Date: Sat, 2 Jul 2005 11:20:01 -0700
From: Man-Cho Anthony So and Yinyu Ye

We truly appreciate the referees for their careful reading of the manuscript
and for their suggestions which improve our presentation.  We have
incorporated most of those suggestions in our revision.  As for our response
to the referees' comments, we would like to mention the following:
--- with regard to item 3 of Referee II's report: We agree that our claim is
unsubstantiated.  Therefore, the corresponding statements have been changed.
--- with regard to Referee IV's report: We are aware of most of the 
literature
cited in the report.  However, we feel that the focus of our work is quite
different from those cited.  In particular,
(i) Most of the work on MDS assumes that the underlying graph is complete,
i.e. all the pairwise distances are given.  However, we do not make such an
assumption.  Although some recent works on MDS address the case of
incomplete distances, there are no theoretical guarantees regarding the
outcome of those algorithms.
(ii) The point of our paper is neither on who first used SDP for sensor
localization nor on which SDP method was faster, but on the realizability of
a graph and other theoretical characterizations of localization problems.
To the best our knowledge, the results presented in our paper and the use of
duality were the first along this research direction.
However, we do agree with the referee that the works on MDS are part of the
history of the problem, and hence we have included a brief summary in
Section 1.1 as well as some of the references.