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- W89252009 abstract "This thesis proposes a decomposition-based algorithmic paradigm, called planning with local experts, where the given global planning problem is decomposed into a set of subproblems that are each solved efficiently in a prescribed sequence and then the solutions of the subproblems are merged together.In the first part of the thesis, we investigate the problems of VLSI routing. In particular, we propose a way of decomposing the problem of routing in a general placement of rectangular modules into a set of subproblems of routing in junctions of L-, S-, T-, and X-shapes. We give non-trivial lower bounds on the channel widths of the associated channels of a junction. For example, we prove that $tsb1$ + $tsb2$ $geq$ ${3over2}$($dsb1$ + $dsb2$) for routing three-terminal nets in an L-shaped junction, where $tsb1$ and $tsb2$ are the widths, and $dsb1$ and $dsb2$ are the densities of the horizontal and vertical channels of the L-shaped junction, respectively. We also give routers for the general junctions, for the cases of routing two-, three-, and multi-terminal nets. For example, we prove that for routing two-terminal nets in an L-shaped junction $tsb1$ + $tsb2$ = $dsb1$ + $dsb2$, $tsb1$ + $tsb2$ $leq$ ${3over2}$($dsb1$ + $dsb2$) for the case of three-terminal nets, and $tsb1$ + $tsb2$ $leq$ 2($dsb1$ + $dsb2$) for the case of multi-terminal nets.In the second part of the thesis, we investigate the problems of robot motion planning. In particular, we consider a technique to decompose the problem of moving a robot among a set of rectangles into a set of subproblems of moving the robot in certain localites. We give local experts for the local planning problems of moving a polygonal robot around a corner, and moving through a junction of general shape. For example, we give an $O$($m$ log $m$) algorithm for moving a convex $m$-gon around the corner in a corridor. Thus, using our decomposition scheme we develop an $O$($mn$ log $m$ + $n$ log $n$) algorithm for moving a convex polygon with $m$ corners among $n$ iso-oriented rectangles." @default.
- W89252009 created "2016-06-24" @default.
- W89252009 creator A5027628320 @default.
- W89252009 date "1989-01-01" @default.
- W89252009 modified "2023-09-26" @default.
- W89252009 title "Geometric planning for vlsi routing and robot motion" @default.
- W89252009 hasPublicationYear "1989" @default.
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