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Subject: [Compgeom-discuss] 
	Re: Compgeom-discuss is dead!  Long live compgeom-discuss!
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Dear subscriber to compgeom-discuss:

I would like to announce the long-anticipated death of the mailing list
   compgeom-discuss@research.bell-labs.com,
and the simultaneous birth of a new list,
   compgeom-discuss@compgeom.poly.edu ,
as hosted by Herve Bronnimann at Poly.

If you were a member of compgeom-discuss@research.bell-labs.com, you are 
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From flis@detk.com Wed Feb  1 17:36:51 2006
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From: "William Flis" <flis@detk.com>
To: "Compgeom" <compgeom-discuss@compgeom.poly.edu>
Date: Wed, 1 Feb 2006 18:23:01 -0500
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Subject: [Compgeom-discuss] Measure of similarity between two shapes?
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I am looking for a quantitative measure as to how similar two shapes are to
each other. (2-D and 3-D shapes would suffice for me.)

One shape is the output of some physical process, and is described as an
image (photograph or computer plot, hence pixel data). The other is a
desired shape, defined by its boundary, which could be a circle/sphere or a
polygon.

William J. Flis
Philadelphia, PA
flis@detk.com


From mohades@aut.ac.ir Tue Feb  7 04:36:03 2006
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Subject: [Compgeom-discuss] the complexity of a walk
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Dear all:

=20

 I am touching the following problem

Having a graph   G(V1UV2 , E)  in which the degree of all vertices in V2 =
is even.

 A tourist wants to take a close walk such that:

1:  All vertices in V2 are visited at least once.

2:  All vertices in V2 are visited at most once.

3: The tourist chooses the middle edge to exit when he visit a vertex =
from  V2  satisfy in 2 and 3 as most as possible.

=20

What is the complexity of the finding this walk?

Is it NP-complete?

 An example is attached.



Regards
Ali Mohades
-----------------------------------------------------
Department of  Computer Science
Faculty of Math & Computer Science
Amirkabir University of Technology
424 Hafez Avenue
Tehran 15914
Iran



