{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/22372"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/22372","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Geometric planning for VLSI routing and robot motion","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Maddila, Sanjeev Rao"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical and Computer Engineering","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T13:37:44Z","date_published":"2011-05-07T13:37:44Z","updated_at":"2026-07-22T22:25:19Z","subjects":["Mathematics","Engineering, Electronics and Electrical","Computer Science"],"languages":["eng"],"rights":["Copyright 1989 Maddila, Sanjeev Rao"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9010946","(UMI)AAI9010946"],"render_values":[{"text":"AAI9010946","href":null,"code":true},{"text":"(UMI)AAI9010946","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/22372","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Maddila, Sanjeev Rao"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T13:37:44Z","10000-01-01","1989"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical and Computer Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","Engineering, Electronics and Electrical","Computer Science"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1989 Maddila, Sanjeev Rao"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9010946","(UMI)AAI9010946","http://hdl.handle.net/2142/22372"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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 $t\\sb1$ + $t\\sb2$ $\\geq$ ${3\\over2}$($d\\sb1$ + $d\\sb2$) for routing three-terminal nets in an L-shaped junction, where $t\\sb1$ and $t\\sb2$ are the widths, and $d\\sb1$ and $d\\sb2$ 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 $t\\sb1$ + $t\\sb2$ = $d\\sb1$ + $d\\sb2$, $t\\sb1$ + $t\\sb2$ $\\leq$ ${3\\over2}$($d\\sb1$ + $d\\sb2$) for the case of three-terminal nets, and $t\\sb1$ + $t\\sb2$ $\\leq$ 2($d\\sb1$ + $d\\sb2$) 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.","Made available in DSpace on 2011-05-07T13:37:44Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9010946.pdf: 5985708 bytes, checksum: 137bdf30bedbd6d7e818bc4cc6897a1e (MD5) Previous issue date: 1989","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:57:11Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:26:47-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["Geometric planning for VLSI routing and robot motion"]}]}],"canonical_facts":{"dc:creator":["Maddila, Sanjeev Rao"],"dc:date":["2011-05-07T13:37:44Z","10000-01-01","1989"],"dc:description":["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 $t\\sb1$ + $t\\sb2$ $\\geq$ ${3\\over2}$($d\\sb1$ + $d\\sb2$) for routing three-terminal nets in an L-shaped junction, where $t\\sb1$ and $t\\sb2$ are the widths, and $d\\sb1$ and $d\\sb2$ 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 $t\\sb1$ + $t\\sb2$ = $d\\sb1$ + $d\\sb2$, $t\\sb1$ + $t\\sb2$ $\\leq$ ${3\\over2}$($d\\sb1$ + $d\\sb2$) for the case of three-terminal nets, and $t\\sb1$ + $t\\sb2$ $\\leq$ 2($d\\sb1$ + $d\\sb2$) 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.","Made available in DSpace on 2011-05-07T13:37:44Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9010946.pdf: 5985708 bytes, checksum: 137bdf30bedbd6d7e818bc4cc6897a1e (MD5) Previous issue date: 1989","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:57:11Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:26:47-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["AAI9010946","(UMI)AAI9010946","http://hdl.handle.net/2142/22372"],"dc:language":["eng"],"dc:rights":["Copyright 1989 Maddila, Sanjeev Rao"],"dc:subject":["Mathematics","Engineering, Electronics and Electrical","Computer Science"],"dc:title":["Geometric planning for VLSI routing and robot motion"],"dc:type":["text"],"thesis:degree_discipline":["Electrical and Computer Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:19Z"}