Demaine, Erik D. 1981
Overview
Works:  33 works in 75 publications in 2 languages and 1,901 library holdings 

Genres:  Interviews 
Roles:  Author, Speaker, Creator, Editor 
Classifications:  TT870, 736.982 
Publication Timeline
.
Most widely held works by
Erik D Demaine
Between the folds a film about finding inspiration in unexpected places
(
Visual
)
2 editions published in 2009 in English and held by 893 WorldCat member libraries worldwide
Origami may seem an unlikely medium for understanding and explaining the world. But around the globe, several fine artists and theoretical scientists are abandoning more conventional career paths to forge lives as modernday paper folders. Through origami, these offbeat and provocative minds are reshaping ideas of creativity and revealing the relationship between art and science. This film chronicles 10 of their stories: three of the world's foremost origami artists, less conventional artists, abstract artists, advanced mathematicians and a remarkable scientist who received a MacArthur Genius Award for his computational origami research. While debates ebb and flow on issues of folding technique, symbolism and purpose, this film shows how closely art and science are intertwined. The medium of paper foldinga simple blank, uncut squareemerges as a metaphor for the creative potential of transformation in all of us
2 editions published in 2009 in English and held by 893 WorldCat member libraries worldwide
Origami may seem an unlikely medium for understanding and explaining the world. But around the globe, several fine artists and theoretical scientists are abandoning more conventional career paths to forge lives as modernday paper folders. Through origami, these offbeat and provocative minds are reshaping ideas of creativity and revealing the relationship between art and science. This film chronicles 10 of their stories: three of the world's foremost origami artists, less conventional artists, abstract artists, advanced mathematicians and a remarkable scientist who received a MacArthur Genius Award for his computational origami research. While debates ebb and flow on issues of folding technique, symbolism and purpose, this film shows how closely art and science are intertwined. The medium of paper foldinga simple blank, uncut squareemerges as a metaphor for the creative potential of transformation in all of us
Geometric folding algorithms : linkages, origami, polyhedra
by
Erik D Demaine(
Book
)
23 editions published between 2007 and 2010 in English and Japanese and held by 437 WorldCat member libraries worldwide
Folding and unfolding problems have been implicit since Albrecht Dürer in the early 1500s, but have only recently been studied in the mathematical literature. Emphasising algorithmic or computational aspects, this treatment of the geometry of folding and unfolding presents over 60 unsolved 'open problems' to spur further research
23 editions published between 2007 and 2010 in English and Japanese and held by 437 WorldCat member libraries worldwide
Folding and unfolding problems have been implicit since Albrecht Dürer in the early 1500s, but have only recently been studied in the mathematical literature. Emphasising algorithmic or computational aspects, this treatment of the geometry of folding and unfolding presents over 60 unsolved 'open problems' to spur further research
A lifetime of puzzles : a collection of puzzles in honor of Martin Gardner's 90th birthday
by
Erik D Demaine(
Book
)
5 editions published in 2008 in English and held by 265 WorldCat member libraries worldwide
"This collection is a tribute to Martin Gardner by mathematicians, puzzle masters, and magicians. It was conceived and initiated in honor of his 90th birthday and is finally published as he celebrates his 94th year, maintaining the inspiring creativity that has motivated so many professional mathematicians and amateurs, who are all dedicated to his unique amalgamation of rational thought and magic. Some of the contributions celebrate the life of Martin Gardner; some tell about his influence on individuals or on the field of recreational mathematics in general; some are puzzles or tricks inspired by Martin Gardner and his work." "Martin Gardner stands at the intersection of magic and mathematics. Mathematical magic, like chess, has its own curious charms, he says. [It] combines the beauty of mathematical structure with the entertainment value of a trick. Martin Gardner has been writing about magic and contributing new effects for nearly seventy years. Today, he keeps in contact with magicians like Penn and Teller by phone and receives occasional visits from magicians who come to trade notes with him. In 1999 he was named one of MAGIC Magazine s 100 most influential magicians of the twentieth century."Jacket
5 editions published in 2008 in English and held by 265 WorldCat member libraries worldwide
