A practical guide to understanding the theory and practice of computational lower bounds.A fundamental question in computer science is: “Given a problem, how hard is it to solve?” Usually, the answer to this question lies in determining how long it will take to solve a problem as a function of the length of the input. Yet this question has two different parts, with two different answers: (1) upper bounds, which show that a problem can be solved in time T(n), and (2) lower bounds, which show that a problem cannot be solved in time T(n). In Computational Intractability, Erik Demaine, William Gasarch, and Mohammad Hajiaghayi focus on the latter, providing a guidebook to navigating lower bounds via the study of P, NP, NP-completeness, and other related notions.Computational Intractability covers virtually all aspects of lower bounds, from parallelism to undecidability, and explores this material from the point of view of actual problems rather than classes of problems. The authors show how to prove lower bounds on problems in a wide variety of settings: polynomial time, classes likely above polynomial time (e.g., polynomial space), and classes within polynomial time (e.g., quadratic time).

Martin Gardner has entertained the world with his puzzles for decades and inspired countless mathematicians and scientists. As he rounds out another decade, his colleagues are paying him tribute with this special collection that contains contributions from some of the most respected puzzlemasters, magicians and mathematicians, including: - John H. Conway - William R. Gosper - Ed Pegg, Jr. - Roger Penrose - Raymond Smullyan - Peter Winkler And of course there is something from the orignal puzzlemaster himself, Martin Gardner.

The tradition of a publication based on the Gathering for Gardner continues with this new carefully selected and edited collection in which Martin Gardner and friends inspire and entertain. The contributors to this volume---virtually a list of Who's Who in the World of Puzzles---trace their inspiration to Martin Gardner's puzzle column in Scientific American and to his contributions to the world of recreational mathematics. Tribute to a Mathemagician contains an author index for the two previous books in the collection of books based on the Gatherings for Gardner. Sample puzzles and games include: - Tripos - Black Jack - Chinese ceramic puzzle vessels - Paper folding - Mongolian interlocking puzzles - Rolling block puzzles - Sliding puzzles - Cryptic crosswords - The Panex puzzle - Polyonimo puzzles - and more

Did you know that any straight-line drawing on paper can be folded so that the complete drawing can be cut out with one straight scissors cut? That there is a planar linkage that can trace out any algebraic curve, or even 'sign your name'? Or that a 'Latin cross' unfolding of a cube can be refolded to 23 different convex polyhedra? Over the past decade, there has been a surge of interest in such problems, with applications ranging from robotics to protein folding. With an emphasis on algorithmic or computational aspects, this treatment gives hundreds of results and over 60 unsolved 'open problems' to inspire further research. The authors cover one-dimensional (1D) objects (linkages), 2D objects (paper), and 3D objects (polyhedra). Aimed at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from school students to researchers.

Did you know that any straight-line drawing on paper can be folded so that the complete drawing can be cut out with one straight scissors cut? That there is a planar linkage that can trace out any algebraic curve, or even 'sign your name'? Or that a 'Latin cross' unfolding of a cube can be refolded to 23 different convex polyhedra? Over the past decade, there has been a surge of interest in such problems, with applications ranging from robotics to protein folding. With an emphasis on algorithmic or computational aspects, this treatment gives hundreds of results and over 60 unsolved 'open problems' to inspire further research. The authors cover one-dimensional (1D) objects (linkages), 2D objects (paper), and 3D objects (polyhedra). Aimed at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from school students to researchers.

Martin Gardner has entertained the world with his puzzles for decades and inspired countless mathematicians and scientists. As he rounds out another decade, his colleagues are paying him tribute with this special collection that contains contributions from some of the most respected puzzlemasters, magicians and mathematicians, including: - John H. Conway - William R. Gosper - Ed Pegg, Jr. - Roger Penrose - Raymond Smullyan - Peter Winkler. And of course there is something from the original puzzlemaster himself, Martin Gardner.

