Adam Hesterberg

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Given a set of pairs of points in the plane, the goal of the shortest separating cycle problem is to find a simple tour of minimum length that separates the two points of each pair to different sides. In this article we prove hardness of the problem and provide approximation algorithms under various settings. Assuming the Unique Games Conjecture, the(More)
For a 0–1matrix Q , ex(n,Q ) is themaximum number of 1s in an n×n 0–1matrix of which no submatrix majorizes Q . We show that if P is a permutation matrix and Q is arbitrary, then the order of growth of ex(n, P ⊗ Q ) is almost the same as that of ex(n,Q ), extending a result used in Marcus and Tardos’s proof of the Stanley–Wilf conjecture. © 2012 Elsevier(More)
Jigsaw puzzles [9] and edge-matching puzzles [5] are two ancient types of puzzle, going back to the 1760s and 1890s, respectively. Jigsaw puzzles involve fitting together a given set of pieces (usually via translation and rotation) into a desired shape (usually a rectangle), often revealing a known image or pattern. The pieces are typically squares with a(More)
In this paper, we study how to fold a specified origami crease pattern in order to minimize the impact of paper thickness. Specifically, origami designs are often expressed by a mountain-valley pattern (plane graph of creases with relative fold orientations), but in general this specification is consistent with exponentially many possible folded states. We(More)
We study the computational complexity of the Buttons & Scissors game and obtain sharp thresholds with respect to several parameters. Specifically we show that the game is NP-complete for C = 2 colors but polytime solvable for C = 1. Similarly the game is NP-complete if every color is used by at most F = 4 buttons but polytime solvable for F ≤ 3. We also(More)
Clickomania is a classic computer puzzle game (also known as SameGame, Chain-Shot!, and Swell-Foop, among other names). Originally developed by Kuniaki “Morisuke” Moribe under the name Chain-Shot! for the Fujitsu FM-8, and announced in the November 1985 issue of ASCII Monthly magazine, it has since been made available for a variety of digital platforms(More)
A conflict-free k-coloring of a graph assigns one of k different colors to some of the vertices such that, for every vertex v, there is a color that is assigned to exactly one vertex among v and v’s neighbors. Such colorings have applications in wireless networking, robotics, and geometry, and are well-studied in graph theory. Here we study the natural(More)
We analyze a directed variation of the book embedding problem when the page partition is prespecified and the nodes on the spine must be in topological order (upward book embedding). Given a directed acyclic graph and a partition of its edges into k pages, can we linearly order the vertices such that the drawing is upward (a topological sort) and each page(More)
We prove the computational intractability of rotating and placing n square tiles into a 1 × n array such that adjacent tiles are compatible—either equal edge colors, as in edge-matching puzzles, or matching tab/pocket shapes, as in jigsaw puzzles. Beyond basic NP-hardness, we prove that it is NPhard even to approximately maximize the number of placed tiles(More)
We study the computational complexity of the Buttons & Scissors game and obtain sharp thresholds with respect to several parameters. Specifically we show that the game is NP-complete for C = 2 colors but polytime solvable for C = 1. Similarly the game is NP-complete if every color is used by at most F = 4 buttons but polytime solvable for F ≤ 3. We also(More)