"This collection is a tribute to Martin Gardner by mathematicians, puzzle masters, and magicians. It was conceived and initiated in honor of his 90th birthday and is finally published as he celebrates his 94th year, maintaining the inspiring creativity that has motivated so many professional mathematicians and amateurs, who are all dedicated to his unique amalgamation of rational thought and magic. Some of the contributions celebrate the life of Martin Gardner; some tell about his influence on individuals or on the field of recreational mathematics in general; some are puzzles or tricks inspired by Martin Gardner and his work." "Martin Gardner stands at the intersection of magic and mathematics. Mathematical magic, like chess, has its own curious charms, he says. [It] combines the beauty of mathematical structure with the entertainment value of a trick. Martin Gardner has been writing about magic and contributing new effects for nearly seventy years. Today, he keeps in contact with magicians like Penn and Teller by phone and receives occasional visits from magicians who come to trade notes with him. In 1999 he was named one of MAGIC Magazine s 100 most influential magicians of the twentieth century."Jacket
Games, puzzles, and computation
by
Robert A Hearn(
Book
)
4 editions published in 2009 in English and held by 229 WorldCat member libraries worldwide
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 computationquite different from the usual models of automata and circuitsoffering a new way of thinking about computation. The appendices provide a substantial survey of all known results in the field of game complexity, serving as a reference guide for readers interested in the computational complexity of particular games, or interested in open problems about such complexities
4 editions published in 2009 in English and held by 229 WorldCat member libraries worldwide
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 computationquite different from the usual models of automata and circuitsoffering a new way of thinking about computation. The appendices provide a substantial survey of all known results in the field of game complexity, serving as a reference guide for readers interested in the computational complexity of particular games, or interested in open problems about such complexities
Open problems from Dagstuhl seminar 07281 structure theory and FPT algorithmcs for graphs, digraphs and hypergraphs
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)
1 edition published in 2007 in English and held by 16 WorldCat member libraries worldwide
1 edition published in 2007 in English and held by 16 WorldCat member libraries worldwide
Structure theory and FPT algorithmics for graphs, digraphs and hypergraphs 07281 abstracts collection ; Dagstuhl seminar/ Erik Demaine
(
)
1 edition published in 2007 in English and held by 16 WorldCat member libraries worldwide
1 edition published in 2007 in English and held by 16 WorldCat member libraries worldwide
Fixedparameter algorithms for the (k, r)center in planar graphs and map graphs
by
Erik D Demaine(
Book
)
3 editions published in 2003 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 2003 in English and held by 5 WorldCat member libraries worldwide
Bidimensional Parameters and Local Treewidth
by
Erik D Demaine(
Book
)
4 editions published between 2000 and 2003 in English and held by 4 WorldCat member libraries worldwide
4 editions published between 2000 and 2003 in English and held by 4 WorldCat member libraries worldwide
Approximation algorithms via contraction decomposition
by
Erik D Demaine(
Book
)
3 editions published in 2006 in English and held by 4 WorldCat member libraries worldwide
We prove that the edges of every graph of bounded (Euler) genus can be partitioned into any prescribed number $k$ of pieces such that contracting any piece results in a graph of bounded treewidth (where the bound dependson~$k$). This decomposition result parallels an analogous, simpler result for edge deletions instead of contractions, obtained by Baker, Eppstein, and others, and it generalizes a similar result for "compression" (a variant of contraction) in planar graphs (Klein). Our decomposition result is a powerful tool for obtaining PTASs for contractionclosed problems (whose optimal solution only improves under contraction), a much more general class than minorclosed problems. We prove that any contractionclosed problem satisfying just a few simple conditions has a PTAS in boundedgenus graphs. In particular, our framework yields PTASs for the weighted Traveling Salesman Problem and for minimumweight $c$edgeconnected submultigraph on boundedgenus graphs, improving and generalizing many previous algorithms. We also highlight the only main difficulty in extending our results to general $H$minorfree graphs