The tradition of a publication based on the Gathering for Gardner continues with this new carefully selected and edited collection in which Martin Gardner and friends inspire and entertain. The contributors to this volume---virtually a list of Who''s Who in the World of Puzzles---trace their inspiration to Martin Gardner''s puzzle column in Scientifi

The authors show that there are underlying mathematical reasons for why games and puzzles are challenging (and perhaps why they are so much fun). They also show that games and puzzles can serve as powerful models of computation-quite different from the usual models of automata and circuits-offering a new way of thinking about computation. The appen

The tradition of a publication based on the Gathering for Gardner continues with this new carefully selected and edited collection in which Martin Gardner and friends inspire and entertain. The contributors to this volume---virtually a list of Who''s Who in the World of Puzzles---trace their inspiration to Martin Gardner''s puzzle column in Scientifi

The authors show that there are underlying mathematical reasons for why games and puzzles are challenging (and perhaps why they are so much fun). They also show that games and puzzles can serve as powerful models of computation-quite different from the usual models of automata and circuits-offering a new way of thinking about computation. The appen

Martin Gardner has entertained the world with his puzzles for decades and inspired countless mathematicians and scientists. As he rounds out another decade, his colleagues are paying him tribute with this special collection that contains contributions from some of the most respected puzzlemasters, magicians and mathematicians, including: - John H. Conway - William R. Gosper - Ed Pegg, Jr. - Roger Penrose - Raymond Smullyan - Peter Winkler. And of course there is something from the original puzzlemaster himself, Martin Gardner.

The tradition of a publication based on the Gathering for Gardner continues with this new carefully selected and edited collection in which Martin Gardner and friends inspire and entertain. The contributors to this volume---virtually a list of Who's Who in the World of Puzzles---trace their inspiration to Martin Gardner's puzzle column in Scientific American and to his contributions to the world of recreational mathematics. Tribute to a Mathemagician contains an author index for the two previous books in the collection of books based on the Gatherings for Gardner. Sample puzzles and games include: - Tripos - Black Jack - Chinese ceramic puzzle vessels - Paper folding - Mongolian interlocking puzzles - Rolling block puzzles - Sliding puzzles - Cryptic crosswords - The Panex puzzle - Polyonimo puzzles - and more

Martin Gardner has entertained the world with his puzzles for decades and inspired countless mathematicians and scientists. As he rounds out another decade, his colleagues are paying him tribute with this special collection that contains contributions from some of the most respected puzzlemasters, magicians and mathematicians, including: - John H. Conway - William R. Gosper - Ed Pegg, Jr. - Roger Penrose - Raymond Smullyan - Peter Winkler And of course there is something from the orignal puzzlemaster himself, Martin Gardner.

A practical guide to understanding the theory and practice of computational lower bounds.A fundamental question in computer science is: “Given a problem, how hard is it to solve?” Usually, the answer to this question lies in determining how long it will take to solve a problem as a function of the length of the input. Yet this question has two different parts, with two different answers: (1) upper bounds, which show that a problem can be solved in time T(n), and (2) lower bounds, which show that a problem cannot be solved in time T(n). In Computational Intractability, Erik Demaine, William Gasarch, and Mohammad Hajiaghayi focus on the latter, providing a guidebook to navigating lower bounds via the study of P, NP, NP-completeness, and other related notions.Computational Intractability covers virtually all aspects of lower bounds, from parallelism to undecidability, and explores this material from the point of view of actual problems rather than classes of problems. The authors show how to prove lower bounds on problems in a wide variety of settings: polynomial time, classes likely above polynomial time (e.g., polynomial space), and classes within polynomial time (e.g., quadratic time).

Martin Gardner has entertained the world with his puzzles for decades and inspired countless mathematicians and scientists. As he rounds out another decade, his colleagues are paying him tribute with this special collection that contains contributions from some of the most respected puzzlemasters, magicians and mathematicians, including: - John H. Conway - William R. Gosper - Ed Pegg, Jr. - Roger Penrose - Raymond Smullyan - Peter Winkler And of course there is something from the orignal puzzlemaster himself, Martin Gardner.

The tradition of a publication based on the Gathering for Gardner continues with this new carefully selected and edited collection in which Martin Gardner and friends inspire and entertain. The contributors to this volume---virtually a list of Who's Who in the World of Puzzles---trace their inspiration to Martin Gardner's puzzle column in Scientific American and to his contributions to the world of recreational mathematics. Tribute to a Mathemagician contains an author index for the two previous books in the collection of books based on the Gatherings for Gardner. Sample puzzles and games include: - Tripos - Black Jack - Chinese ceramic puzzle vessels - Paper folding - Mongolian interlocking puzzles - Rolling block puzzles - Sliding puzzles - Cryptic crosswords - The Panex puzzle - Polyonimo puzzles - and more

Did you know that any straight-line drawing on paper can be folded so that the complete drawing can be cut out with one straight scissors cut? That there is a planar linkage that can trace out any algebraic curve, or even 'sign your name'? Or that a 'Latin cross' unfolding of a cube can be refolded to 23 different convex polyhedra? Over the past decade, there has been a surge of interest in such problems, with applications ranging from robotics to protein folding. With an emphasis on algorithmic or computational aspects, this treatment gives hundreds of results and over 60 unsolved 'open problems' to inspire further research. The authors cover one-dimensional (1D) objects (linkages), 2D objects (paper), and 3D objects (polyhedra). Aimed at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from school students to researchers.

