{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/23253"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/23253","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"The mesh of trees architecture for parallel computation","abstract":"This thesis considers the mesh of trees architecture as both a special-purpose and a general-purpose parallel computer. A family of special-purpose VLSI architectures for computing an ($n\\sb1 \\times n\\sb2 \\times \\cdots \\times n\\sb{d}$)-point multidimensional DFT over $\\doubz\\sb{M}$, the ring of integers modulo $M$, is proposed. Using the two-dimensional mesh of trees as a component, these architectures achieve optimal VLSI area $A$ = $\\Theta((N\\sp2\\log\\sp{2}M)/T\\sp2)$ for any given computation time $T\\ \\epsilon$ ($\\Omega(\\log N),O(\\sqrt{N\\log M})\\rbrack.$","abstract_html":"This thesis considers the mesh of trees architecture as both a special-purpose and a general-purpose parallel computer. A family of special-purpose VLSI architectures for computing an ($n\\sb1 \\times n\\sb2 \\times \\cdots \\times n\\sb{d}$)-point multidimensional DFT over $\\doubz\\sb{M}$, the ring of integers modulo $M$, is proposed. Using the two-dimensional mesh of trees as a component, these architectures achieve optimal VLSI area $A$ = $\\Theta((N\\sp2\\log\\sp{2}M)/T\\sp2)$ for any given computation time <span class=\"etd-inline-math\">T &epsilon;</span> ($\\Omega(\\log N),O(\\sqrt{N\\log M})\\rbrack.$","abstract_has_math":true,"creators":["Hornick, Scot W."],"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":"2011-05-07T14:07:35Z","date_published":"2011-05-07T14:07:35Z","updated_at":"2026-07-22T22:25:21Z","subjects":["Engineering, Electronics and Electrical","Computer Science"],"languages":["eng"],"rights":["Copyright 1989 Hornick, Scot Wayne"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI8924842","(UMI)AAI8924842"],"render_values":[{"text":"AAI8924842","href":null,"code":true},{"text":"(UMI)AAI8924842","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/23253","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Hornick, Scot W."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T14:07:35Z","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":["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 Hornick, Scot Wayne"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI8924842","(UMI)AAI8924842","http://hdl.handle.net/2142/23253"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This thesis considers the mesh of trees architecture as both a special-purpose and a general-purpose parallel computer. A family of special-purpose VLSI architectures for computing an ($n\\sb1 \\times n\\sb2 \\times \\cdots \\times n\\sb{d}$)-point multidimensional DFT over $\\doubz\\sb{M}$, the ring of integers modulo $M$, is proposed. Using the two-dimensional mesh of trees as a component, these architectures achieve optimal VLSI area $A$ = $\\Theta((N\\sp2\\log\\sp{2}M)/T\\sp2)$ for any given computation time $T\\ \\epsilon$ ($\\Omega(\\log N),O(\\sqrt{N\\log M})\\rbrack.$","The convergence properties of Newton's method are studied. By introducing and formalizing the notion of attunement of a linear system of equations, it is shown that Newton's method provides polylog-time solutions for a broader class of linear systems than was previously supposed. In particular, the system matrix need not be well-conditioned; all that is required is that the known vector be well-attuned to the system matrix. It is then shown that Newton's method can be implemented on a special-purpose architecture based on the three-dimensional mesh of trees. This same architecture can be used to construct the stiffness equations arising from a finite element approximation. Furthermore, it can be hybridized with a systolic array to achieve a processor-time or area-time tradeoff.","Then, in a different vein, the two-dimensional mesh of trees is studied as a general-purpose parallel computer. It is shown that this architecture can afford finer memory granularity and, thereby, reduce the memory redundancy required for deterministic P-RAM simulation. A distributed-memory, bounded-degree network model of parallel computation is proposed that allows one to take greater advantage of the potential for fine-grain memories without sacrificing other aspects of realism. The simulation scheme presented is admitted by this new model and achieves constant memory redundancy.","Made available in DSpace on 2011-05-07T14:07:35Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 8924842.pdf: 4069878 bytes, checksum: a429fd5e69e455130261aa6590dc275a (MD5) Previous issue date: 1989","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T15:03:13Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:30:07-05:00 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":["The mesh of trees architecture for parallel computation"]}]}],"canonical_facts":{"dc:creator":["Hornick, Scot W."],"dc:date":["2011-05-07T14:07:35Z","10000-01-01","1989"],"dc:description":["This thesis considers the mesh of trees architecture as both a special-purpose and a general-purpose parallel computer. A family of special-purpose VLSI architectures for computing an ($n\\sb1 \\times n\\sb2 \\times \\cdots \\times n\\sb{d}$)-point multidimensional DFT over $\\doubz\\sb{M}$, the ring of integers modulo $M$, is proposed. Using the two-dimensional mesh of trees as a component, these architectures achieve optimal VLSI area $A$ = $\\Theta((N\\sp2\\log\\sp{2}M)/T\\sp2)$ for any given computation time $T\\ \\epsilon$ ($\\Omega(\\log N),O(\\sqrt{N\\log M})\\rbrack.$","The convergence properties of Newton's method are studied. By introducing and formalizing the notion of attunement of a linear system of equations, it is shown that Newton's method provides polylog-time solutions for a broader class of linear systems than was previously supposed. In particular, the system matrix need not be well-conditioned; all that is required is that the known vector be well-attuned to the system matrix. It is then shown that Newton's method can be implemented on a special-purpose architecture based on the three-dimensional mesh of trees. This same architecture can be used to construct the stiffness equations arising from a finite element approximation. Furthermore, it can be hybridized with a systolic array to achieve a processor-time or area-time tradeoff.","Then, in a different vein, the two-dimensional mesh of trees is studied as a general-purpose parallel computer. It is shown that this architecture can afford finer memory granularity and, thereby, reduce the memory redundancy required for deterministic P-RAM simulation. A distributed-memory, bounded-degree network model of parallel computation is proposed that allows one to take greater advantage of the potential for fine-grain memories without sacrificing other aspects of realism. The simulation scheme presented is admitted by this new model and achieves constant memory redundancy.","Made available in DSpace on 2011-05-07T14:07:35Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 8924842.pdf: 4069878 bytes, checksum: a429fd5e69e455130261aa6590dc275a (MD5) Previous issue date: 1989","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T15:03:13Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:30:07-05:00 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":["AAI8924842","(UMI)AAI8924842","http://hdl.handle.net/2142/23253"],"dc:language":["eng"],"dc:rights":["Copyright 1989 Hornick, Scot Wayne"],"dc:subject":["Engineering, Electronics and Electrical","Computer Science"],"dc:title":["The mesh of trees architecture for parallel computation"],"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":"2026-07-22T22:25:21Z"}