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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, Mohammad Taghi; 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, Mohammad Taghi; 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, Mohammad Taghi; 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 ...
  • Abel, Zachary Ryan; Demaine, Erik D.; Demaine, Martin L.; Ito, Hiro; Snoeyink, Jack; Uehara, Ryuhei (2014-08)
    We investigate folding problems for a class of petal polygons P, which have an n-polygonal base B surrounded by a sequence of triangles. We give linear time algorithms using constant precision to determine if P can fold ...
  • 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.; Huang, Yamming; Liao, Chung-Shou; Sadakane, Kunihiko (Springer-Verlag, 2014)
    We study online algorithms for the Canadian Traveller Problem (CTP) introduced by Papadimitriou and Yannakakis in 1991. In this problem, a traveller knows the entire road network in advance, and wishes to travel as quickly ...
  • Aloupis, Greg; Demaine, Erik D.; Guo, Alan; Viglietta, Giovanni (Wiley Blackwell, 2014)
    We prove NP-hardness results for five of Nintendo’s largest video game franchises: Mario, Donkey Kong, Legend of Zelda, Metroid, and Pokemon. Our results apply to generalized versions of Super Mario Bros. 1, 3, Lost Levels, ...
  • 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; 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 ...
  • Demaine, Erik D.; Okamoto, Yoshio; Uehara, Ryuhei; Uno, Yushi (Institute of Electronics, Information and Communications Engineers, 2014-06)
    Shakashaka is a pencil-and-paper puzzle proposed by Guten and popularized by the Japanese publisher Nikoli (like Sudoku). We determine the computational complexity by proving that Shakashaka is NP-complete, and furthermore ...
  • 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 ...
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