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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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  • Algorithmic folding complexity 
    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 ...
  • Algorithms for solving rubik's cubes 
    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 ...
  • Any Monotone Boolean Function Can Be Realized by Interlocked Polygons 
    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 ...
  • Approximation Algorithms via Contraction Decomposition 
    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 ...
  • Approximation algorithms via structural results for apex-minor-free graphs 
    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, ...
  • Basic Network Creation Games 
    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 ...
  • Bounded-Degree Polyhedronization of Point Sets 
    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 ...
  • Cache-oblivious dynamic dictionaries with update/query tradeoffs 
    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 ...
  • Common unfoldings of polyominoes and polycubes 
    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 ...
  • Computing Signed Permutations of Polygon 
    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 ...
  • Constant Price of Anarchy in Network Creation Games via Public Service Advertising 
    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 ...
  • Continuous Blooming of Convex Polyhedra 
    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 ...
  • Contraction decomposition in h-minor-free graphs and algorithmic applications 
    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. ...
  • Coverage with k-Transmitters in the Presence of Obstacles 
    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 ...
  • Decomposition, approximation, and coloring of odd-minor-free graphs 
    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 ...
  • Deploying Sensor Networks With Guaranteed Fault Tolerance 
    Hajiaghayi, Mohammad Taghi; Bredin, Jonathan L.; Demaine, Erik D.; Rus, Daniela L. (Institute of Electrical and Electronics Engineers (IEEE), 2010-02)
    We consider the problem of deploying or repairing a sensor network to guarantee a specified level of multipath connectivity (k-connectivity) between all nodes. Such a guarantee simultaneously provides fault tolerance against ...
  • A distributed boundary detection algorithm for multi-robot systems 
    McLurkin, James; Demaine, Erik D. (Institute of Electrical and Electronics Engineers, 2009-12)
    We describe a distributed boundary detection algorithm suitable for use on multi-robot systems with dynamic network topologies. We assume that each robot has access to its local network geometry, which is the combination ...
  • Embedding Stacked Polytopes on a Polynomial-Size Grid 
    Demaine, Erik D.; Schulz, Andre (Society of Industrial and Applied Mathematics (SIAM), 2011-01)
    We show how to realize a stacked 3D polytope (formed by repeatedly stacking a tetrahedron onto a triangular face) by a strictly convex embedding with its n vertices on an integer grid of size O(n4) x O(n4) x O(n18). ...
  • Filling holes in triangular meshes by curve unfolding 
    Demaine, Erik D.; Bose, Prosenjit; Shu, Chang; Wuhrer, Stefanie; Brunton, Alan (Institute of Electrical and Electronics Engineers, 2009-07)
    We propose a novel approach to automatically fill holes in triangulated models. Each hole is filled using a minimum energy surface that is obtained in three steps. First, we unfold the hole boundary onto a plane using ...
  • Flattening fixed-angle chains is strongly NP-hard 
    Demaine, Erik D.; Eisenstat, Sarah Charmian (Springer Berlin / Heidelberg, 2011-08)
    Planar configurations of fixed-angle chains and trees are well studied in polymer science and molecular biology. We prove that it is strongly NP-hard to decide whether a polygonal chain with fixed edge lengths and angles ...
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