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11 Results:
@article{aos-mlcps-94
, author = "John Adegeest and
Mark Overmars and Jack Snoeyink"
, title = "Minimum-link
$C$-oriented paths: {Single}-source queries"
, journal = "Internat. J. Comput. Geom.
Appl."
, volume = 4
, number = 1
, year = 1994
, pages = "39--51"
, keywords = "shortest path, link distance,
rectilinear link distance"
, update = "98.03 mitchell, 96.09
devillers, 96.05 mitchell"
, annote = "They consider a set
of obstacles given by $n$ line
segments having disjoint interiors, and being at $c$
different fixed orientations. For a fixed source
point, they build a data structure (SPM) of size
$O(cn)$ that supports min-link queries from the
source to any query point in time $O(c\log n)$ (with
additional time $O(k)$ to report a path, if it has
$k$ links). Here, link distance is $C$-oriented
link distance. The preprocessing is done with
$O(c^2 n\log n)$ time and space, OR with $O(c^2 n
\log^2 n)$ time and $O(c^2 n)$ space."
}
@article{ac-prspr-91
, author = "M. J. Atallah and
D. Z. Chen"
, title = "Parallel rectilinear
shortest paths with rectangular obstacles"
, journal = "Comput. Geom. Theory Appl."
, volume = 1
, number = 2
, year = 1991
, pages = "79--113"
, comments = "They preprocess a set of $n$
disjoint axis-aligned rectangles (obstacles),
within a rectilinearly convex polygon $P$,
for 2-point shortest path queries (rectilinear shortest paths).
The query time is $O(\log n)$, on one processor.
The sequential preprocessing time is $O(n^2)$ (no space
bounds seem to be stated explicitly).
Their parallel (CREW) algorithms take time $O(\log^2 n)$,
on either $O(n^2/\log^2 n)$, $O(n^2/\log n)$, or $O(n^2)$ processors,
depending on whether 2, 1, or 0 of the points $\{s,t\}$ lie
on the boundary of $P$."
, update = "98.11 bibrelex, 98.03
mitchell"
}
@article{b-srvmc-91
, author = "Timothy J. Baker"
, title = "Shape Reconstruction
And Volume Meshing For Complex Solids"
, journal = "Internat. J. Numer. Methods
Eng."
, volume = 32
, number = 4
, month = sep
, year = 1991
, pages = "665--675"
, keywords = "shape reconstruction, volume
meshing"
, annote = "An interior point
is generated for each section
vertex. This is placed on the line bisecting the corner
$ABC$, at a distance $\min(AB,BC,d/3)$, where $d$ is
the length of the segment from $B$ to where it first
leaves the polygon. Dt of these points is constructed
and the surface is the boundary between tetras
containing only section vertices and the other
tetras."
, abstract = "The reconstruction of a solid
surface from a series of
cross-sections and the generation of a volume mesh that
conforms with a prescribed surface are issues that
arise in numerous applications. We describe an approach
to both these problems that is based on the generation
of a tetrahedral mesh which automatically captures a
triangulation of the surface points. A simple algorithm
for introducing a set of interior points permits a
simple partition of the volume mesh into two disjoint
sets of tetrahedra such that one set determines the
interior of the solid while the second determines the
exterior. (Author abstract) 10 Refs."
}
@inproceedings{bms-plpco-93
, author = "M. de Berg and J.
Matou{\v s}ek and O. Schwarzkopf"
, title = "Piecewise Linear
Paths Among Convex Obstacles"
, booktitle = "Proc. 25th Annu. ACM Sympos. Theory
Comput."
, year = 1993
, pages = "505--514"
, url = "ftp://ftp.cs.ruu.nl/pub/RUU/CS/techreps/CS-1993/1993-20.ps.gz"
, keywords = "configuration space, motion
planning, convex, robotics"
, precedes = "bms-plpco-95"
, update = "96.09 agarwal, 95.09
aronov, 94.05 devillers+schwarzkopf, 93.09 milone+mitchell, 93.05 schwarzkopf"
, abstract = "Let $B$ be a set of $n$ arbitrary
(possibly intersecting)
convex obstacles in ${\bf R}^d$. It is shown that any
two points which can be connected by a path avoiding
the obstacles can also be connected by a path
consisting of $O(n^{(d-1)\lfloor{d/2+1}\rfloor})$
segments. The bound cannot be improved below
$\Omega(n^d)$. For disjoint obstacles, a $\Theta(n)$
bound is proved. By a well-known reduction, the
general case result also upper bounds the complexity
for a translational motion of an arbitrary convex
robot among convex obstacles. In the planar case,
asymptotically tight bounds and efficient algorithms
are given."
}
@inproceedings{bht-esdls-94
, author = "P. Bose and M. E.
Houle and G. Toussaint"
, title = "Every Set of
Disjoint Line Segments Admits a Binary Tree"
, booktitle = "Proc. 5th Annu. Internat. Sympos.
Algorithms Comput."
, nickname = "ISAAC '94"
, series = "Lecture Notes Comput.
Sci."
, volume = 834
, publisher = "Springer-Verlag"
, address = "Beijing"
, year = 1994
, pages = "??"
, update = "98.03 smid, 96.05
mitchell"
}
@article{cl-olanu-93
, author = "K. F. Chan and T.
W. Lam"
, title = "An on-line algorithm
for navigating in unknown environment"
, journal = "Internat. J. Comput. Geom.