3 editions published in 2006 in English and held by 4 WorldCat member libraries worldwide
We prove that the edges of every graph of bounded (Euler) genus can be partitioned into any prescribed number $k$ of pieces such that contracting any piece results in a graph of bounded treewidth (where the bound dependson~$k$). This decomposition result parallels an analogous, simpler result for edge deletions instead of contractions, obtained by Baker, Eppstein, and others, and it generalizes a similar result for "compression" (a variant of contraction) in planar graphs (Klein). Our decomposition result is a powerful tool for obtaining PTASs for contractionclosed problems (whose optimal solution only improves under contraction), a much more general class than minorclosed problems. We prove that any contractionclosed problem satisfying just a few simple conditions has a PTAS in boundedgenus graphs. In particular, our framework yields PTASs for the weighted Traveling Salesman Problem and for minimumweight $c$edgeconnected submultigraph on boundedgenus graphs, improving and generalizing many previous algorithms. We also highlight the only main difficulty in extending our results to general $H$minorfree graphs
Folding and unfolding
by
Erik D Demaine(
)
2 editions published between 2001 and 2004 in English and held by 4 WorldCat member libraries worldwide
The results of this thesis concern folding of onedimensional objects in two dimensions: planar linkages. More precisely, a planar linkage consists of a collection of rigid bars (line segments) connected at their endpoints. Foldings of such a linkage must preserve the connections at endpoints, preserve the bar lengths, and (in our context)prevent bars from crossing. The main result of this thesis is that aplanar linkage forming a collection of polygonal arcs and cycles can be folded so that all outermost arcs (not enclosed by other cycles) become straight and all outermost cycles become convex. A complementary result of this thesis is that once a cycle becomes convex, it can be folded into any other convex cycle with the same counterclockwise sequence of bar lengths. Together, these results show that the configuration space of all possible foldings of a planar arc or cycle linkage is connected. These results fall into the broader context of folding and unfolding kdimensional objects in $n$dimensional space, k <= n. Another contribution of this thesis is a survey of research in this field. The survey revolves around three principal aspects that have received extensive study: linkages in arbitrary dimensions (folding onedimensional objects in two or more dimensions, including protein folding), paper folding (normally, folding twodimensional objects in three dimensions), and folding and unfolding polyhedra (twodimensional objects embedded in threedimensional space)
2 editions published between 2001 and 2004 in English and held by 4 WorldCat member libraries worldwide
The results of this thesis concern folding of onedimensional objects in two dimensions: planar linkages. More precisely, a planar linkage consists of a collection of rigid bars (line segments) connected at their endpoints. Foldings of such a linkage must preserve the connections at endpoints, preserve the bar lengths, and (in our context)prevent bars from crossing. The main result of this thesis is that aplanar linkage forming a collection of polygonal arcs and cycles can be folded so that all outermost arcs (not enclosed by other cycles) become straight and all outermost cycles become convex. A complementary result of this thesis is that once a cycle becomes convex, it can be folded into any other convex cycle with the same counterclockwise sequence of bar lengths. Together, these results show that the configuration space of all possible foldings of a planar arc or cycle linkage is connected. These results fall into the broader context of folding and unfolding kdimensional objects in $n$dimensional space, k <= n. Another contribution of this thesis is a survey of research in this field. The survey revolves around three principal aspects that have received extensive study: linkages in arbitrary dimensions (folding onedimensional objects in two or more dimensions, including protein folding), paper folding (normally, folding twodimensional objects in three dimensions), and folding and unfolding polyhedra (twodimensional objects embedded in threedimensional space)
Subexponential parametrized algorithms on graphs of bounded genus and Hminorfree graphs
by
Erik D Demaine(
Book
)
3 editions published in 2003 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 2003 in English and held by 3 WorldCat member libraries worldwide
Straightening polygonal arcs and convexifying polygonal cycles
by Robert Conelly(
Book
)
1 edition published in 2002 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2002 in English and held by 3 WorldCat member libraries worldwide
