A constant-work-space algorithm has read-only access to an input array and may use only O(1) additional words of O(log n) bits, where n is the input size. We show how to triangulate a plane straight-line graph with n vertices in O(n 2 ) time and constant workspace. We also consider the problem of preprocessing a simple polygon P for shortest path queries, where P is given by the ordered sequence of its n vertices. For this, we relax the space constraint to allow s words of work-space. After quadratic preprocessing, the shortest path between any two points inside P can be found in O(n 2 /s) time.
Abstract. Linear cartograms visualize travel times between locations, usually by deforming the underlying map such that Euclidean distance corresponds to travel time. We introduce an alternative model, where the map and the locations remain fixed, but edges are drawn as sinusoid curves. Now the travel time over a road corresponds to the length of the curve. Of course the curves might intersect if not placed carefully. We study the corresponding algorithmic problem and show that suitable placements can be computed efficiently. However, the problem of placing as many curves as possible in an ideal, centered position is NP-hard. We introduce three heuristics to optimize the number of centered curves and show how to create animated visualizations.
In a rolling block maze, one or more blocks lie on a rectangular board with square cells. In most mazes, the blocks have size k × m × n where k, m, n are integers that determine the size of the block in terms of units of the size of the board cells. The task of a rolling block maze is to roll a particular block from a starting to an ending placement. A block is rolled by tipping it over one of its edges. Some of the squares of the board are marked as forbidden to roll on. We show that solving rolling block mazes is PSPACE-complete.
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