Appl."
, volume = 3
, year = 1993
, pages = "227--244"
, keywords = "on-line algorithms, motion-planning,
competitiveness, shortest paths, computational geometry"
, succeeds = "cl-olanu-91"
, update = "98.03 mitchell, 96.09
devillers"
, annote = "They consider on-line
navigation among a disjoint set of
non-aligned rectangular obstacles, having aspect
ratio at most $r$. They give a strategy that has
competitive ratio $({r\over 2}+1)$, and show that
this is tight."
}
@inproceedings{c-apesp-95
, author = "Danny Z. Chen"
, title = "On the All-Pairs
{Euclidean} Short Path Problem"
, booktitle = "Proc. 6th ACM-SIAM Sympos. Discrete
Algorithms"
, year = 1995
, pages = "292--301"
, keywords = "shortest paths among obstacles,
two-point query, approximation algorithm"
, update = "98.03 mitchell, 96.09
agarwal, 96.05 mitchell"
, abstract = "
Given a set of polygonal obstacles of $n$ vertices in the plane,
the problem of processing the all-pairs Euclidean {\em short}
path
queries is that of reporting an obstacle-avoiding path $P$ (or
its length) between two arbitrary query points $p$ and $q$ in
the
plane, such that the length of $P$ is within a small factor
of the
length of a Euclidean {\em shortest} obstacle-avoiding path
between
$p$ and $q$. The goal is to answer each short path query
quickly
by constructing data structures that capture path information
in
the obstacle-scattered plane. For the related all-pairs
Euclidean
{\em shortest} path problem, the best known algorithms for even
very simple cases (e.g., {\em rectilinear} shortest paths among
disjoint {\em rectangular} obstacles in the plane) require
at least quadratic space and time to construct a data structure,
so that a length query can be answered in polylogarithmic time.
The previously best known solution to the all-pairs Euclidean
{\em short} path problem also uses a data structure of quadratic
space and superquadratic construction time, in order to answer
a
length query in polylogarithmic time. In this paper, we
present a
data structure that requires nearly linear space and takes subquadratic
time to construct. Precisely, for any given $\epsilon$
satisfying
$0$ $<$ $\epsilon$ $\leq$ $1$, our data structure can be
built
in $o(q^{3/2})$ $+$ $O((n\log n)/\epsilon)$ time and
$O(n\log n+n/\epsilon)$ space, where $q$, $1$ $\leq$ $q$ $\leq$
$n$,
is the minimum number of faces needed to cover all the vertices
of
a certain planar graph we use. This data structure enables
us to
report the length of a short path between two arbitrary query
points
in $O((\log n)/\epsilon+1/\epsilon^2)$ time and the actual path
in $O((\log n)/\epsilon+1/\epsilon^2+L)$ time, where $L$ is
the
number of edges of the output path. The constant approximation
factor, $6+\epsilon$, for the short paths that we compute is
quite
small. Our techniques are parallelizable and can also
be used
to improve the previously best known results on several related
graphic and geometric problems."
}
@inproceedings{gt-ltasc-83
, author = "H. Gabow and R. Tarjan"
, title = "A linear time
algorithm for a special case of disjoint set union"
, booktitle = "Proc. 15th Annu. ACM Sympos. Theory
Comput."
, year = 1983
, pages = "246--251"
, update = "98.07 bibrelex"
}
@article{gt-ltasc-85
, author = "H. Gabow and R. Tarjan"
, title = "A linear time
algorithm for a special case of disjoint set union"
, journal = "J. Comput. Syst. Sci."
, volume = 30
, year = 1985
, pages = "209--221"
, update = "97.11 bibrelex"
}
@article{gi-dsads-91
, author = "Z. Galil and G. F.
Italiano"
, title = "Data Structures
and Algorithms for Disjoint Set Union Problems"
, journal = "ACM Comput. Surv."
, volume = 23
, number = 3
, year = 1991
, pages = "319--344"
, update = "97.03 tamassia"
}
@article{ylw-rppro-95
, author = "C. D. Yang and D.
T. Lee and C. K. Wong"
, title = "Rectilinear paths
problems among rectilinear obstacles revisited"
, journal = "SIAM J. Comput."
, volume = 24
, year = 1995
, pages = "457--472"
, keywords = "shortest paths, rectilinear
geometry, bicriteria paths, VLSI, wire routing"
, succeeds = "ylw-rpror-92"
, update = "98.03 mitchell, 96.05
mitchell"
, annote = "They consider shortest
paths (also MST) in the $L_1$ geodesic
metric. They use a path-preserving graph approach, together
with
segment draggin. For a set of disjoint rectilinear obstacles
having $m$ edges, $t$ of which are ``extreme'' (locally -- having
both adjacent edges on the same side of the line through the
edge),
they compute a shortest path in time $O(m\log t+ t\log^{3/2}
t)$, using
$O(m+t\log^{3/2} t)$ space. They also consider the minimum-bend
shortest path (MBSP), shortest minimum-bend path (SMBP), and
minimum-cost (MCP -- using a monotonic function of rectilinear
link length and $L_1$ length) problems; these alsorithms take
time
$O(m\log^2 m)$ ($O(m\log m)$ space), or $O(m\log^{3/2} m)$ time
and space.
This improves previous bound of $O(mt+m\log m)$ in
\cite{ylw-blrpg-92}."
}