Planar embeddings of graphs with specified edge lengths
by Sergio Cabello(
)
3 editions published between 2004 and 2007 in English and held by 3 WorldCat member libraries worldwide
We consider the problem of finding a planar embedding of a (planar) graph with a prescribed Euclidean length on every edge. There has been substantial previous work on the problem without the planarity restrictions, which has close connections to rigidity theory, and where it is easy to see that the problem is NPhard. In contrast, we show that the problem is tractable  indeed, solvable in linear time on a real RAM  for planar embeddings of planar 3connected triangulations, even if the outer face is not a triangle. This result is essentially tight: the problem becomes NPhard if we consider instead planar embeddings of planar 3connected infinitesimally rigid graphs, a natural relaxation of triangulations in this context
3 editions published between 2004 and 2007 in English and held by 3 WorldCat member libraries worldwide
We consider the problem of finding a planar embedding of a (planar) graph with a prescribed Euclidean length on every edge. There has been substantial previous work on the problem without the planarity restrictions, which has close connections to rigidity theory, and where it is easy to see that the problem is NPhard. In contrast, we show that the problem is tractable  indeed, solvable in linear time on a real RAM  for planar embeddings of planar 3connected triangulations, even if the outer face is not a triangle. This result is essentially tight: the problem becomes NPhard if we consider instead planar embeddings of planar 3connected infinitesimally rigid graphs, a natural relaxation of triangulations in this context
The geometry of origami from science to sculpture
(
Visual
)
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
"Come explore origami as you've never seen it before with world famous MIT professor and author, Erik Demaine. Erik's creativity blends art and mathematics so seamlessly that his works have been included in the permanent collection of the Museum of Modern Art."Container
1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide
"Come explore origami as you've never seen it before with world famous MIT professor and author, Erik Demaine. Erik's creativity blends art and mathematics so seamlessly that his works have been included in the permanent collection of the Museum of Modern Art."Container
Resizable arrays in optimal time and space
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1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
V članku so predstavljene preproste, praktične in učinkovite podatkovne strukture za hranjenje eno razsežnostnih polj $A[l...l+n1]$, v katerih so shranjeni elementi enakih velikosti. Polja se povečujejo ali zmanjšujejo, če dodajamo ali odvzemamo elemente na enem oziroma obeh konceh. Poleg tega lahko tudi dostopamo do poljubnega elementa v polju. Vse operacije imajo časovno zahtevnost $O(1)$, velikost dodatnega prostora (poleg $n$ za hranjenje elementov pa je $O(\sqrt{n})$, kar je optimalno
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
V članku so predstavljene preproste, praktične in učinkovite podatkovne strukture za hranjenje eno razsežnostnih polj $A[l...l+n1]$, v katerih so shranjeni elementi enakih velikosti. Polja se povečujejo ali zmanjšujejo, če dodajamo ali odvzemamo elemente na enem oziroma obeh konceh. Poleg tega lahko tudi dostopamo do poljubnega elementa v polju. Vse operacije imajo časovno zahtevnost $O(1)$, velikost dodatnega prostora (poleg $n$ za hranjenje elementov pa je $O(\sqrt{n})$, kar je optimalno
Approximation algorithms via contraction decomposition
by
Erik D Demaine(
)
1 edition published in 2007 in English and held by 1 WorldCat member library worldwide
We prove that the edges of every graph of bounded (Euler) genus can be partitioned into any prescribed number $k$ of pieces such that contracting any piece results in a graph of bounded treewidth (where the bound dependson~$k$). This decomposition result parallels an analogous, simpler result for edge deletions instead of contractions, obtained by Baker, Eppstein, and others, and it generalizes a similar result for "compression" (a variant of contraction) in planar graphs (Klein). Our decomposition result is a powerful tool for obtaining PTASs for contractionclosed problems (whose optimal solution only improves under contraction), a much more general class than minorclosed problems. We prove that any contractionclosed problem satisfying just a few simple conditions has a PTAS in boundedgenus graphs. In particular, our framework yields PTASs for the weighted Traveling Salesman Problem and for minimumweight $c$edgeconnected submultigraph on boundedgenus graphs, improving and generalizing many previous algorithms. We also highlight the only main difficulty in extending our results to general $H$minorfree graphs
