Shor, Peter W.
Overview
Works:  11 works in 18 publications in 1 language and 29 library holdings 

Roles:  Author 
Classifications:  QA76.M41, 
Publication Timeline
.
Most widely held works by
Peter W Shor
Efficient NC algorithms for set cover with applications to learning and geometry by
Bonnie Anne Berger(
Book
)
3 editions published in 1989 in English and held by 7 WorldCat member libraries worldwide
3 editions published in 1989 in English and held by 7 WorldCat member libraries worldwide
Tight bounds for minimax grid matching, with applications to the average case analysis of algorithms by
Frank Thomson Leighton(
Book
)
4 editions published in 1986 in English and held by 6 WorldCat member libraries worldwide
The minimax grid matching problem is a fundamental combinatorial problem associated with the average case analysis of algorithms. The problem has arisen in a number of interesting and seemingly unrelated areas, including waferscale integration of systolic arrays, twodimensional discrepancy problems, and testing pseudorandom number generators. However, the minimax grid matching problem is best known for its application to the maximum upright matching problem. The maximum upright matching problem was originally defined by Karp, Luby and MarchettiSpaccamela in association with algorithms for 2dimensional bin packing. More recently, the upright matching problem has arisen in the average case analysis of online algorithms for 1dimensional bin packing and dynamic allocation. In this paper, the authors solve both the minimax grid matching problem and the maximum upright matching problem. As a direct result, they obtain tight upper bounds on the average case behavior of the best algorithms known for 2dimensional bin packing, 1dimensional online packing and online dynamic allocation. The results also solve a longopen question in mathematical statistics
4 editions published in 1986 in English and held by 6 WorldCat member libraries worldwide
The minimax grid matching problem is a fundamental combinatorial problem associated with the average case analysis of algorithms. The problem has arisen in a number of interesting and seemingly unrelated areas, including waferscale integration of systolic arrays, twodimensional discrepancy problems, and testing pseudorandom number generators. However, the minimax grid matching problem is best known for its application to the maximum upright matching problem. The maximum upright matching problem was originally defined by Karp, Luby and MarchettiSpaccamela in association with algorithms for 2dimensional bin packing. More recently, the upright matching problem has arisen in the average case analysis of online algorithms for 1dimensional bin packing and dynamic allocation. In this paper, the authors solve both the minimax grid matching problem and the maximum upright matching problem. As a direct result, they obtain tight upper bounds on the average case behavior of the best algorithms known for 2dimensional bin packing, 1dimensional online packing and online dynamic allocation. The results also solve a longopen question in mathematical statistics
Approximation algorithms for the maximum acyclic subgraph problem by
Bonnie Anne Berger(
Book
)
3 editions published in 1989 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 1989 in English and held by 5 WorldCat member libraries worldwide
A linear time algorithm for computing the Voronoi diagram of convex polygons by
Alok Aggarwal(
Book
)
1 edition published in 1987 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1987 in English and held by 2 WorldCat member libraries worldwide
The averagecase analysis of some online algorithms for the bin packing by
Peter W Shor(
Book
)
1 edition published in 1986 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1986 in English and held by 2 WorldCat member libraries worldwide
ICM '98 : International Congress of Mathematicians, August 1827, 1998, Berlin by International Congress of Mathematicians(
Book
)
1 edition published in 1998 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1998 in English and held by 2 WorldCat member libraries worldwide
Cube tilings of R[superscript n] and nonlinear codes by
Jeffrey C Lagarias(
Book
)
1 edition published in 1992 in English and held by 1 WorldCat member library worldwide
Abstract: "Families of nonlattice tilings of R[superscript n] by unit cubes are constructed. These tilings are specializations of certain families of nonlinear codes over GF(2). These cubetilings provide building blocks for the construction of cubetilings such that no two cubes have a highdimensional face in common. We construct cubetilings of R[superscript n] such that no two cubes have a common face of dimension exceeding n  1/3 [square root of n]."
1 edition published in 1992 in English and held by 1 WorldCat member library worldwide
Abstract: "Families of nonlattice tilings of R[superscript n] by unit cubes are constructed. These tilings are specializations of certain families of nonlinear codes over GF(2). These cubetilings provide building blocks for the construction of cubetilings such that no two cubes have a highdimensional face in common. We construct cubetilings of R[superscript n] such that no two cubes have a common face of dimension exceeding n  1/3 [square root of n]."
Approximation algorithms for the maximum acyclic subgraph problem by
Bonnie Anne Berger(
)
1 edition published in 1990 in English and held by 1 WorldCat member library worldwide
1 edition published in 1990 in English and held by 1 WorldCat member library worldwide
On the pagenumber of planar graphs by Jonathan Frederick Buss(
Book
)
1 edition published in 1984 in English and held by 1 WorldCat member library worldwide
1 edition published in 1984 in English and held by 1 WorldCat member library worldwide
Local rule switching mechanism for viral shell geometry by
Massachusetts Institute of Technology(
Book
)
1 edition published in 1995 in English and held by 1 WorldCat member library worldwide
1 edition published in 1995 in English and held by 1 WorldCat member library worldwide
Efficient NC Algorithms for Set Cover Applications to Learning and Geometry(
)
1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
In this paper we give NC approximation algorithms for the unweighted and weighted set cover problems. Our algorithms use a linear number of processors and give a cover that has at most log n times the optimal size/ weight, thus matching the performance of the best sequential algorithms (H, Lo, C). We apply our set cover algorithm to learning theory, giving an NC algorithm to learn the concept class obtained by taking the closure under finite union or finite intersection of any concept class of finite VCdimension which has an NC hypothesis finder. In addition, we give a linearprocessor NC algorithm for a variant of the set cover problem first proposed by (cf), and use it to obtain NC algorithms for several problems in computational geometry. (KR)
1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
In this paper we give NC approximation algorithms for the unweighted and weighted set cover problems. Our algorithms use a linear number of processors and give a cover that has at most log n times the optimal size/ weight, thus matching the performance of the best sequential algorithms (H, Lo, C). We apply our set cover algorithm to learning theory, giving an NC algorithm to learn the concept class obtained by taking the closure under finite union or finite intersection of any concept class of finite VCdimension which has an NC hypothesis finder. In addition, we give a linearprocessor NC algorithm for a variant of the set cover problem first proposed by (cf), and use it to obtain NC algorithms for several problems in computational geometry. (KR)
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Related Identities
 Berger, Bonnie Author
 Massachusetts Institute of Technology Laboratory for Computer Science
 Rompel, J.
 Rompel, John
 Leighton, Tom Author
 Leighton, Frank Thomson Author
 Aggarwal, Alok Author
 MASSACHUSETTS INST OF TECH CAMBRIDGE LAB FOR COMPUTER SCIENCE
 Buss, Jonathan Frederick Author
 Lagarias, Jeffrey C. 1949 Author
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Alternative Names
Peter Shor American professor of applied mathematics at MIT
Peter Shor Amerikaans wiskundige
Peter Shor amerikansk datavetare och matematiker
Peter Shor amerikansk informatiker og matematiker
Peter Shor informatyk amerykański
Peter Shor mathématicien américain
Peter Shor US amerikanischer Mathematiker und Informatiker
Peter Shor usona matematikisto
Peter W. Shor informatico statunitense
Пітер Шор
Шор, Питер
פיטר שור
بيتر شور
پیتر شر ریاضیدان و دانشمند علوم کامپیوتر آمریکایی
피터 쇼어
ピーター・ショア
彼得·秀爾
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