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Browsing MIT Open Access Articles by Author "Demaine, Erik D."

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Browsing MIT Open Access Articles by Author "Demaine, Erik D."

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  • Cardinal, Jean; Demaine, Erik D.; Demaine, Martin L.; Imahori, Shinji; Langerman, Stefan; Uehara, Ryuhei (Springer, 2009)
    How do we most quickly fold a paper strip (modeled as a line) to obtain a desired mountain-valley pattern of equidistant creases (viewed as a binary string)? Define the folding complexity of a mountain-valley string as the ...
  • Abel, Zachary Ryan; Demaine, Erik D.; Demaine, Martin L.; Eisenstat, Sarah Charmian; Lubiw, Anna; Schulz, Andre; Souvaine, Diane L.; Viglietta, Giovanni; Winslow, Andrew (Schloss Dagstuhl Publishing, 2013-02)
    We prove that every simple polygon can be made as a (2D) pop-up card/book that opens to any desired angle between 0 and 360°. More precisely, given a simple polygon attached to the two walls of the open pop-up, our ...
  • Demaine, Erik D.; Demaine, Martin L.; Eisenstat, Sarah Charmian; Lubiw, Anna; Winslow, Andrew (Springer Berlin / Heidelberg, 2011-08)
    The Rubik’s Cube is perhaps the world’s most famous and iconic puzzle, well-known to have a rich underlying mathematical structure (group theory). In this paper, we show that the Rubik’s Cube also has a rich underlying ...
  • Demaine, Erik D.; Demaine, Martin L.; Uehara, Ryuhei (University of Manitoba, 2010)
    We show how to construct interlocked collections of simple polygons in the plane that fall apart upon removing certain combinations of pieces. Precisely, interior-disjoint simple planar polygons are interlocked if ...
  • Demaine, Erik D.; Demaine, Martin L.; Uehara, Ryuhei (MDPI AG, 2012-03)
    Suppose there is a collection of n simple polygons in the plane, none of which overlap each other. The polygons are interlocked if no subset can be separated arbitrarily far from the rest. It is natural to ask the ...
  • Ito, Takehiro; Demaine, Erik D. (Springer-Verlag, 2011-05)
    The subset sum problem is a well-known NP-complete problem in which we wish to find a packing (subset) of items (integers) into a knapsack with capacity so that the sum of the integers in the packing is at most the capacity ...
  • Hajiaghayi, MohammadTaghi; Demaine, Erik D.; Mohar, Bojan (Bolyai Society/Springer-Verlag, 2010-09)
    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 depends ...
  • Demaine, Erik D.; Hajiaghayi, MohammadTaghi; Kawarabayashi, Ken-ichi (Springer Berlin/Heidelberg, 2009-07)
    We develop new structural results for apex-minor-free graphs and show their power by developing two new approximation algorithms. The first is an additive approximation for coloring within 2 of the optimal chromatic number, ...
  • Alon, Noga; Demaine, Erik D.; Hajiaghayi, MohammadTaghi; Leighton, Tom (Association for Computing Machinery (ACM), 2010-06)
    We study a natural network creation game, in which each node locally tries to minimize its local diameter or its local average distance to other nodes, by swapping one incident edge at a time. The central question is what ...
  • Demaine, Erik D.; Panchekha, Pavel; Wilson, David A.; Yang, Edward Z. (Springer-Verlag Berlin Heidelberg, 2013)
    We consider the problem of merging individual text documents, motivated by the single-file merge algorithms of document-based version control systems. Abstracting away the merging of conflicting edits to an external conflict ...
  • Barequet, Gill; Benbernou, Nadia M.; Charlton, David; Demaine, Erik D.; Demaine, Martin L.; Ishaque, Mashhood; Lubiw, Anna; Schulz, Andre; Souvaine, Diane L.; Toussaint, Godfried T.; Winslow, Andrew (University of Manitoba, 2010-08)
    In 1994 Grunbaum [2] showed, given a point set S in R3, that it is always possible to construct a polyhedron whose vertices are exactly S. Such a polyhedron is called a polyhedronization of S. Agarwal et al. [1] extended ...