Did you know that any straight-line drawing on paper can be folded so that the complete drawing can be cut out with one straight scissors cut? That there is a planar linkage that can trace out any algebraic curve, or even 'sign your name'? Or that a 'Latin cross' unfolding of a cube can be refolded to 23 different convex polyhedra? Over the past decade, there has been a surge of interest in such problems, with applications ranging from robotics to protein folding. With an emphasis on algorithmic or computational aspects, this treatment gives hundreds of results and over 60 unsolved 'open problems' to inspire further research. The authors cover one-dimensional (1D) objects (linkages), 2D objects (paper), and 3D objects (polyhedra). Aimed at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from school students to researchers.

Martin Gardner has entertained the world with his puzzles for decades and inspired countless mathematicians and scientists. As he rounds out another decade, his colleagues are paying him tribute with this special collection that contains contributions from some of the most respected puzzlemasters, magicians and mathematicians, including: - John H. Conway - William R. Gosper - Ed Pegg, Jr. - Roger Penrose - Raymond Smullyan - Peter Winkler. And of course there is something from the original puzzlemaster himself, Martin Gardner.

The tradition of a publication based on the Gathering for Gardner continues with this new carefully selected and edited collection in which Martin Gardner and friends inspire and entertain. The contributors to this volume---virtually a list of Who''s Who in the World of Puzzles---trace their inspiration to Martin Gardner''s puzzle column in Scientifi

The authors show that there are underlying mathematical reasons for why games and puzzles are challenging (and perhaps why they are so much fun). They also show that games and puzzles can serve as powerful models of computation-quite different from the usual models of automata and circuits-offering a new way of thinking about computation. The appen

The tradition of a publication based on the Gathering for Gardner continues with this new carefully selected and edited collection in which Martin Gardner and friends inspire and entertain. The contributors to this volume---virtually a list of Who''s Who in the World of Puzzles---trace their inspiration to Martin Gardner''s puzzle column in Scientifi

The authors show that there are underlying mathematical reasons for why games and puzzles are challenging (and perhaps why they are so much fun). They also show that games and puzzles can serve as powerful models of computation-quite different from the usual models of automata and circuits-offering a new way of thinking about computation. The appen

Martin Gardner has entertained the world with his puzzles for decades and inspired countless mathematicians and scientists. As he rounds out another decade, his colleagues are paying him tribute with this special collection that contains contributions from some of the most respected puzzlemasters, magicians and mathematicians, including: - John H. Conway - William R. Gosper - Ed Pegg, Jr. - Roger Penrose - Raymond Smullyan - Peter Winkler. And of course there is something from the original puzzlemaster himself, Martin Gardner.

The tradition of a publication based on the Gathering for Gardner continues with this new carefully selected and edited collection in which Martin Gardner and friends inspire and entertain. The contributors to this volume---virtually a list of Who's Who in the World of Puzzles---trace their inspiration to Martin Gardner's puzzle column in Scientific American and to his contributions to the world of recreational mathematics. Tribute to a Mathemagician contains an author index for the two previous books in the collection of books based on the Gatherings for Gardner. Sample puzzles and games include: - Tripos - Black Jack - Chinese ceramic puzzle vessels - Paper folding - Mongolian interlocking puzzles - Rolling block puzzles - Sliding puzzles - Cryptic crosswords - The Panex puzzle - Polyonimo puzzles - and more

Martin Gardner has entertained the world with his puzzles for decades and inspired countless mathematicians and scientists. As he rounds out another decade, his colleagues are paying him tribute with this special collection that contains contributions from some of the most respected puzzlemasters, magicians and mathematicians, including: - John H. Conway - William R. Gosper - Ed Pegg, Jr. - Roger Penrose - Raymond Smullyan - Peter Winkler And of course there is something from the orignal puzzlemaster himself, Martin Gardner.