389	30 T	S
	8222	2389	27 T	S
 % fs19: 14 10 1
	14 T	606	8201	S
	606	8201	10 T	S
	606	8201	1 T	C
 % fs21: 17 0 9
	17 T	1857	1630	S
	1857	1630	0 T	S
	1857	1630	9 T	C
 % fs31: 24 20 6
	24 T	2588	4045	C
	2588	4045	20 T	S
	2588	4045	6 T	S
 % fs35: 29 25 18 32
	29 T	4853	447	C
	4853	447	25 T	S
	4853	447	5468	447	S
	5468	447	18 T	S
	5468	447	32 T	S
 % fs51: 36 33 35 26 38
	36 T	7970	3322	S
	7970	3322	33 T	S
	7970	3322	7970	4825	S
	7970	4825	35 T	S
	7970	4825	8240	5346	C
	8240	5346	26 T	S
	8240	5346	38 T	S
 % fs59: 26 31
	26 T	31 T	C
 % fs64: 5 34
	34 T	5 T	C
 % fs66: 11 21
	21 T	11 T	C
 % fs68: 15 35
	15 T	35 T	C
 % fs69: 8 10
	10 T	8 T	C
 % fs73: 1 28
	1 T	28 T	C
 % fs74: 5 29
	5 T	29 T	C
 % fs75: 4 34
	4 T	34 T	C
 % fs77: 12 23
	23 T	12 T	C
 % fs89: 19 38
	19 T	38 T	C
  (Steiner Minimal Tree:  40 points,  length = 44290,  0.01 seconds)
EndPlot

% @0 
% N M Nodes LPs P1CPU P2CPU TotCPU
% @1 40 94 1 2 0.00 0.01 0.01
% Z RootZ %Gap RootLPs RootCPU RedMST
% @2 44290 44290.000000 0.00000 2 0.01 10.8692
% InitPRows InitPNZ InitLPRows InitLPNZ
% @3 109 630 41 459
% RootPRows RootPNZ RootLPRows RootLPNZ
% @4 141 1100 96 953
% FinalPRows FinalPNZ FinalLPRows FinalLPNZ
% @5 141 1100 96 953
% SMTFSTs SMTAvgFSTSz SMTMaxFSTSz #2FSTs #3FSTs ... #10FSTS #>10FSTs
% @6 22 2.772727 5 10 8 3 1 0 0 0 0 0 0