  • Brodal, Gerth Stolting; Demaine, Erik D.; Fineman, Jeremy T.; Iacono, John; Langerman, Stefan; Munro, J. Ian (Society for Industrial and Applied Mathematics, 2010-01)
    Several existing cache-oblivious dynamic dictionaries achieve O(logB N) (or slightly better O(logB N over M )) memory transfers per operation, where N is the number of items stored, M is the memory size, and B is ...
  • Demaine, Erik D.; Iacono, John; Langerman, Stefan; Ozkan, Ozgur (Springer-Verlag, 2013-07)
    We present a general transformation for combining a constant number of binary search tree data structures (BSTs) into a single BST whose running time is within a constant factor of the minimum of any “well-behaved” bound ...
  • Aloupis, Greg; Bose, Prosenjit K.; Collette, Sebastien; Demaine, Erik D.; Demaine, Martin L.; Douieb, Karim; Dujmovic, Vida; Iacono, John; Langerman, Stefan; Morin, Pat (Springer Berlin / Heidelberg, 2011-11)
    This paper studies common unfoldings of various classes of polycubes, as well as a new type of unfolding of polyominoes. Previously, Knuth and Miller found a common unfolding of all tree-like tetracubes. By contrast, we ...
  • Aloupis, Greg; Bose, Prosenjit; Demaine, Erik D.; Langerman, Stefan; Meijer, Henk; Overmars, Mark; Toussaint, Godfried T. (World Scientific, 2011)
    Given a planar polygon (or chain) with a list of edges {e[subscript 1], e[subscript 2], e[subscript 3], …, e[subscript n-1], e[subscript n]}, we examine the effect of several operations that permute this edge list, resulting ...
  • Demaine, Erik D.; Zadimoghaddam, Morteza (Springer Science + Business Media B.V., 2010-01)
    Network creation games have been studied in many different settings recently. These games are motivated by social networks in which selfish agents want to construct a connection graph among themselves. Each node wants to ...
  • Demaine, Erik D.; Demaine, Martin L.; Hart, Vi; Iacono, John; Langerman, Stefan; O’Rourke, Joseph (Springer-Verlag, 2011-05)
    We construct the first two continuous bloomings of all convex polyhedra. First, the source unfolding can be continuously bloomed. Second, any unfolding of a convex polyhedron can be refined (further cut, by a linear number ...
  • Demaine, Erik D.; Hajiaghayi, MohammadTaghi; Kawarabayashi, Ken-ichi (Association for Computing Machinery (ACM), 2011-06)
    We prove that any graph excluding a fixed minor can have its edges partitioned into a desired number k of color classes such that contracting the edges in any one color class results in a graph of treewidth linear in k. ...
  • Ballinger, Brad; Benbernou, Nadia M.; Bose, Prosenjit; Damian, Mirela; Demaine, Erik D.; Dujmovic, Vida; Flatland, Robin; Hurtado, Ferran; Iacono, John; Lubiw, Anna; Morin, Pat; Sacristan, Vera; Souvaine, Diane; Uehara, Ryuhei (Association for Computing Machinery, 2010-12)
    For a fixed integer k [greater than or equal to] 0, a k-transmitter is an omnidirectional wireless transmitter with an in nite broadcast range that is able to penetrate up to k "walls", represented as line segments in ...
  • Demaine, Erik D.; Hajiaghayi, MohammadTaghi; Kawarabayashi, Ken-ichi (Association for Computing Machinery / Society for Industrial and Applied Mathematics, 2010-01)
    We prove two structural decomposition theorems about graphs excluding a fixed odd minor H, and show how these theorems can be used to obtain approximation algorithms for several algorithmic problems in such graphs. Our ...
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