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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=3DContent-Type content=3D"text/html; =
charset=3Dwindows-1256">
<META content=3D"MSHTML 6.00.2600.0" name=3DGENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=3D#ffffff>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; DIRECTION: ltr; unicode-bidi: embed; =
TEXT-ALIGN: left"><FONT=20
face=3D"Times New Roman">Dear all:<SPAN=20
style=3D"mso-bidi-language: AR-SA"><?xml:namespace prefix =3D o ns =3D=20
"urn:schemas-microsoft-com:office:office" =
/><o:p></o:p></SPAN></FONT></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; DIRECTION: ltr; unicode-bidi: embed; =
TEXT-ALIGN: left"><FONT=20
face=3D"Times New Roman"><SPAN style=3D"mso-bidi-language: =
AR-SA">&nbsp;</SPAN><SPAN=20
lang=3DFA dir=3Drtl><o:p></o:p></SPAN></FONT></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; DIRECTION: ltr; unicode-bidi: embed; =
TEXT-ALIGN: left"><FONT=20
face=3D"Times New Roman"><SPAN lang=3DFA dir=3Drtl>&nbsp;</SPAN>I am =
touching the=20
following problem<SPAN lang=3DFA dir=3Drtl><o:p></o:p></SPAN></FONT></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; DIRECTION: ltr; unicode-bidi: embed; =
TEXT-ALIGN: left"><FONT=20
face=3D"Times New Roman">Having a&nbsp;graph&nbsp;&nbsp; G(V<FONT=20
size=3D1>1</FONT>UV<FONT size=3D1>2</FONT> , E) <SPAN=20
style=3D"mso-spacerun: yes">&nbsp;</SPAN>in which the degree of all =
vertices in=20
V<FONT size=3D1>2</FONT><SPAN style=3D"mso-spacerun: =
yes">&nbsp;</SPAN>is=20
even.</FONT></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; DIRECTION: ltr; unicode-bidi: embed; =
TEXT-ALIGN: left"><FONT=20
face=3D"Times New Roman"><SPAN style=3D"mso-spacerun: =
yes">&nbsp;</SPAN>A tourist=20
wants to take a close walk such that:<SPAN lang=3DFA=20
dir=3Drtl><o:p></o:p></SPAN></FONT></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; DIRECTION: ltr; unicode-bidi: embed; =
TEXT-ALIGN: left"><SPAN=20
dir=3Dltr></SPAN><SPAN dir=3Dltr></SPAN><SPAN dir=3Dltr></SPAN><SPAN=20
dir=3Dltr></SPAN><FONT face=3D"Times New Roman">1:<SPAN=20
style=3D"mso-spacerun: yes">&nbsp; </SPAN>All vertices in&nbsp;V<FONT=20
size=3D1>2</FONT><SPAN style=3D"mso-spacerun: yes">&nbsp;</SPAN>are =
visited at least=20
once.</FONT></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; DIRECTION: ltr; unicode-bidi: embed; =
TEXT-ALIGN: left"><FONT=20
face=3D"Times New Roman">2:<SPAN style=3D"mso-spacerun: yes">&nbsp; =
</SPAN>All=20
vertices in V<FONT size=3D1>2</FONT><SPAN=20
style=3D"mso-spacerun: yes">&nbsp;</SPAN>are visited at most =
once.</FONT></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; DIRECTION: ltr; unicode-bidi: embed; =
TEXT-ALIGN: left"><FONT=20
face=3D"Times New Roman">3: The tourist chooses the middle edge to exit =
when he=20
visit a vertex from&nbsp; V<FONT size=3D1>2</FONT> &nbsp;</FONT><FONT=20
face=3D"Times New Roman">satisfy in 2 and 3 as most as =
possible.</FONT></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; DIRECTION: ltr; unicode-bidi: embed; =
TEXT-ALIGN: left"><o:p><FONT=20
face=3D"Times New Roman">&nbsp;</FONT></o:p></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; DIRECTION: ltr; unicode-bidi: embed; =
TEXT-ALIGN: left"><SPAN=20
style=3D"mso-bidi-language: AR-SA"><FONT face=3D"Times New Roman">What =
is the=20
complexity of&nbsp;the finding this walk?<o:p></o:p></FONT></SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; DIRECTION: ltr; unicode-bidi: embed; =
TEXT-ALIGN: left"><SPAN=20
style=3D"mso-bidi-language: AR-SA"><FONT face=3D"Times New Roman">Is it=20
NP-complete?<o:p></o:p></FONT></SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; DIRECTION: ltr; unicode-bidi: embed; =
TEXT-ALIGN: left"><SPAN=20
style=3D"mso-bidi-language: AR-SA"><FONT face=3D"Times New =
Roman">&nbsp;An example=20
is attached.</FONT></SPAN></P>
<P class=3DMsoNormal=20
style=3D"MARGIN: 0cm 0cm 0pt; DIRECTION: ltr; unicode-bidi: embed; =
TEXT-ALIGN: left"><SPAN=20
style=3D"mso-bidi-language: AR-SA"></SPAN>&nbsp;</P><SPAN=20
style=3D"FONT-SIZE: 10pt; FONT-FAMILY: Arial; mso-bidi-language: AR-SA; =
mso-fareast-font-family: 'Times New Roman'; mso-ansi-language: EN-US; =
mso-fareast-language: EN-US">Regards<BR>Ali=20
Mohades<BR>-----------------------------------------------------<BR>Depar=
tment=20
of&nbsp; Computer Science<BR>Faculty of Math &amp; Computer =
Science<BR>Amirkabir=20
University of Technology<BR>424 Hafez Avenue<BR>Tehran 15914<BR>Iran<BR=20
style=3D"mso-special-character: line-break"><BR=20
style=3D"mso-special-character: line-break"></SPAN></BODY></HTML>

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=00=00=00=00=00=00=11=11=11=0A=

endstream=0Dendobj=0D345 0 obj<</Length 10/Width 3/Height =
1/BitsPerComponent 