rsmt15.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

15 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

%%EndSetup

 % initialize_constraint_pool: 0.00 seconds.
 % Constraint pool initialized with:
 %	1	Total degree rows	41	coeffs.
 %	15	Cutset rows		124	coeffs.
 %	0	Incompatibility rows	0	coeffs.
 %	31	2-terminal SEC rows	134	coeffs.
 %	46	Total rows in pool	16	in LP
 % @PMEM 46 rows, 1 blocks, 854 nzfree, 0 nzwasted, 1196 nztotal
 % build_initial_formulation: 0.00 seconds.
% Resuming node 0
  % @PAP adding 16 rows, 165 nz to LP
  % @PL 16 rows, 41 cols, 206 nonzeros, 7 slack, 9 tight.
  % @PAP adding 3 rows, 15 nz to LP
  % @PL 19 rows, 41 cols, 221 nonzeros, 7 slack, 12 tight.
  % @PAP adding 2 rows, 7 nz to LP
  % @PL 21 rows, 41 cols, 228 nonzeros, 8 slack, 13 tight.
  % @PAP adding 2 rows, 13 nz to LP
  % @PL 23 rows, 41 cols, 241 nonzeros, 8 slack, 15 tight.
  % @PAP adding 1 rows, 4 nz to LP
  % @PL 24 rows, 41 cols, 245 nonzeros, 8 slack, 16 tight.
  % Node 0 LP 1 Solution, length = 27567.000000, 0.00 0
 % 0 fractional variables
 % @LO 0.00 27567.00000000000000000000 99.9000000000
 % @LN 0.00 27567.00000000000000000000 99.9000000000
 % @UO 0.00 30990.00000000000000000000 11.0454985479
 % @UN 0.00 30990.00000000000000000000 11.0454985479
 % @cutset: 3 connected components.
 % initially 4 congested vertices:
 % find_congested_components found 1 components:
 %	component 0:	4 verts,	5 edges
 % @D deleting 8 slack rows
  % @PAP adding 6 rows, 84 nz to LP
 % @PMEM 52 rows, 1 blocks, 764 nzfree, 0 nzwasted, 1196 nztotal
  % @PL 22 rows, 41 cols, 254 nonzeros, 4 slack, 18 tight.
  % @PAP adding 1 rows, 2 nz to LP
  % @PL 23 rows, 41 cols, 256 nonzeros, 3 slack, 20 tight.
  % Node 0 LP 2 Solution, length = 29815.000000, 0.00/0.00/0.00/0.00/0.00/0.00/0.00 6
 % 0 fractional variables
 % @LO 0.00 27567.00000000000000000000 11.0454985479
 % @LN 0.00 29815.00000000000000000000 3.7915456599
 % @UO 0.00 30990.00000000000000000000 3.7915456599
 % @UN 0.00 30433.00000000000000000000 2.0306903690
 % Fixed 3 vars to 0 and 1 vars to 1.
 % @cutset: 2 connected components.
 % initially 3 congested vertices:
 % find_congested_components found 1 components:
 %	component 0:	3 verts,	3 edges
 % @D deleting 3 slack rows
  % @PAP adding 2 rows, 16 nz to LP
 % @PMEM 54 rows, 1 blocks, 746 nzfree, 0 nzwasted, 1196 nztotal
  % @PL 22 rows, 41 cols, 241 nonzeros, 3 slack, 19 tight.
  % Node 0 LP 3 Solution, length = 30056.500000, 0.00/0.00/0.00/0.00/0.00/0.00/0.00 2
 % 6 fractional variables
 % @LO 0.00 29815.00000000000000000000 2.0306903690
 % @LN 0.00 30056.50000000000000000000 1.2371438899
 % Fixed 10 vars to 0 and 0 vars to 1.
 % initially 6 congested vertices:
 % find_congested_components found 1 components:
 %	component 0:	6 verts,	5 edges
 % @D deleting 3 slack rows
  % @PAP adding 11 rows, 195 nz to LP
 % @PMEM 65 rows, 1 blocks, 540 nzfree, 0 nzwasted, 1196 nztotal
  % @PL 30 rows, 41 cols, 402 nonzeros, 11 slack, 19 tight.
  % @PAP adding 1 rows, 4 nz to LP
  % @PL 31 rows, 41 cols, 406 nonzeros, 15 slack, 16 tight.
  % @PAP adding 1 rows, 5 nz to LP
  % @PL 32 rows, 41 cols, 411 nonzeros, 12 slack, 20 tight.
  % Node 0 LP 4 Solution, length = 30367.000000, 0.00/0.00/0.00/0.00/0.00/0.00/0.00 11
 % 0 fractional variables
 % @UO 0.00 30433.00000000000000000000 1.2371438899
 % @UN 0.00 30367.00000000000000000000 1.0224915204
  % *     0     0    30367.0000    30367.0000
 % @LO 0.00 30056.50000000000000000000 1.0224915204
 % @LN 0.00 30367.00000000000000000000 0.0000000000

 % Certificate of solution:
 % @C	2983	2738
 % @C	2983	5183
 % @C	6045	5208
 % @C	3221	934
 % @C	606	8201
%%Page: 1 1
BeginPlot
	Plot_Terminals
 % fs3: 0 6 4
	0 T	2983	2738	S
	2983	2738	6 T	S
	2983	2738	4 T	C
 % fs10: 2 6 7
	2 T	2983	5183	S
	2983	5183	6 T	S
	2983	5183	7 T	C
 % fs19: 7 11 3
	7 T	6045	5208	S
	6045	5208	11 T	S
	6045	5208	3 T	C
 % fs20: 9 4 5
	9 T	3221	934	S
	3221	934	4 T	S
	3221	934	5 T	C
 % fs23: 14 10 1
	14 T	606	8201	S
	606	8201	10 T	S
	606	8201	1 T	C
 % fs28: 8 10
	10 T	8 T	C
 % fs34: 2 8
	8 T	2 T	C
 % fs36: 3 12
	3 T	12 T	C
 % fs39: 11 13
	11 T	13 T	C
  (Steiner Minimal Tree:  15 points,  length = 30367,  0.00 seconds)
EndPlot

% @0 
% N M Nodes LPs P1CPU P2CPU TotCPU
% @1 15 41 1 4 0.00 0.00 0.00
% Z RootZ %Gap RootLPs RootCPU RedMST
% @2 30367 30367.000000 0.00000 4 0.00 6.8897
% InitPRows InitPNZ InitLPRows InitLPNZ
% @3 46 296 16 206
% RootPRows RootPNZ RootLPRows RootLPNZ
% @4 65 591 32 411
% FinalPRows FinalPNZ FinalLPRows FinalLPNZ
% @5 65 591 32 411
% SMTFSTs SMTAvgFSTSz SMTMaxFSTSz #2FSTs #3FSTs ... #10FSTS #>10FSTs
% @6 9 2.555556 3 4 5 0 0 0 0 0 0 0 0