1 edition published in 2007 in English and held by 1 WorldCat member library worldwide
We prove that the edges of every graph of bounded (Euler) genus can be partitioned into any prescribed number $k$ of pieces such that contracting any piece results in a graph of bounded treewidth (where the bound dependson~$k$). This decomposition result parallels an analogous, simpler result for edge deletions instead of contractions, obtained by Baker, Eppstein, and others, and it generalizes a similar result for "compression" (a variant of contraction) in planar graphs (Klein). Our decomposition result is a powerful tool for obtaining PTASs for contractionclosed problems (whose optimal solution only improves under contraction), a much more general class than minorclosed problems. We prove that any contractionclosed problem satisfying just a few simple conditions has a PTAS in boundedgenus graphs. In particular, our framework yields PTASs for the weighted Traveling Salesman Problem and for minimumweight $c$edgeconnected submultigraph on boundedgenus graphs, improving and generalizing many previous algorithms. We also highlight the only main difficulty in extending our results to general $H$minorfree graphs
Data structures Dagstuhl Seminar Proceedings 10091, 28. 2.  5. 3. 2010
by Dagstuhl Seminar(
)
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
Approximation algorithms via contraction decomposition
by
Erik D Demaine(
)
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
We prove that the edges of every graph of bounded (Euler) genus can be partitioned into any prescribed number $k$ of pieces such that contracting any piece results in a graph of bounded treewidth (where the bound dependson~$k$). This decomposition result parallels an analogous, simpler result for edge deletions instead of contractions, obtained by Baker, Eppstein, and others, and it generalizes a similar result for "compression" (a variant of contraction) in planar graphs (Klein). Our decomposition result is a powerful tool for obtaining PTASs for contractionclosed problems (whose optimal solution only improves under contraction), a much more general class than minorclosed problems. We prove that any contractionclosed problem satisfying just a few simple conditions has a PTAS in boundedgenus graphs. In particular, our framework yields PTASs for the weighted Traveling Salesman Problem and for minimumweight $c$edgeconnected submultigraph on boundedgenus graphs, improving and generalizing many previous algorithms. We also highlight the only main difficulty in extending our results to general $H$minorfree graphs
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
We prove that the edges of every graph of bounded (Euler) genus can be partitioned into any prescribed number $k$ of pieces such that contracting any piece results in a graph of bounded treewidth (where the bound dependson~$k$). This decomposition result parallels an analogous, simpler result for edge deletions instead of contractions, obtained by Baker, Eppstein, and others, and it generalizes a similar result for "compression" (a variant of contraction) in planar graphs (Klein). Our decomposition result is a powerful tool for obtaining PTASs for contractionclosed problems (whose optimal solution only improves under contraction), a much more general class than minorclosed problems. We prove that any contractionclosed problem satisfying just a few simple conditions has a PTAS in boundedgenus graphs. In particular, our framework yields PTASs for the weighted Traveling Salesman Problem and for minimumweight $c$edgeconnected submultigraph on boundedgenus graphs, improving and generalizing many previous algorithms. We also highlight the only main difficulty in extending our results to general $H$minorfree graphs
Realizing partitions respecting full and partial order information
(
)
1 edition published in 2005 in English and held by 1 WorldCat member library worldwide
1 edition published in 2005 in English and held by 1 WorldCat member library worldwide
Planar embeddings of graphs with specified edge lenghts
by Sergio Cabello(
Book
)
1 edition published in 2005 in English and held by 1 WorldCat member library worldwide
1 edition published in 2005 in English and held by 1 WorldCat member library worldwide
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Art Art and science Art in education Artists Biologists Career changes France GamesMathematical models Israel Japan Logic, Symbolic and mathematical Mathematical recreations Mathematicians Mathematics Mathematics in art Origami OrigamiMathematics Paper sculpture Paper work PolyhedraModels Problem solvingMathematical models Science Science in art Scientists United States